ELECTRONIC DEVICES

Energy Bands & Current Carriers in Semiconductors

2
P-N Junction 35
Bipolar Junction Transistor
85
MOSFET
103
Opto-Electronics 140
Integrated Circult 158

NOTE:
MAKAUT course structure and syllabus of 3 semester has been changed from 2019.
The sylabus of SOLID STATE DEVICES has been completely redesigned and
restructured as ELECTRONIC DEVICES in the present curriculum. Taking special
care of this matter we are providing the relevant MAKAUT university solutions of
sOLID STATE DEVICES and some model questions & answers for newly introduced
topics, so that students can get an idea about university questions patterns.
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ENERGYBANDS CURRENT
& CARRIERS IN
SEMICONDUCTORS

Chapter at a Glance
a systematic array or atoms. A three
dimensional lattice
Introduction: The crystal is i
vectors. A pure crystal is constructed in such a way that it maintains direcctional
defined by the
point in space and Is a mathematical abstraction
invariance. The lattice is a periodic
The total energy E or a conduction electron is given hu
Fneroy Bands theory in crystals: by

E=h
between the energy and wave vector as shown in the
This indicates the parabolic dependence
m. In this figure the horizontal line Ec indicates the edge
Figure for constant effective mass
of the conduction band, the
horizontal line Ey is called edge of valence band, the dotted
NpD, the dotted horizontal line near Ey is
horizontal line near Ec is called the donor level
called the acceptor level Na.
The band gap E is defined as E -Ec- Ey.
energy gap is very large, both bands being
Insulator: In some crystalline solids, the forbidden
parabolic in nature. In such solids, at ordinary temperatures only a few electrons can acquire
enough thermal energy to move from the valence band into the conduction band.
Metals: A crystalline solid is called a metal if the uppermost energy band is partly filled or
uppermost filled band and the next unoccupied band overlap in energy. Metal has Inter
the
penetrating band strueture in, metal, the electronsin the uppermost band find neighbouring
vacant states to move in, and thus behave as free particles.
Semiconductors: The crystalline material for which the width of the forbidden energy gap
varies between metal and insulator is referred to as semiconductors. The Germanium and
silicon having forbidden gaps of 0.78eV and 1.12eV, respectively at OK, are typical
elemental semiconductors.
Intrinsic & Extrinsic Semiconductor: The electron and hole concentration in an intrinsic
semiconductor are equal because carriers within a very pure material are created in pairs.
Doped semiconductors whose properties are controlled by adding the impurity atoms are
called extrinsic semiconductors. Doping increases the conductivity of a semiconductor.
Carrier Drift: Any motion of free carriers in a semiconductor leads to a current. This motion
Cat De caused by an electric field due to an externally applied volage, since the carriers au
charged particles. We will refer to this transport
mechanism as carrier artts
nted
Ditiusion: The transportation of charge in semiconductors may De
for by a mechanism carriers
called diffusion.

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Multiple Choice Type Questions

of a given semiconductor depends on
1. Intrinsic carrier concentration
WBUT 2006, 2014, 2015, 2017]1
a) Bandgap b) temperature
c) Bandgap and temperature d) none of these
Answer: (c)

2. Diffusion current in semiconductor flows due to [WBUT 2007]

a) concentration gradient of carrier
b) electric field
c) both concentration & electric field current
d) none of these
Answer: (a)

3.If temperature increases from very low value to high, then electron mobility
a) decreases b) increases WBUT 2007
c) increases then decreases d) remains constant
Answer: (c)

4. Electric field increases from very low value to high value then carrier velocity
WBUT 2007]
a) increases b) decreases
c)increases then saturate d) decreases then saturate
Answer: (c)

5. The electrical resistivity of a semiconductor is TWBUT 2007]

a) about 10 ohm metre b) in the range of 10- 10 ohm metre
c) about 10° ohm metre d) less than 10 ohm metre
Answer: (a)

6. Which is the correct statement? WBUT 2007]

a) Effective mass m* is positive when E(k) is concave up
b) Effective mass m* is negative when E(k) is concave down
c Effective mass m* is infinite at points where the curve changes concave up
to concave down or vice-versa (called "point of inflection")
d) All of these
Answer: (d)
7. In GaAs when the electron rises from central valley to satellite valley, the
effective mass of electron becomes WBUT 2007, 2010]
a) less 5) more c) zero d) infinity
Answer: (b)

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ne intercepts
axis at 1,
,, Miller indices of that plane is
c) (100)
WRUIT 2008)
d) [100
b) (1 o)
a) {111)
Answer: (d)
suitable for ohmic
contact with p-type silicon? WBUT 2008
9. Which metal is b) Cu
c) AI ) Au
a) Fe
Answer: (C)
in direct band gap
semiconductor involves (WBUT 2008
Electron transition b) Dependence on band gap
10. momentum of electron e
a) a change of
momentum for electron d) None of thes
c) No change of
Answer: (b)
mass depends on WBUT 2008, 2010, 2014
11. Electron effective b) band gap
a) Curvature of band d) temperature
c) Doping concentration
Answer: (a)
WBUT 2008]
12. At OK semiconductor has
filled conduction band
a) Empty valence band and
empty conduction band
b) Filled valence band and
c) Partially filled valence and
conduction band
d) Holes in valence band
Answer: (b)
WBUT 2008]
13. In a degenerate n-type semiconductor Fermi level lies
b) near the valance band
a) Inside the conduction band
c) near the conduction band d) at the middle of for bidden band
Answer: (a)
WBUT 2009
14. Si has the lattice patterns of
a) FCC type b) Hexagonal type
c) Diamond type d) Zinc blende type
Answer: (c)
WBUT 2009
15.Doping effect of semiconductor results with the change of
a) Fermi level only b) Bandgap only
c) Electrical conductivity only d) all of these
Answer: (d)

16. The WBUT 2009]

doping level of emitter region of a transistor is
a) greater than collector and base regions
b)
less than collector and base regions
C.less than base region but greater than collector region
0 greater than base region but less than collector region
Answer: (a)

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17.When a positivo voltago ls appllod to an n-typo semiconductor with respect to

the motal, the barrior botwoon tho somiconductor with rospect to tho metal, the
barrier botwoon the somi-conductor and metal [wBUT 2010]
a) incroas0s b) docreas0s c) romains same d) none of these
Answer: (b)
18.GaAs is proferred to Si for high tomporature operation of semi-conductor
device because GaAs [WBUT 2011]
a) is direct band gap in nature
b) possesses higher onergy band gap
c) is a compound semi-conductor
d) possesses smaller carrier effective mass
Answer: (c)

19. The basic lattice structure of silicon is [WBUT 2011]

a) simple cubic b) edge-centered cubic
c) face-centered cubic body-centered cubic
Answer: (¢)

20. At T 0K , the Fermi-Dirac distribution function vs energy plot takes the form
************* [WBUT 2011]
stepa) b) linear c) parabolic d) exponential
Answer: (a)
21. A p-type semiconductor contains holes and WBUT 2012]
a)
Positive ions b) Negative ions
c) Acceptor atoms d) Donor atoms
Answer: (c)

22. Diffussion of free electrons across, the junction of an unbiased diode

produces [WBUT 2012]
a) Forward bias b) Reverse bias
c) Breakdown d) the Depletion Layer
Answer: (d)

23. When a pentavalent impurity is added a semiconductor becomes

a) Positively charged b) Negatively charged WBUT 2012]
c) Neutral d) None of these
Answer: (c)

24. Under high electric fields , in a semiconductor with increasing electric

field WBUT 2012, 2014]
a) The mobility of charge carriers decreases
b) The mobility of charge carriers increases
c) Velocity of carriers saturate
d) both (a) and (c)
Answer: (d)
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proportiona
recombination of EHP in semiconductor is al to
probability of WBUT 2012
AThe b) density of holes and electrons
a) denslty of electrons d) none of these
of holes
c) density
Answer: (b)
Then the
and olectrons are in ratio 4:
1.
holo8 ity
26. Diffussion
constant of ratio [WBUT 2012, 2014]
electrons will be in the
of holes and
b) 16:1 c) 1:4 d) 1:16
a) 4:1
Answer: (a)
which behaves like an insulator at zero Kelvin is called
27. A semiconductor WBUT 2013]
semiconductor b) extrinsic semiconductor
a) intrinsic d) degenerate semiconductor
c) elemental semiconductor
Answer: (¢)
L, is given by WBUT 2013]
28. In a semiconductor the hole diffusion length

a) D, b)(D, c) D,'t d) D,,)

Answer: (d)

29.Hal voltage is proportional to

WBUT 2014
a) velocity
b) magnetic field
c) both (a) and (b) parallel to velocity
d) both (a) and (b) perpendicular to velocity
Answer: (b)

30. When a positive voltage is applied to a p-n junction structure the barrier
potential WBUT 2015, 2017]
a) increases b) decreases c) remains same d) none of these
Answer: (b)

31. Electron transition in in-direct band gap semiconductor involves WBUT 2015)
a) a change of momentum of electron b) dependence on band gap
c)no change of momentum of electron d) none of these
Answer: (b)

32. Effective electron

mass depends on WBUT 2015, 2017]
a) curvature of band
b) band gap
c) doping concentration
Answer: (a)
d) temperature

33. Metal n-4type

semiconductor form ohmic contact If WBUT 2015, 2017]
a) none of these
PP
Answer: (a)
b) P. Pan )

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34. Energy bandgap of GaAs at 0 K is WBUT 2016]

a) 1.12 eV b) 0.66 eV c) 1.43 eVv d) 3.40 eVV
Answer: (d)

35. According to the E-k diagram, Si is WBUT 2016]

a) direct bandgap b) indirect bandgap
c) both (a) and (b) d) none of these
Answer: (b)

36. Boltzmann approximation is valid for WBUT 2016

a) higher energy states b) lower energy states
c) both (a) and (b) d) None of these
Answer: (d)

37. Under forward bias, p - n junction current flows mainly due to WBUT 2016
a) diffusion b) drift
c) both (a) and (b) d) none of these
Answer: (c)

38. Intrinsic Fermi level (Ewill be slightly above the midgap energy level

Edenif WBUT 2016]

a) m,> m, b) m, <m, c)m,=m, d) any one of these
Answer: (d)

39. Solar cell is a WBUT 20171

a) photodetector b) photodiode
c) photovoltaic device d) optical emitter
Answer: (c)

40. If V is the voltage applied to the metal with respect to the p-type semiconductor
in a MOS capacitor then V< 0 corresponds to [WBUT 20171
a) Depletion b) Accumulation c) Inversion d) Strong inversion
Answer: (a)

41. The unit of Density of State Function is WBUT 2018

a) numberlunit energyl unit volume b) energy/ unit volume
energy/ unit area
c) d) None of these
Answer: (a)
42. K-space diagram in a crystal is a plot of [WBUT 2018]
a) electron density versus momentum
b) electron energy versus momentum
c) quantum number versus momentum
d) electron energy versus density of
energy states
Answer: (b)
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43. Intrinsic
carrier concentration is given by WBUT 2018

a) n =n,Po
b) n, Poln c) n=
nP d) n, = n,Po

Answer: (C)

44. Conductivity is defined as the ratio of WBUT 2018

a) drift current density
to electric field
b) drift current density to practical density gradient
c) particle flux to particle density
gradient
d) drift velocity to electric field
Answer: (a)

45. Mobility is a parameter which relates WBUT 2018]

a) drift current density to electric field b) carrier drift velocity to electric field
c) resistance to current d) mobility to diffusion coefficient
Answer: (b)

Short Answer Type 9uestions

1. What is Miller indices of a crystal? A plane intercepts at 2a, b/2, 3c in a simple

cubic unit cell. What are the Miller indices of the plane? WBUT 2007]
Answer:
1" Part:
Miller Indices are defined as the reciprocals of the fractional intercepts which the plane
makes with the crystallographic axes.
The method by which indices are determined is best shown by example. Recal, that there
are three axes in crystallographic systems. Miller indices are represented by a set of 3
integer numbers.

Part: Reciprocal of the intercept will

be2 and It means intercepts along x,y

dzaxes are .2 and respective.

2

2. Draw and explain E-K diagram for a direct and an indirect band gap
semiconductor with suitable example. wBUT 2008, 2012]
Answer:

The total energy E of a conduction electron is given by E = h

2m
This indicates the parabolic dependence
between the energy and wave vector as shown in
the Figure for constant effective
mass m. In this figure the horizontal line Ec indica
the edge of the conduction band,
the horizontal line Ey is called edge of valence band, he
doted horizontal line near Ec
is called the donor level N (to be explained later On the

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dotted horizontal line near Ey is called the acceptor level Na (to be explained later on),
The band gap E, is defined as E, Ec-Ev.

EpND)------.
-
EANT * -*****

Fig: Typical model of an energy band stnucture of the

crystalline material

ww hv= Es

The above first figure shows direct band gap semiconductor as the minima of the CB and
maxima of the valance band are at the same line. So the electrons from CB can jump to
valance band without any extra loss of energy. It is suitable for optoelectronic devices.
Example GaAs
The above second figure shows indirect band gap semiconductor as the minima of the CB
and maxima of the valance band are not vertically at the same line. So the electrons from
CB can jump to valance band indirectly with extra loss of energy. It is not suitable for
optoelectronic devices. Example Si, Ge.

3. a)What are mobility and conductivity? WBUT 2008, 2012, 2013, 2017]
b) What are the effects of temperature and doping on mobility?
WBUT 2008, 2013, 20171
Answer:
a) The mobility u of a carier in an operational sense is defined as the proportionality
constant between the average drift velocity Vp of a (ensemble of) carriers in the presence
ofan electrical fieldE
Vp E
Conductivity can be defined simply by Ohms Law.
V= IR

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in the material. Thus
the
I current and V the voltage present
resistance, on the number of
Where R is the found The conductivity depends
conductivity is
from this relationship in the material and their
mobility.
(number of electrons)
charge carriers

increases for both increase of doping and increase in temperature.

b) Mobility

Compare 'drift' and 'diffusion'

transport in a semiconductor. [WBUT 2008, 2015]
4.
Answer: the application of an applied
particle
with
Drift is. by definition, motion of charged
a semiconductor, the carriers start
electric field. When an electric field is applied across
moving. producing a current. The positively charged
holes maye with the electric field,
the electric field. The motion of
whereas the negatively charged electrons move against
This constant takes into
each carrier can be described as a constant drift velocity, Va.
from one place to
consideration the collisions and setbacks each carrier has while moving
eventually go the
another. It is considered a constant though, because the carriers will
you look at the
direction they are supPposed to go regardless of any setbacks, especially if
direction of all the carriers, instead of each one individually.
are talking
Drift current in a semiconductor is the resultant of carrier drift. Because we
in the
about a semiconductor, or specific areas in a semiconductor, we are interested
current density. When dealing with drift current, we are interested in the current density
on
due to drift, and drift arises in response to an electric field. Drift current also depends
the ability of the carriers to move around in the semiconductor, or the electron and hole
mobility. Another parameter drift current depends on is the carrier concentration, because
you have to have carriers in order for there to be current. Each one of these carriers has
a
charge, but in this case we will only take q as a magnitude.
Diffusion is the process of particles distributing themselves from regions of high
concentration to regions of low concentration. If this process is left unperturbed, there
will eventually be a uniform distribution of particles. Diffusion does not need external
forces to act upon a group of particles. The particles move about using only thermal
motion. If we let the particles be carriers, so as they move around they take charge with
them. The moving of charge will result in a current. We call this current due to diffusion.
The diffusion current in a metal-semiconductor diode is derived based on the assumption
that the depletion layer is large compared to the mean free path, so that the concepts of
drift and diffusion are valid. We start from the expression for the total curent and then
integrate it over the width of the depletion region:

J.-otune+ Ddn
The first part of the current density equation is for drift and second part is for diffusion.

5. A Si sample is doped with 10 as atoms Icm (n, = 1.5 x10). What is the
equilibrium hole concentration po at 300 k? Determine the difference between
Fermi level and intrinsic level. Draw the energy band diagram with proper labels.
WBUT 2009]

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Answer:
Po non
or, 10 p(1.5°10°)
or
2.25102.25*10
Po10
The energr band diagram
Total energy E of conduction electron is given by hk
E=*
2m
The parabolic dependence between the energy and wave vector is shown in the Figure for
constant effective mass m,. The band gap E, is defined as E,= Ec- Ey.
Where E = Conduction band edge
E = Valence band edge
E, =Band gap
E, is the energy of the Fermi-level which is exactly at the centre of the forbidden energy
gap in the case of intrinsic semiconductor.
i.e. E, -[E
2
-E
EDNp)--
EAON

Fig: Energy band structure of the crystalline material

6.Qualitatively discuss the variation of carrier concentration with

temperature for
extrinsic Si with the help of proper diagram. WBUT 2009]
Answer:
The Fermi-Dirac statistics expresses the probability with which the
electron will occupy
the energy level E.

SE)4,Vk
where k Boltzmann's constant and E, is Fermi level of energy. The function
is

S(E), the Fermi-Dirac distribution function gives the probability that an available
energy state E will be occupied by an electron at absolute
temperature T.
The plot of f(E) as a function of E is given in figure.

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T-0

T<TT
Maxwell-Bollzmann
1/2 Tail

function of E at different
ig: The plot of fE) as a
tcmperatures

when energy
of occupancy of electron
IfT>0 K, is
- Ep, f(E)= % i.e. the probability
Case If
I: E
becomes equal to Fermi energy.

For T >0,
Case l: If E = Ep,
f(EF) indicates the transition point.
for holes in Si. What do
you mean by
7. Derive the steady stato diffusion equation
WBUT 2009]
diffusion length?
Answer: be accounted for by a mechanism
Transport of charge carriers in semiconductors may
called diffusion. Diffusion current is the net flow of
the randomly moving electrons and
to regions of lower carrier density. It is
holes from a region of high carrier concentration
analogous to Fick 's law of classical thermodynamics.
For electrons, the diffusion-current density is given by:
=eD, |Vn
Where Vn is the gradient of electron concentration and D, is the electron diffusion
constant. The total current due to the motion of holes by drift and diffusion is:
J, el4, P, E, -D, Vp)
Diffusion length means the depth of diffusion of impurity carriers doped within the
semiconductor material.
8.Sketch the ideal energy band diagram of metal-semiconductor junction when
gM <4S. Explain why this is ohmic contact.
WBUT 2010]
Answer:
Ideal metal-semiconductor contacts are ohmic
when the charge in-duced in the
semiconductor in aligning the Fermi levels is provided by
majority carriers. For example,
in the <0, (n-type) case of Fig: a,
the Permi levels are aligned
transferring electrons fro the metal to the at equilibrium by
semiconductor. This raises
electron energies (lowers the electrostatic the semiconductor
potential) relative to the metal
at equilibrium
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(Fig b). In this case the bariers to electron flow between the metal and the semiconductor
is small and easily overcome by small voltage.
Metal Semicoffector
n-type

EFm
Etm
gx-

(a)
(b)

9. What do you mean by effective mass? Derive the expression of effective mass.
How can effective mass differ from actual mass and in which condition effective
mass will be positive, negative and infinity? [WBUT 2010, 2012, 2016]
Answer:
The concept of mass of the carriers is extremely important in solid-state electronics. This
mass is different from that of free carrier mass and the free carrier mass nceds to be
replaced by the effective mass to account for the effects of crystalline force
The effective carrier mass along a particular direction (m*) is given below
momentum (p) along this direction
m*
velocity (v) along the same direction
we can write,

The term .) is called h and is called the normalized Planck's constant or the Dirac's

constant and the term (2 is known as the carrier wave vector| k. Therefore the

equation can be expressed as,

pk =h
velocity
The velocity as written in equation must be the group
E which E is the total energy of the carrier and not at
where the frequency w=in
do
Thus the mass of the
all the phase velocity. Therefore the
velocity of the carrier is.Ok
carrier should, in general, be written as

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hk hk
mdw1OE
h ok expressed as,
mass of the carriers can be
Therefore the effective
with the slope of the
that effective mass changes
above equation. We observed relation which changes from
From the the dispersion
E-k relation is called Thus, mass can
Ek curve. This
consequently the m also changes. Incidentally, from
and
semiconductor to semiconductor, external physical conditions.
energy and changes with
be a function of acceleration effective mass
prove that the
Newton's second law we can

=*
Derivation: F on the carrier is
given by:
can write the force
From Newton's second law, we
= }K, Since p= hk
F
dt dt al carrier.
Also F can be described as F=m,a, where a is acceleration of the
Thus a C1hOkGE
=E-

We know that v, = OE is the group velocity.

k
m,
Combining the above three equations, we get:

The acceleration effective mass also called the

curvature effective mass. These two
is parabolic. For any
definitions yield the same result when Eck* i.e. E-k relation
deviation from the parabolicity these two definitions of the effective mass will not
converge to the same expression. The effective momentum mass of the carriers as given
by equation affects all the properties of semiconductors such as electronic heat capacity
diffusivity to mobility ratio, the Hall co-efficient, all types of transport co-cfficient and
changes with electron concentration and other externally controllable parameters.
In the expression of effective mass we have d' Eldk<.The curvature of the band determines
the electron effective mass. The curvature of dEldk is positive at conduction band
minima,but is negative at the valence band maxima.Thus electrons near the top of the
valence band have negative effective mass.Valence band electrons with
negative charge
and negative mass move in an electric field in the same direction
as holes with positive
charge and positive mass.

10. Whatare direct band gap and indirect band

gap semiconductors? Draw the
E-K diagrams for Si and GaAs.
WBUT 2011, 2017]

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Answer:
Refer to Question No. 2 of Short Answer Type & 1
of Long Answer Type
Questions.
11. What is am bipolar transport? Why carrier generation and recombination rates
are equal in thermal equilibrium? [WBUT 2011]
Answer:
Am bipolar transport is a process in which electrons and holes diffuse, drift end
recombine with some effective diffusion co-efficient, mobility and life time.
In thermal cquilibrium, concentration of electrons and holes in conduction and valence
bands are time independent. Since the net carrier concentrations are independent of time
in thermal equilibrium, the rate at which electrons and holes are generated at the rate at
which they reconsise must be end.

12. Define mobility and write down its unit. Also give an equation that relates the
mobility and diffusivity of carriers in a semi-conductor. What is the significance of
the equation? WBUT 2011]
OR,
Derive the Einstein Relation. WBUT 2015]
Answer:
Mobility = Drift velocity per unit electric field is called mobility.
Its unit is, cm/V-S
=
For non-uniformly doped semiconductor, J, 0= en p,E, +eD, dx
For quasiment ratingn N^(n) so it may be written,

=0=e h,N,(n)E, eD, j)dn

+

So it may be written, 0 -e
KT N,n) +eD. N,)
dn")+eb,N,()
=
hNU e N,(n) dn
, In semiconductor, hole current
The above equations is valid for the condition,=

must also be zero. So _A

finally it may be written as, D,/4, = D,l4,
= KT|e.
So
This relation is known as Einstein relation.
momentum. [WBUT 2012]
energy &
13. Derive relationship between
Answer:
We know the total energy of a particle
E =K E + rest energy
m,c
E= mc"
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mo is the rest mass,

When m is the mass;
c is the velocity of light,
v is the velocity of
the particle.
as, p=mv=
m,
Momentum varies with velocity

Again, E =me' = 1-v/c2

so, me'(1-v/e)=m^«"
= m2¢*
or, e-m'v'e
or, me = E (1-v/2)=me' +mic
+c*p? is p is very small then, E=mc+
again momentum p =mv so, E=yme
WBUT 2013, 2017]
14. a) What is density of states? function with energy for different
b) Explain the plot of Fermi-Dirac distribution [WBUT 2013, 2017]
temperatures.
Si bar. Determine mobility when the drift
c) 3 Volts is applied across a 1-cm long WBUT 2013]
velocity is 10cm/sec.
Answer:
electrons per unit volume per unit k-space.
a) Density of States is defined as number of
the density of states of a system describes
In solid-state and condensed matter physics,
energy level that are available to be
the number of states per interval of energy at each
occupied by electrons.
Type Questions.
b) Refer to Question No. 6 of Short Answer
10(cm/sec)Y3 (v/cm) = 3.33*10 cm?vs
c)4=v/E =

the mass action law for the carrier concentration in a semiconductor?

15. What is
Write down the mathematical expression for Fermi Dirac probability function
E) and plot S(E) vs EIE for three different temperatures
T=0K, 300K, 2000K and explain it. WBUT 2014]

A
Answer:
theoretical analysis leads to the result that under thermal equilibrium, the product of
the free negative and positive concentrations is a constant independent of the amount of
donor and acceptor impurity doping. It is given by
nn where n, is temperature dependent.
Electrons are indistinguishable and identical particles with half-integer spin and obey the
Pauli's exclusion principle. The energy distribution of electrons in a solid is governed by
the Fermi-Dirac statistics. The probability of occupying any electronic state E by an
electron is given by Fermi-Dirac distribution function as:

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SE)=
E
1+expkT
where
k Boltzmann's constant
T Absolute temperature
E = Reference energy, called Fermi level
The Fermi-Dirac distribution function is generally called the Fermi function.
Consider two cases at T =OK .
This shows that the distribution takes the simple rectangular form at T = 0K as shown in
fig. below.

Temp
Fig Fermi-Dirac distribution at T OK

F(E)
I+exp AT

05
000
300 K

00 K

05 04 403 02 01 0 01 02 03
E-EeV)
Fig: Fermi distribution function F(E) versus (E- E,) for various temperatures

16.What is a hetero-junction? How types of hetero-junctions are possible?

Draw the band diagrams of each types of hetero-junction, considering
straddling.
WBUT 2015]
Answer:
A heterojunction is the interface that occurs between two layers or regions
of dissimilar
crystalline semiconductors. These semiconducting materials have unequal band gaps as
opposed to a homojunction. It is often advantageous to engineer the electronic energy
bands in many solid state device applications including semiconductor lasers,
solar cells
and transistors ("heterotransistors") to name a few. The combination
of multiple
heterojunctions together in a device is called an heterostructure although the two terms

ECDV-17
 PUBLICATIONS
POPULAR material be a
requirement that cach length
interchangeably. The loose especially on small
comnmonly uscd somewhat definition
are unequal band gaps is properties. A more modern
semiconductor with spatial including
clectronic properties depend on solid-state materials,
two
interface between any insulating, fast 1on conductor
scales where and
heterojunction is the
of amorphous structures of metallic,
crystalline and alignment. Band
materials. organized by band
semiconducting
semiconductor heterojunctions heterojunction at
equilibrium.
ypes of the
ne three straddling gap. n-n semiconductor crucially on the alignment of
depends types
diagram for semiconductor junction can be organized into three
The behaviour of
a interfaces
interface. Semiconductor
energy bands at the
of heterojunctions:
gap (type I).
() straddling junction, the band bending
(2) staggered gap (type I) seen in the figure. Away from the equation.
broken gap (type III) as of solving Poisson's
3) based on the usual
procedure
can be computed the band
predict the band alignment. rule, which predicts
Various models exist to is Anderson's particular the
least accurate model vacuum-semiconductor interfaces in
The simplest and
alignment based on the
properties of
is its neglect of
chemical bonding.
limitation related
vacuum electron affinity.
The mai
guesses that since the valence band is
A common anion rule
was proposed which should have very small
valence band
with the same anions materials
anionic states, materials but is related to the trend that two
to
explain the data band
offsets. This however did not larger valence band offsets than conduction
to have
with different anions tend
metal-semiconductor
offsets.
model based on more familiar
Tersoff proposed a gap
state
is given by the difference in
Schottky barrier
band offset
junctions where the conduction layer at the interface between the two
a dipole
height. This model includes tunneling from the conduction band of
one
semiconductors, which arises from electron both
other. This model agrees well with systems where
material into the gap of the GaAs/AIGaAs. The typical method for
lattice matched such as
materials are closely exciton energies in the
band offsets is by calculating them from measuring
measuring
luminescence spectra.
Conduction Band (CB)
-

Valence Band (VB)-

Sraddling Gap Staggered Gap Broken Gap
(ype ) (type It (Lype lt)

17. 3 volt is applied across a 1 cm long Si bar. Determine mobility with the drift
velocity is 104 cm/ s. WBUT 2017]

ECDV-18
 ELECTRONIC DEVICES
Answer:
3V is applied across a 1
cm long Si bar.
cm/s. Calculate mobility with drift velocity
1s T04
We know that, V, =
V
uE where u = mobility]
= Drift velocity, E = Electric
field
104 x1
So
--04d
E
3 34.6cm/ volt
18. Derive the drift
equation of current for
by Einstein Relationship? electrons and holes. What do you mean
Answer: WBUT 2018]
1 Part:
In a p-n junction diode,
electrons and holes are the minority
region and the n-region, charge carriers in the p-
respectively. In an unbiased
charge carriers, the diffusion junction, due to the diffusion of
current, which flows from the p
balanced by the equal and opposite to n region, is exactly
is independent of the biasing, drift current. In a biased p-n junction, the drift current
as the number of minority carriers
biasing voltages. But as minority is independent of the
charge carriers can be thermally generated,
is temperature dependent. drift current
When an electric field is applied across
the
attain a certain drift velocity. This combinedsemiconductor material, the charge carriers
effect of movement of the charge
constitutes a current known as "drift carriers
current". Drift current density
carriers such as free electrons and holes due to the charge
is the current passing through a square
area perpendicular to the direction of flow. centimeter
) Drift current density J,, due to free
electrons is given by:
(ii) Drift current density J,=qnu,E(AWcm)
J,, due to holes is given by: qP4,E (A/cm)
where, n =Number of free electrons per cubic
centimeter
p =Number of holes per cubic centimeter.
=Mobility of electrons in cm/Vs
= Mobility of holes in cm/Vs
E=Applied electric field intensity in V/cm
q= Charge of an electron = 1.6x 10 coulomb

2nd
Part:
The equation which relates the mobility
4 (of electrons or holes) and the diffusion
coefficient (of electrons D, or holes D,) is known as Einstein Relationship.
The Einstein Relationship is expressed as

DD-V
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POPULAR

coefficient of holes
where, D, = Diffusion
electrons
D, = Diftusion coefticient of
Mobility of holes
H, =
Mobility of electrons cxpressed as
=
called voltage equivalent of
temperature and it can be
,is
11600
mV at 300 K
=26 indirect and band gap
for a direct and WBUT 2018]
19. Draw and
explain E-K diagram
example.
semiconductor with suitable
difference between the,top of the valence
Answer: valence band and
gap represents the minimum energy the top of the
The band however, electron
the bottom of the conduction band, the same value of the
band and generally at
bottom of the conduction band are not
the top of the valence band and the
the gap semiconductor, momentum, as in the schematic
momentum. In a direct band same value of
band occur at the
bottom of the conduction
Conduction band
below.

Band gap

alance band

Momentum band
semiconductor, the maximum energy of the valence
In an indirect band gap minimum in the conduction band energy:
momentum to the
occurs at a different value of

Band gap

Valance band

Momentum
The difference between the two is most important in optical devices. As has been
nentioned in the section charge carriers in semiconductors, a photon can provide the
energy to produce an electron-hole pair.

ECDV-20
 LLECIRONIC DEYICES

ach photon of energy has momentum p,

where eis the velocity light. An
optical photon has an energy of
of the order of 10 "),
photon has a very small amount
of momentum
and, since e3 10 ms', typicala
A photon of energy
E,, where E, is the band gap energy, can
pair in a direct band gap produce an electron-hole
semiconductor quite easily,
to be given very much momentum. because the electron does not need
However, an electron must also
change in its momentum for undergo a significant
a photon of energy
E, to produce an electron-hole pair in an
indirect band gap semiconductor.
This is possible, but it
interact not only with the requires such an electron to
phonon in order to either
photon to gain energy, but also with a lattice vibration
gain or lose momentum. called a
The indirect process
proceeds
nterscct in order to proceed: at a much slower rate, as it requires three entities to
an clectron, a photon and
chemical reactions, where, in a phonon. This is analogous
a particular reaction step, a to
will proceed at a much reaction between two molecules
greater rate than a process which
involves three molecules.

Long Answer Type guestions

1. Give the E-K diagram of
Si and GaAs and oxplain
between intrinsic electron briefly. What is the relation
the semiconductor made byconcentration and oxtrinsic electron concentration?If
Si
extrinsic Fermi level energy is the difference botweon conduction band energy
and
form in the semiconductor 0.05 oV, what is the
extrinsic
at room temperature? electron concentration
Answer: [WBUT 2008]
E-K diagram of Si & GaAs:

GaAs onduction
Si
Band Conduction
Band

***

Valance
Band Valance
Band
100)
1001
() GaAs
(6) Si

ECDV-21
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band maximum and
POPULAR the
valance
for GaAs. The the conduction band
E-versus K diagram electrons in
The Similarly holes
Fig (a) shows theminimum both occur at k = 0. which is at k=0.
conduction band band energy energy. A Semi
conduction valence band
the minimumcongregate at the uppermost
tend to settle at tend to bandgap semi conductor. energy occurs
band direct
n the valance property is said to be
a
in the valance
band
conductor with this .
for Si The
maximum
occurs not at k = 0, but
diagram energy
Fig (b) shows
the E-K
the
conduction band
conduction band energy
in
before. The minimum between the
minimum
gap energy Eg. semi
A
at k =Oas direction. The difference the band
as energy
along the [100] valance band energy is still defined minimum conduction band
maximum and
and the maximum valence band energy gap semi conductor.
whose band
conductor
same k value is called an
indirect
extrinsic electron concentration
the concentration and
do not occur at intrinsic electron
between
The relation

is, n, =N, exp -E-E

T density of
is the effective
denoted by n,N,
intrinsic electron concentration is temperature k=Boltzmann's
Where absolute
conductor. T is the Fermi level energy.
state function for semi is the intrinsic
conduction band energy and E, band energy of
constant. E, is the difference between conduction
made by Si and the equation we can calculate
the
If the semi conductor energy is 0.05 ev, from the
extrinsic to Fermi level
room temperature:
extrinsic electron conduction at

n, =n N, exp|

=2.8x10" exp(-E-E n
kT
0.05ev
n=2.8x10 exp 38x103 J/kx300k)
2.8x10
significance. WBUT 2011]
2. What is 'law of mass action'? Explain its
Answer:
holes below a level that could
Addition of N type impurities decreases the number of
have been available in a pure semiconductor. Similarly
addition of P-type impurities
decreases the number of electrons below a level. Experimentally had been
it found that
under thermal equilibrium, protect of number of holes and number of electrons
is

constant and is independent of the amount of donor and acceptor impurity doping.
ThHs
relation is known as mass action law.
Mathematically it may be written as, n P=n
Where n free electron concentration
ECDV-22
 ELECTRONICDEVICES
p hole concentration
n= Infinite concentration.
a) Find the
3.
expression of drift current
Answer: in a p-n junction diode.
WBUT 2012]
Refer to Question No. 18(1"
Part) of ShortAnswer Type Questions.
b) Derive the
expression for the depletion
Answer: width along a p-n junction. wBUT 20121
The diagram is the
change density diagram is PN
q is change of carriers a junction.
again g4xN. =qAx f Charge density
N,
using Poisson equation
we get
0<x<x 0. =4N
dE
N -0<x
where Na. Ng are acceptor and
<0 .-qdx,N. qN.

donor concentration. E is the electric

field.
again we get, E, =

where E
-N-N
is the electric field at
x=0
again Ex) = -dMr)
dr
or, - JE(r)d
where v, is the voltage at x = 0
so, we get, v, =.
-EW=5N,W
since the balance of change requirement is
N XoN, and W =
X+*
WN,
YN+N
NN
2eN, +N
or, W
NN
sotheexpression for depletion with along a p-n junction is w=
N,NG

ECDV-23
 PUBLICATIONSs wBUT 2014]
POPULAR
semiconductors? category.
indirect example ot each
and
meant by direct neat diagram and give energy of the Fermi
leval
4. a) What is a semiconductors, the
with the help of valence bands
b) Explain for intrinsic and nds
Show that the conduction
c)
are energy of
E, =+ 2
where E, E,

respectively.
Answer: below.
E-K diagram is given
a) &b) direct bandgap semiconductor whose
GaAs is a

**

EpGNo) ----

******f****
**********
EARN

Semiconductor GaAs
Direct Bandgap
the
bandgap means that the minimum of
In physics of
semiconductor device, a direct momentum
the maximum of the valence band in
above
conduction band lies directly electrons at the conduction-band
minimum can
semiconductor,
space. In a direct bandgap maximum, while conserving momentum.
at the valance band
combine directly with holes bandgap will be emitted in the form of
a
recombination across the
The energy of the
light. This is radiative recombination which is also called spontaneous
photon of
semiconductors such as crystalline silicon, the momentum
emission. In Indirect bandgap same, so a
the conduction band minimum and valence band maximum are not the
of
not conserve momentum and i forbidden.
direct transition across the bandgap does
as a phonon or a
Recombination occurs with the mediation of a third body, such
These
crystallographic defect, which allows for conservation of momentum.
and
recombinations will oflen release the bandgap energy as phonons. instead of photons,
is very inefticient
thus do not emit light. Light enmission from indirect semiconductors
and weak, So imany new techniques are there to improve light emission by indirect
semiconductors. Prime example of a direct bandgap semiconductor is gallium arsenide
a material commonly used in laser diodes Si is an indirect band gap semiconductors so it
is not used and optoelectronic source.

ECDV-24
 ELECTRONIC DEVICES

EDNp)-..
2m
W k

EAN
***.

InDirect Bandgap Semiconductor

In Si
semiconductor physics, an
energy in the conduction indirect bandgap is a
bandgap in which the minimum
band is shifted by a k-vector
k-vector difference represents relative to the valence band.
The
a difference in momentum.
Indirect bandgap semiconductor
are inefficient at emitting
present in the conduction light as because any electrons
band quickly settle into the
Electrons in this minimum energy minimum of that band.
require some source of momentum
overcome the offset and fall allowing them to
into the valence band. Photons
compared to this energy offset - have very little momentum
The momentum "kick" of a photon
absorbed is negligible and direct transitions being emitted or
Since the electron cannot rejoin are essentially 'vertical' in k-space.
the valence band by radiative
band electrons typically last recombination, conduction
quite some time before recombining
means. Silicon is an indirect bandgap through less efficient
semiconductor, and hence is
for light-emitting diodes or laser diodes. not generally useful

Some example of direct and indirect material

are,
direct band gap semiconductor is GaAs.

Refer to Question No. 2 of Short Answer Type Questions.

c) An intrinsic semiconductor is an undoped semiconductor.
This means that holes in the
valence band are vacancies created by electrons
that have been thermally excited
conduction band, as opposed to doped to the
semiconductors where holes or electrons
supplied by a "foreign" atom acting as an impurity. are
In order to better understand
the behavior of semiconductors, we need
more deeply what are the electron and hole densities to investigate
in the conduction and valence
bands, respectively. We first need to introduce
the notion of energy density
of states N(E). This parameter gives the number states
of (per unit volume and per unit
energy) between E and EtdE: NC(E) (respectively, NyE)) physically
represents the
"room" available for electrons (resp. holes) in the conduction
band (resp. valence

ECDV-25
 POPULAR PUBLICATIONS
density of
two bands, the
to the extrema of these
are close
band). For energies that with E:
dependence
states has a quadratic

N,(E) E-E
cmle]
2m
and me (resp. my)
Planck constant (h=6.626.10-34Js)
the normalized
Where
h=is conduction band (resp. of the valence band). For a
(resp. a
is the
average effective mass of the
the effective mass of an electron me
semiconductor, mc (resp. my) is
direct gap
hole mh) in the crystal. mass allows
considering electrons (and
effective The
The above-mentioned
concept of
free particles, like free quasi-particles.
as almost and
holes) inside the crystal electron (and hole) gas, but in which electrons
semiconductor then becomes an particle
which may be very different of the mass of the
mass
holes have an effective mo=0,91 1.10-50kg is
example, for GaAs mc/mo=0,066 avec
moving in free space. For
the
the free electron mass.
number of electrons and holes present in each band,
In order to know what
is the the
information that we need. We also have to know
only
density of states is not the level with a given energy E. This
probability is
occupy a
probability for an electron to
distribution function
given by the Fermi-Dirac

+exp[(E- E, )/ET]
n=N,(E)(E)dE
Er

p= M,(E)1-S(E)dE

N, = N,(E)exp dE
with

p=N, exp N,= N,(E).exp

T
dE

density
Where Ne et Ny are called the effective densities of states. They represent the
of "useful" states, at a given temperature T, in their respective energy band.

ECDV-26
 ELECTRONIC DEVICES
Let's note that the product
of the two densities turns out to be
position of the Fermi level. This is independent on the
still true even for extrinsic semiconductors. It
known as the law of mass action. is
Each electron in the conduction
conclude that the electron band is associated with a hole in the valence
and hole densities are equal: band. We
n=p=n,
By substituting the carrier
densities by their respective expressions,
allows defining the this relationship
Fermi level for an intrinsic
temperature kal is significantly semiconductor EFi. Since at room
middle of the forbidden lower than the energy gap, this level is
band: located near the

E,5
5. a) What is Hall
field? Why Hall Effect is
How can we calculate important in semiconductor physics?
Effect? mobility of electron in p-type semiconductor
using Hall
Answer: WBUT 2015]
The motion of carriers in the
presence of electric and magnetic
number of galvanometric effects. fields gives rise to a
The most important of these effects
is the Hall Effect.
When a semiconductor, sample
field B, then an electric field Eo
carrying a current I is placed in a
is induced in the specimen, in
transverse magnetic
to both B and I. This phenomenon called
is the Hall Effect.
the direction perpendicular
The Hall Effect may be used
for determining whether a semiconductor
by finding the carrier is n-type or p-type
concentration and calculating
conductivity o. the mobility u, by measuring
the
Let us consider a rectangular bar
of n-type semiconductor of length
thickness d as shown in Fig. 1. L, width W and

.
B
Fig. 1
Schematie diagram of Hall Effect.
The carriers (electrons or holes)
are subjected to a magnetic force in
the negative y-direction.

ECDV-27
POPULAR PuBLICATIONSs field B is
applied in the
a magnetic Curre
positive r-direction and negative y-direction of the
applied in the exerted in the semiconductor is
t a current / is will be I to side 2, tt the clectric fiela
positive
Z-direction, a force from side 2. The d
carried by electron surfaces and
current is appears between
camers. The
Hall voltage y
pe. Therefore E, is given by
developed in y - direction equilibrium state the electric fieia
Vd-Edistance between surfaces and 2. In the
1

carrier, which Just

balances the
where d is the on the
Effect must exert a force
Hall
E, due to the
can write
magnetic force. and we
vo is the drift
speed.
eE, - Bev, carriers,
the
is the magnitude of the charge of
where e given by
Therefore current density Jis in the
direction of the
pWd of the specimen
density and W is the width
where p is the charge
magnetic field.
Combining Eq.s, we find
d=Bvod=BJdp=BlpW
can be measured from the above
VuE, the charge densityp
B, W and I are measured, 1
then the carrier must be an electron and
if V terminal positively
Eq. If the polarity of
Va is positive at the terminal 2 becomes
concentration. If
where no is the electron must be of p-type and p= poe where
p noe
terminal I the
semiconductor
charged with respect to
concentration.
Po is the hole
R lp coefficient
Where R is the Hall
RVuw/BI
by
Conductivity a is related to mobility u

d Po
where p noe =
coeffricient, mobility p can be determined
by
measured with Hall
If the conductivity is
J=pp
L-E-R
From the above Equations we get
R pa
a Ru
In the presence of scattering the mobility can approximately be written as
8a

ECDV-28
 ELECTRONICDEVICES
Applications Hall
of
1. Experimental
Effect
determination of carrier
From the basic formula concentration:
determined by using of Hall Effect,
the experimental the electron and hole concentrations can
be
2. By using Hall
Eftect, the type of values of Hall coefficient.
RA>O forp-type the
semiconductors and semiconductor can be determined as follows:
3. Determination
of the mobility RK0 for n-type semiconductors.
The equation
= [oRH} determines
4. Hall Effect multiplier the mobility by using the experimental
values of Ra
If the magnetic field B
duces current 7 then Hall voltage
multiplier generates an output Vu o II. The Hall Effect
can be used for proportional to the product
analogue multiplication. of two signals. Thus Hall Effect
S. The power
flow in an electromagnetic
Effect. wave can be measured by
the help of Hall
6. Experimental determination
By knowing the of the magnetic field.
values of Vi, 1, p and W, we
experimentally. can determine the value of B

b)In a Hall experiment

length of semiconductor specimen
W =10 cm
and depth d = 10 cm and L=10 cm, width
I, =1.0 mA, applied voltage V,
current through semiconductor
=12.5V, magnetic flux density B, = substrate
voltage VH = -625 mV. What type 500 gauss, Hall
of majority carrier is there in
substrate? Calculate majority carrier concentration semiconductor
Answer: and mobility. WBUT 2015]
As the Hall voltage Vu is negative,
therefore the.sample Specimen is
majority carriers in the sample are electrons. n-type, i.e.,

For n-type specimen the Hall voltage can

have their usual meaning. From the above
be expressed as Vy
ned
-
where the terms
equation we can write, the electron
concentration.
-(10 )(5x10*)
n= -B
edV 1.6x10 10)(-625x10) = 5x10 m3

:5x10" cm'
(1Gauss=10 Tesla)
The mobility of electrons from Hall experiment can be expressed
as

L 10)10)
enWdv, (1.6x10")5x 10")(12.5)(10 )(10*)
= 10m/V-S=10° cm/V-S

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POPULAR PUBLICATIONS (WBUT 2016

c) What is quasi-Fermi
level?
i solid sla
Answer: mechaniesand especytne population
quanitum
term used in thal deseries
Aquasi Fermi level is a electrons)
(chemical potential of valence baid, wlie tne
popululims
Fermi level
physics for the
of electrons separately in the conduetion band and could be caused by
equilibrium. This
displacement e
which aller he
upplicalin
populations of
are displaced from exposure to light of
energy,
recombinatiOn rale tends be to
an external voltage, or by band. Since band and
the conduction band and valence each band, the coduction
clectrons in relaxation rate within internally n equilibium
than the energy population that is
uch slower have an individual exchange of electrons, The
Valence band can each with respect to
the bands are not in cquilibrium carrier populations can o longer be
even though quas
is such that the describe using separate
drsplacement from equilibrium possible to
level, however it is
described by a single Fermi
Fermi levels for each band. distribution function of the electrons
in thermal equilibrium,
the case the
When a semiconductor is Fermi-Dirac distribution function, In this
presented by ol electron at
a the energy level of Easis the level in which the probability of occupation distinguish between
Fermi level is defined there is no need to
In thermal cquilibrium, quasi-Fermi level as they ure simply
that energy is 1/2. valence band
level and
conduction band quasi-Fermi
situation occurs, the populations
of the
equal to the Fermi level. equilibrium
thermal
When a disturbance from a valence band change. If the disturbanee is not too
band and thermal
electrons in the conduction the bands cach relax to a state of quasí
quickly,
great, or not changing too time for electrons within the
conduction band is
equilibrium. Because the relaxation thermal
gap, we can consider that the electrons are in
band
much lower than across the is also applicable for clectrons
in the valence
conduction band. This
equilibrium in the and quasi temperature due to
thermal
quasi Fermi level
band. We can define a temperature
'electrons in conduction band, and quasi Fermi level and quasi
cquilibrium
for the valence band similarly

instrinsic semiconductor, the energy of Formi level,

Show that for
onergy of conduction band and valance
E,
=
(E E, )/2, where Ec and Ey aro
+
WBUT 2017]
band
Answer:
valence band are
The electron and hole concentration in conduction and

N epE-E) E)
exp
and N,
KT KT

For Intrinsic Semiconductor,

. exp-E) KT KT

ECDV-30
 ELECTRONIC DEVICES
Taking Log on both sides
we have,

E,-5(E+E,)+ KTIni N
and
E-E+E) [E=Fermi-energy
Ec Conduction Band energy
Ey= Valence Band energy]
7. Derive Einstein relationship.
different from Fermi energy What are quasi-Fermi levels? In what way are they
Fermi level lies at the level? Show that in case of intrinsic
midway of the energy band gap. semiconductor,
Answer: [WBUT 2018]
Part: Refer to Question No. 12 of Short
Answer Type Questions.
2nd
Part: Refer to Question No. 5(c)
of Long Answer Type Questions.
3rd
Part:
When a semiconductor is in
thermal equilibrium, the distribution function
at the energy level of E is presented by of the electrons
a Fermi-Dirac distribution function.
the Fermi level is defined as the level in In this case
which the probability of occupation of
electron
at that energy
is.2 In thermal equilibrium, there is
no iieed to distinguish between
conduction band quasi-Fermi level and valence
band quasi-Fermi level as they are simply
equal to the Fermi level.

4th Part: Refer to Question No. 6 of Long Answer Type Questions.

8. Write short notes on the following:
a) Miller indices
WBUT 2006, 2008, 2010, 2014]
b) Transferred electron devices
c) Hall effect [WBUT 2008]
WBUT 2011, 2017, 2018]
d) Effective masss
e) Effective cell WBUT 2011, 2015]
WBUT 20171
Answer:
a) Miller indices:
Miller Indices are defined as the reciprocals of the fractional intercepts
which the plane
makes with the crystallographic axes.
The method by which indices are determined is best shown
by example. Recall, that there
are three axes in crystallographic systems. Miller indices are
represented by a set of 3
integer numbers.

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 PUBLICATIONSs
POPULAR

(nkI) = parenthesi
esis
Crystallographic indices considered here. yielding
being respectively, thus
unique surface such as that and 0
A throughou
reciprocals of 1
and eoare planes
The
face or a family of
designate a crystal lattice
a crystal
lattice.
a direction in the
designate collectively include
hklsquare bracked Used to edges)
from the origin
to a point. intersects (i.e., as
whose
faces of a crystal refered to
all the are
other. These represent a direction in a (0,0)
parallel each they
crystallographic zones and
illustrated using
an, x
the crystal lattice. easily
The procedure
is most
consider the following
will first
example so we
axes. surface js
surface/plane:
on the x-, y- and z- point a(0,0) ), but the
the intercepts = a (at the on these two axes
but
Srep 1: ldentifyintercept on the x-axis is at x intercept
In this case the strictly therefore there is no case where the plane is
z-axes -
for the special
parallel to the y- and be at infinity (o) z-axes are thus
the intercept to
we shall consider intercepts on the x-, y-
and
The
parallel to an axis.
Intercepts: 4,00, 0 co-ordinates respective cell.
the intercepts in fractional dividing by the
Step 2: Specify co-ordinates by
dimensions a x b xc
fractional has
Co-ordinates are converted to in a unit cell of each co
a point (x,y,z) a cubic unit cell
dimension for example, In the case of
xla , y/b , z/c ).
This gives
fractional co-ordinates of ( cubic cell constant, a.
divided by the
ordinate will simply be
1/a i.e. 1, co, a
Fractional Intercepts: a/a, l/a, intercepts
reciprocals of the fractional then
Step 3: Take the
the Miller Indices which (by convention) should
generates symbols. The Miller
This final manipulation any commas or other
being separated by
be specified without when one is specifying
Indices are also enclosed within standard brackets (....)
Miller Indices: (100)
So the surface/plane
illustrated is the (100) plane of the cubic crystal.

b) Transferred electron devices:

Transferred electron devices In some materials the energy of electrons can
be raised by
to
an applied field to the point that they transfer from one
region of the conduction band
another higher energy region. The band diagram for GaAs is shown in Fig.

ECDV-32
 ELECTRONICDEVICES

Satellite
Valley
Upper
valley
A Conduction
Lower band
valley

Valence band

In n-type GaAs, valence band

is filled at central valley of the conduction band at T [at
K=0] normally contains conduction
electrons.
There is a set of subsidiary minima at L. These are called
Satellite Valleys. Once the
electrons have gained enough energy from the field
to be transferred into higher energy
valley, they remain there as long as field is greater
than critical value. As a result, once
the field increases above the critical value, most conduction
electrons in GaAs reside in
satellite valley and exhibit properties typical of that region of conduction
band. This
mechanism is called transferred electron mechanism.

c) Hall Effect:
Forces exerted on moving charges by electric and magnetic fields
give rise to Hall Effect.
It is used for distinguishing whether any semiconductor
is n-type or p-type.
The force on a particle having charge q, moving in magnetic field
is described by
F-4xB)
If a Fermi-conductor is subject to both electric field and magnetic field then
a surface
charge is being developed. In steady state, the magnetic field force will
be exactly
balanced by induced electric field force. It may be written as,
F=q|F+VxB=0
qEg =q VB. Induced electric field in y direction is called Hall field. It produces
a
voltage across semiconductor, known as Hall voltage.
TuEyw
Substituting value of V4 in F we have, V, = v,w B,

For a P-type semiconductor, drift velocity of holes can be written as,

v=s
(ePXWd)
So, V,
ePd
So
P- eVpd

ECDV-33
POPULARPUBLICATIONS

3
So, n-type semiconductor, n=

semiconductor.
For a P-type
J=eP p,E
S Wd
P L *enV}¥Wa
electron mobilny. K,
Now hole mobility. and
HrP V,Wd

Type Questions.
Refer to Question No.
9of ShortAnswer
d)

e) Effective cell: electron,

Energy-momentum relation for free

E=4
2m 2m
hP
SO

So. =, where V Velocity of the particle

Again, *m
So,
1

dE
hdk m

ss it is a parameter that relates the quantum mechanical

results to the classical force equations. In most cases, the electron in the bottom of the
conduction band can be that of a classical particle whose motion
can be modeled by
Newtonian mechanics, provided that the internal forces
and quantum mechanical
properties are taken into account through the effective
mass. If we apply an electric fiekd
to the electron in the bottom of the allowed
energy band, acceleration,
-eE =effective mass
a where m,
ofthe electron

ECDV-34
 ELECTRONICDEVICES

P-N JUNCTION
Chapter at a Glance
P-N Junction: When p type
semiconductor is selectively doped in n type
the same monolithic structure semiconductor in
then a p-n junction is formed
Normaly we think that if anyone joins two regions then diffusion
place because of large of carrier will take
carrier concentration gradients at the junction. Thus
from p-side into n side and holes diffuse
electrons from n-side to p-side.
The diffusion current, resulting from
electric field is being created that cannot build up indefinitely as an opposing
at the junction.
But this cannot occur in
case of charged particles in a p-n junction
region is being developed in it and an electric field is developed because space charge
a drift component of current in it. So the field creates
from n to p that opposes diffusion current.
Schottky Junction: Schottky diode or
contact is a metal semiconductor diode or contact
having characteristics similar to a
p-n junction. When the metal is posited directly on the
semiconductor surface, the Schottky contact is
The fabrication structure is shown in Fig. produced.
1.
Metal (Al or Au)

n-t SPe
semiconductor
Fig.1 Schottky contact
The direct metal-semiconductor contact produces a contact
potential barrier known as
Schottky barrier. This barrier produces the rectifying
behavior. Thus, the Schottky barrier
diode is designed.
The Schottky Diode: In Fig. 2 the terminal 1 forms the ohmic
contact because Al is
deposited on the n region and not on
then region, but terminal 2 forms the Schottky contact.
The Schottky contact together with the two terminals forms the Schottky
diode
2,4) (C)

Anode Cathode
n-type substrate, (4) (C)

p-type substrate

Fig: 2 Cross-sectional view of a Schottky diode

ECDV-35
POPULARPUBLIGATIONa
guentlona
LMultlple CholoeType WBUT 2006, 2009
capacitOr
varlable
b) these
1. Varactor diode act as d) none of
a) Variable resistor
c) Switching
device
Answer: (b)
dominated by
current le WBUT 2007
blas, forward current
junction ie foward
drift
b) dieplacement current
2. When PN
diffusion current ourrent d)
a)
c) drift or
diffusion
WBUT 2007
Answer: (a)
due to oarrlers
in the PN junction ls b) minortty
Storage capacitance these
3.
majority carriers d) none of
a)
c) both (a) and (b)
Answer: (c)
WBUT 2007)
under blae
4. A Varactor diode
is operated o) wlthout
b) forward blas
a) reverse bias
Answer: (a) WBUT 2007, 2010]
nogatlve roslstance roglon? d) LED
a
5.
has
Which of the following Tunnel dlode c) Photo diode
diode b)
a) Zener
Answer: (b) WBUT 2007, 2009
a
6. IMPATT diode is dovlco
a) negative
conductance mlcrowave
rectifying devico
b) high frequency
semiconductor dovice
c) degenerate conductance devlce
difforential
d) bulk negative
Answer: (a)
WBUT 2007]
7. Operation of Gunn
diode is oxplalnod with
b) avalanche transit time offect
electron effect
a) transferred d) Schottky offect
c) tunneling effect
Answer: (c)
in. WBUT 2008, 2010
8. Tunnel diode is used
b) r.f. oscillator
a) microwave oscillator
d) video amplifler
c) audio oscillator
Answer: (c)

9. Reverso saturation current of p-n Junetion diode is WBUT 2008, 2010]

a) diffusion current b) drift current
c) displacement current d) none of these
Answer: (b)

ECDV-36
 ELECTRONIC DEVICES

10. if ,reverse bias voltage, then transition capacitance (C;) for hyper abrupt
is
p-n junction diode is proportional to
WBUT 2008]
a) b) V,3 d)
Answer: (d)

11. 7 is p-n junction diode forward current. Diffusion capacitance is proportional

to WBUT 2008]
a) b)
Answer: (a)
c)I d) 2
Zener effect is operative at
12.
WBUT 2008]
a) high reverse voltage
and for heavily doped junction
b) low reverse voltage and for heavily doped
c) high reverse voltage and for
junction
lightly doped junction
d) low reverse voltage and for lightly doped
junction
Answer: (b)

13. IMPATT diode works by the mechanism of

WBUT 2008]
a) electron tunneling b) transferred electron
c) avalanche multiplication d) none of these
Answer: (a)

14. Schottky diode is used in high speed operation because of

WBUT 2008]
a) Small contact potential b) high speed of electrons
c) small size d) insignificant storage delay
Answer: (6)

15. Gunn diode is used in WBUT 2009]

a) microwave oscillator b) r.f. oscillator
c)
audio oscillator d) audio amplifier
Answer: (a)

16. Zener diodes are WBUT 2009]

a) specially doped p-n junction b) normally doped p-n junction
c) lightly doped p-n junction d) none of these
Answer: (a)

17. Diffusion current in a p-n junction is influenced by WBUT 2009]

a) concentration gradient of carriers b) applied voltage
c) concentration of carriers d) none of these
Answer: (a)

ECDV-37
 respect
EOPULAR euaLICATIONS semiconductor with
[WBUT 2009]
applled to an
ntype
voltage is
18. When a positive between the semiconductor andsame etad) none of these

ee etal, the barrier b) decreases ) remains

a) inereases WBUT 2009, 2010]
Ausner? (a)
in b) forward blasconnect in any bias
photodetector diodebias
We can connect reverse to
19
in fonward bias
and d) no need
on
reverse bias
c)
Answer: ()
WBUT 2010]
d) zero bias
is operated under c)without bias
0. A varactor diode b) forward bias
a) revese bias WBUT 2011]
Answer: (a) of a solar cell is
d) 4th
-V plot relevant to operation
o) 3rd
21. The quadrant of
a) 1st b) 2nd
Answer: (d) negative resistance region 2011]
in its
WBUT
diodes not possess
a
22. Which of the following d) IMPATT diode
characteristics? c) Zener diode
b) Gunn diode
a) Tunnel diode
Answer: (c) WBUT 2011

23. Tunnel diode is used in b) r.f. oscillator

d) mm-wave
oscillator
a) audio oscillator
c) microwave
oscillator
Answer: (a) Germanium p-n
across the terminal of an unbiased WBUT 2011]
connected
24. fa voltmeter is will be
voltmeter reading o)0.6 V d) 1.0 V
junction diode, the 0.3 V
a) 0v b)
Answer: (a) WBUT 2011]
be changed by varying
capacitance of a varactor diode can d) all of these
25. The level c) size of the diode
a) bias voltage b) doping
Answer: (a)
WBUT 2011]
26. A voltage variable
capacitance can be realized in
b) Avalanche diode
a) Zener diode
d) Varactor diode
c) Schottky diode
Answer: (d)
WBUT 2012, 2014]
27. PIN diode has
a) p and n layers separated by 1 layer
b) pt andn+ layers separated by1
1
layer
c) p- and n- layers separated by layer
d) either (b) or (c)
Answer: (b)
ECDV-38
 ELECTRONIC DEVICESs

28.Consider the following w.r.t. tunnel diode

1. It is a 2 terminal
wBUT 2012]
device with no isolation between input and output
2. Some current can be
Of these achieved at 3 different voltage levels.
a) (1) only b) (2) only c) (1) and (2) d) none of these
Answer: (6)
29. In a voltage regulator
circuit, the maximum value of load current can be
a) 2.5 mA
WBUT 20121
b) 0.9 mA c) 1.6 mA d) 3.4 mA
Answer: (d)
30. LED works on the principle of
a) photoltuminescence WBUT 2013]
b) electroluminescence
c) cathodoluminescence d) radioluminescence
Answer: (a)
31. Which of the following diodes does not posses a negative differential
resistance region? WBUT 2013]
a) Tunnel diode b) Gunn diode c) Zener diode d) IMPATT diode
Answer: (c)
32. Varactor diodes are commonly used
WBUT 2014]
a) as voltage controlled capacitance b) as a constant current source
c)as voltage multiplier d) as a constant voltage source
Answer: (a)
33. The ideal barrier height between the metal and the semiconductor of a
Schottky
barrier diode is WBUT 2014]
a) the difference between the metal work function and semiconductor
electron affinity
b) the difference between the metal work function and semiconductor work
function
c) the difference between the metal electron affinity and
semiconductor work
function
d) the difference between the metal electron affinity and semiconductor
electron affinity
Answer: (b)
34. Photodetector diode is WBUT 2014]
a) triangular device b) square law device
c) linear device d) both (a) and (b)
Answer: (c)
35. In Schottky barrier diode, the current mechanism is due to WBUT 2015
a) minority carrier b) majority carrier
c) both (a) and (b) d) none of these
Answer: (c)
ECDV-39
POPULAR PUBLIGATIONS WBUT 2015
varying
changed by
be b) biasing
36. Capacitance of
varactor diode can these
d) all of
a) doping
c) size of the diode WBUT 2015
Answer: (b) cell is
operation of solar d) 4th
relevant to c) 3
37. Quadrant of l-V plot
b) 2d
[WBUT 201
016, 2017]
Answer: (d)
negative resistance device? d) LED
following is not a c) Gunn diode
38. Which of the diode
a) Zener diode
b) IMPATTT
Answer: (c) Germanium
terminal of an unbiasedWBUT 2016]
connected across thewill be
39. If a voltmeter is voltmeter reading d) 1.0V
junction diode. The c) 0.6V
P-na) Ov 0.3V
b)
Answer: (a) WBUT 2018
impurity is d) Phosphorus
40. Example of pentavalent c) Antimony
Boron b) Bismuth
a)
Answer: (d)
WBUT 2018]
a pn junction is
41. Junction capacitance of
forward bias b) the capacitance under no bias
a) the capacitance under d) None of these
c) the capacitance under
reverse bias
Answer: (c)
WBUT 2018]
42. External Quantum Efficiency is
the ratio of reflected to incident photons
a)
b) the fraction of current that produces luminescence
c) the relative number of photons absorbed per unit distance
d) the ratio of emitted photons to generated photons
Answer: (a)

Short Answer Type Questions

1.For which condition metal-semiconductor junction behaves as WBUT 2007]
i) Ohmic contact
i)Rectifying contact
With E- k diagram, explain why LED emits light but PN junction
rectifier diode
doesn't. WBUT 2007, 2014]
Answer:
1" part:
i) Ohmic contact
Ohmic contact and schottkey contact both
are metal semiconductor
diode or contact is a metal semiconductor contact. A Schottke
diode or contact having
similar characteristic
ECDV-40
 ELECTRONIC DEVICES

a p-n junction. When the metal is deposited directly on the semiconductor surface that
produces the schottkey contact. The fabrication structure is shown in Fig: (a).
direcct netal-semiconductor contact produces a contact potential barrier known as
he
Schottky barrier. This barrier produces the rectifying behavior. Thus the Schottky barrier
diode is designed.
In case of ohmic contact. metal is
not directly deposited on semiconductor surtace,
instead of that a high doped laycr (cither n' or p') is placed in between the semiconductor
and metal to make the gradual change in barrier potential. So there is no rectitying
behaviour.
The junction of Metal-same metal doped layer-semiconductor produces a
liner behaviour
i.e. ohmiC behavior. This junction which follows ohm's law i.e. linear nature in -v
characteristics, forms a ohmic contact.
For example, Al-Al+ doped Si-nSi forms a ohmic contact.
Metal (Al or Au)

S1O

n-type
semiconductor n-Si

Fig: (a) Schottky contact Fig: (b) Ohomic contact

n region formed with highly
doped Al, same metal is used for metallic contact.

i) Rectifying contact
lt is a low resistance junction providing conduction in both directions between metal and
semiconductor.
Charge cariers recombination takes place at the p-n junction as electron crosses
from the n-side and reconmbines with holes on the p-side. When the junction is
forward-biased the free electron is in the conduction band and is at a higher
energy level than the hole located at valence band. The recombination process
involves radiation of energy in the form of photons. If the semiconductor
material is translucent, the light will be emitted and the junction becomes a light
source i.e. a light-emitting diode (LED). LEDs are pn junctions that can emit
spontaneous radiation in ultraviolet, visible, or infrared regions.

ECDV41
POPULAR PUBLICATIONS

is given below
2d Part: semiconductor whose E-K diagram
bandgap
dairect
E-
2m *

EooMo)

*******
EN ***1

Semiconductor GaAs the conduction

Direct Bandgap means that the minimum
of
semiconductor physcs, a drect bandgap valence band in momentum
space. In a
in maximum of the combine
band lies directly above the at the conduction-band minimum can
electrons
direct bandgap semiconductor, maximum, while conserving momentum. The
band
directly with holes at the valance bandgap will be emitted in the
form of a photon of
recombination across the
energy of the
recombination, also called spontaneous emission. In indirect
light. This is radiative silicon, the momentum of the
conduction
bandgap semiconductors such as crystalline across
not the same, s a direct transition
band minimum and valence band maximum are
momentum and is forbidden. Recombination occurs
with
the bandgap does not conserve
phonon or a crystallographic defect, which allows
the mediation of a third body, such as a
for conservation of momentum. These recombinations will
often release the bandgap
energy as phonons, instead of photons, and thus do not emit light. As such, light emission
from indirect semiconductors is very inefficient and weak. There are new techniques
to
improve the light emission by indirect semiconductors. The prime example of a direct
bandgap semiconductor is gallium arsenide-a material commonly used in laser diodes.
Si is an indirect band gap semiconductors so it is not used and optoelectronic source.

Zm

EoONo)-.

EA r****-

InDirect Bandgap
Semiconductor
Si
ECDV-42
 ELECTRONIC DEVICES
In semiconductor physics,
an indirect bandgap is a bandgap in which
energy in the conduction the minimum
band is shifted by a k-vector relative to the
k-vector difference represents a valence band. 1 ne
difference in momentum. Silicon is an indirect bandgap
semiconductor, and hence is
not used as 1light-emitting diodes or laser
diodes.
2. Describe briefly the basic
suitable on high frequency structure of a Schottky diode and explain why
operation. it is
WBUT 2007, 2009, 2014]
Explain working principle OR,
of Schottky Diode. [WBUT 2015]
Answer:
The Schottky barrier diode
can be manufactured in a variety of forms. The most
the point contact diode where simple is
a metal wire is pressed against a clean
surface. semiconductor

v2 (E2-E)
E
E
(a)
Fig: (a) Schematic showing the basic process
of absorption and (b) emission
This was how the early Cat's Whisker
detectors were made, and they
were found to be very unreliable, requiring
frequent repositioning of the
Wire to ensure satisfactory operation. In fact Meta
the diode that is formed
may either be a Schottky barrier diode or
a standard PN
dependent upon the way in which the wire and semiconductor junction
meet and N
the resulting forming process.
Metd
Although point contact diodes were manufactured
many years later,
these diodes were also unreliable and they were
subsequently replaced
N by a technique in which metal was vacuum deposited.
One of the problems with the simple deposited
metal diode is
that breakdown effects are noticed around the edge
of the Odde
metalised area. This arises from the high electric fields
that are
present around the edge of the plate. Leakage effects are also
noticed. To overcome these problems a guard ring N
of P+
semiconductor fabricated using a diffusion process is
used along with an oxide layer
around the edge. In some instances metallic silicides may be
used in place, of the metal
A further advantage of the whole Schottky
structure is that it can be fabricated using
relatively low temperature techniques, and does
not generally need the high temperature
steps needed in impurity diffusion.

ECDV-43
 semiconductor devic
POPULAR PUBLICATIONS
a
"majority carrier" ony the n-type m
n-type,
cis
Schottky diode is is doped or the device. The jority
It is often said that the body operation on the
semiconductor normal imetal
contact
means that if the significant role in band of the no slow, tan
a conduction heretore
(mobile electrons) play T

this diode can

injected into the electrons.
camiers are quici moving so that
free
to become carriers is
involved, property in turn allo
side of the drode type diode. This
another reason why
recombination of n- and p- ordinary p-n rectifer transition. I his S the diode
conduction faster than an makes for a fasterconverters; the hign speed of allou
which also MHz,
smaller device: area, switch-mode power range 200 RHZ to 2
useful in in the be possih
Scnotky diodes are can operate at frequenciesgreater etficiency tnan would detect
neans that the circuit andcapacitors with ot RF ctors
inductors diodes are the heart
of small
he useother types.
Small-area Schottky
diode
wth to 50 GHz.
mixers, which often operate up explain how
and
VI
characteristics ow
With
degenerate
semiconductor?
from tunnel diode. WBUT 2007, 2010
3. What is resistance is obtained
differential negative OR, diagram)? Draw the
with band
degenerate semiconductor (explain explain the OCcurrence of negative
What is diode and WBUT 2016]
characteristics of a Tunnel I-V characteristics.
differential resistance in the
Answer:
band and
1" Part:
present namely Conduction band, Valence
bands are effective
In a semiconductor three electron concentration, n exceeds the
band
Forbidden band. If the conduction longer within the band gap but lies within
the
level is no
density of states, N, the Fermi is called degenerator, n type. So in
occurs, material
conduction band. When this Ec and Er is for the most part filled with
between
degenerate n type sample, the region complete
degenerate p-type, the region between Ec and Er is almost
electrons and in
filled with holes.

2nd Part: Refer to Question No.

1 of Long Answer Type Questions.
4. What are Quantum efficiency and responsivity? WBUT 2007, 2010, 2016
Answer:
Quantum eficiency is defined as ratio of radiative recombination rate to tola
recombination rate.

Mathematically, n=In=Quantum efticiency R,radiative recombination rate;

R Total recombination rate of the carrier.]
Responsivity:
It is
directly proportional to the quantum efficiency at a
particular wavelength.
Mathematically R= where n = quantum efticiency.
hv

ECDV-44
 ELECTRONIC DEVICES

5. Write the differences between avalanche breakdown and zener breakdown.

[WBUT 2008]
Answer:
Zener Breakdown
. Narrow depletion region and quantum
Avalanche Breakdown_
Higher Depletion region width and electron
mechanical tunneling takes place.
2. Highly doped diode with reverse
tunneling is negligible.
bias is| Low doped diode with reverse bias s
required.
sufficient.
3. Operates at low voltage up
to few volts Breakdown occurs at high reverse bias
reverse bias. Impact ionization does
not occur from a few volts to thousands of volts. This
in this case. Breakdown voltages decrease breakdown mechanism involves the impact
with increase in temperature. ionization of host atoms.
6. State the differences between a p-n junction diode and Schottky
diode.
WBUT 2008, 2012]
Answer:
Schottky diodes (Schottky barrier diodes, Schottky diodes) consist of a
metal layer which
contacts semiconductor element. The metal layer is heavily occupied
with conduction-
band electrons but the N type semiconductor region is liquidated. When forward-
-

biased, the higher- energy electrons in the N- region are injected into the metal
region,
where they give up their excess energy very rapidly. The metal-semiconductor
junctions
show rectifying behaviour, allows the current to pay through the structure more readily
with one polarity than the other. Most Schottky diodes are used in high
frequency
applications and fast-switching digital circuits. Those hot carrier diodes operate only
with
majority carriers. Because there are no minority carriers, there is no reverse-current
leakage as with othwer types of diodes. Moreover, unlike convensional rectifier diodes,
Schottky diodes exhibit a very rapid change in response to bia.

7. Explain how negative differential resistance (NDR) occurs in an IMPATT

diode.
WBUT 2008, 2012]
Answer:
Microwave device employing transit time effects is called impact avalanche transit
time
(IMPATT) diode.
This device consists essentially of two regions
i) The n'p region at which avalanche multiplication occurs and
ii) The i (essentially intrinsic) region through which generated holes
must drift in
moving to the p contact.
Normally the device is in n pnp' structure.
The device operates in a negative conductance mode. When the a.c. component
of current
is negative over a portion of the cycle during which the ac voltage
is positive and vice
versa. The negative conductance occurs because of two processes causing
the currTent to
lag behind the voltage in time (1) a delay due to the avalanche process and
(2) a further
delay due to the transit time of the carriers across the drift region.
If the sum of their delay times is approximately one half cycle of the operating frequency,
negative conductance occurs and the device can be used for oscilation and amplification.

ECDV-45
 POPULAR PUBLICATIONS

actually increases while he

.
Operation: through the region i
operation, the drift of holes very narrow and all the
assume that the p region is
''
nela 1s decreasing. Let us
in a thin region
near the ntpJunctlo.
Valanche multiplication takes place
Avalanche region

rift region

(a)

E(x)

(b) contiguration
Read diode (a) basic device
device under reverse bias
(b) electric field distribution in the the n'p
such that the critical field for avalanche E, is just met in space
If the de bias is
0. Electrons generated in the
charge region. Avalanche multiplication begins at t=
I drift region. Let us assume that
avalanche move to the n' region and holes enter the.
so that an ac signal can be maintained
device is mounted in a resonant microwave circuit
at a given frequency. As the applied ac
voltage goes positive, more and more holes are
generated in the avalanche region.
The time dependence of the growth and drift of holes
during a cycle is shown in the
following figure.

Wt
K <L (a)
V

E.

W
K L
(b)

ECDV-46
 ELECTRONICDEVICES

(c)

wt

(d)
In fact holes (dotted line) generated by the multiplication process continues to grow as
long as the electric field is above Ea. It can be shown that the particle current due to
avalanche increases exponentially with time while the field is above the critical value.
The important thing to be noted is that the hole pulse reaches its peak value not
at n/2
when the voltage is maximum, but at n [Figure (c)]. Therefore there is a phase delay of
w2 inherent in the avalanche process itself. A further delay is provided by the drift
region. Once the avalanche multiplication stops (wt> T), the pulse of holes simply drifts
towards the p contact (Figure (d). But during this period, the ac terminal voitage is
negative. Therefore the dynamic conductance is negative and energy is supplied to ac
field.

8. a) Define step graded junction and linearity graded junction.

b) Define diffusion capacitance and transition capacitance. WBUT 2010, 2016]
Answer:
a) Step graded junction:
A p-n junction can be step-graded or linearly graded. In a step-graded or abrupt p-n
junction, the acceptor and the donor concentrations in the semiconductor are constants up
to the junction. To produce this kind of junctions, a small pellet
of a trivalent impurity
ike aluminium is placed on a wafer of n-type silicon and the system is heated to a high
temperature for a short period. Aluminium dissolves in silicon in the process, so that over
a portion silicon changes from n-type to p-type. A p-n junction is thus formed.
Linearity graded junction:
a
In linearly-graded junction, the impurity concentration varies almost linearly with
distance from the junction. This kind of junctions can be obtained by drawing a single
crystal from a melt of silicon containing the impurity of one type at the beginning. As the

ECDV-47
 chanoe
POPULARPUBLICATIiONS controlled rate to ange the
is added at a
other type
purity of the
crystal is drawn, the capacitance comes int
semiconductor type. junction a
the junction is
forward bias potential barrier at
Diffusion capacitance For a direction the electrons from n side de move into
b) (i) forward
play.Since the bias is in
the
n side.
Similarly
excess hole density falls ofr
SIde enter the takes place and increamental capacitance is
lowered and holes from p
i.e.,minority carrier injectionjunction. Thus an charge with applied
the p side, rom the injected
exponentially with distance of
of changestorage,capacitance.
as the rate
introduced which is define
called the
diffusion,or
space charge regiona around a p-n
capacitance Cp is Capacitance: The in the n side
and immobile
ge.Ihis Depletion Layer
(i) Transition or immobile positively charged
donor ions
junction.Also,the application ofa
the regtion. This voltape
junction consists of ions in the p side of space charge
acceptor
negatively charged increases the width of the from each other, endows the
reverse bias to a pn junction charges,spatially separated or depletion layer
aependent positive and negative transition,space-charge
with a capacitance termed as
pn Junction
capacitance. impurity
expression for it involving
potential? Derive an WBUT 2011]
9. What is contact structure.
concentration on either.side of the into
Answer: a potential barrier when it tries to move
n region see
Electrons in conduction band of termed as built in potential
region. This potential barrier is
conduction band ofp
barrier.
Mathematically, built in potential, V =®pn +Pp
electron concentration in conduction band, n, = N,
expl E2|
In n region, Kt
where n, = Íntrinsic carrier concentration
, E-Ep
ePKTE=Infinite Fermienergy
.e, = E,,-E

n", eAPKT
= tm Nd seting n, = N,
e

For Pregion, P = N, =n,F exp

L KT

ECDV-48
 ELECTRONICDEVICES

So built in potential, , =
t n,v
=V,en Na|
n,v
Where
V==|A = Thermal voltage.

10. What is contact potential?

Derive an expression for it. A Si p-n junction diode
with doping concentration in p
and n-regions 10"cm and 5x10"cm respectively
is in equilibrium.
Calculate the contact potential for the junction
at room temperature. [WBUT 2013]
Anwer:
E, in the neutral n material and a constant E, in the neutral p material
and a potential
difference V, = (E, -E,)
between the two. This potential is called contact potential.
The contact potential separates
the bands. The valence and conduction bands are higher
on the p side of the junction than on
the n-side by the amount q V, doping concentration in
p and n-regions 10' cm and
5x10 cm respectively is in equilibrium.
N =10"/cm, N, =10"/cm
Contact Potential, V,
=In
k=1.38x10-3 J/k; q=1.6x10"c
n, =1.5x10°/cm; T =300K
=36 *10x 300, 10 x10!5
= 0.0694 eV
1.6x101 2.25x 1020
11. What is Depletion Capacitance? Establish a mathematical relation of the
depletion capacitance.
Answer: WBUT 2018]
Refer to Question No. 10(b)
of Long Answer Type Questions.
Long Answer Type Questions
1.What is a tunnel diode? Draw the volt-ampere
explain the occurrence of the negative differential
characteristic of such a diode and
Briefly describe transferred electron effect. resistance in the characteristic.
Mention some. uses of tunnel diode.
[WBUT 2006]
OR,
With the help of energy band diagram, explain the 1-V characteristics of a tunnel
diode.
WBUT 2011]

ECDV49
 POPULAR PUBLICATIONS
hig in both
impurity atom isis very high
Answer concentration of depletion region width of the DP-n
a p-n junction diode when the
In junction is abrupt, the
n-region and the
and
junction is very small(= 10nm). the diode shows a
negatiye slope when
quantum
current-voltage characteristics of slope can be explained using
pical
ne forward bias is increased.
This negative
termed as tunnel
diode.
the diode is
Cchanism tunneling and hence

D Negative slope

Foreward voltage

O operation of Tunnel diode

Fig: Forward bias
diode is
The circuit symbol of Tunnel
very fast operation
semiconductor diode which is capable of
Tunnel diode is a type of
effects.
uses quantum mechanical L
The equivalent circuit is,
R

Where -Ra= Negative resistance

R Series ohmic resistance
L Inductance
C-Junction capacitance
diode for various biasing conditions
I-V charucteristies of Tunnel
The current voltage characteristics of
tunnc diode for various biasing conditions like (a
small reverse bias (c) small forward bias and d) increased forward bias are
zero bias (b)
shown below.

a) Zero bias:
(EF) is constant across the junction at ther
When there is no bias, the Femi level
equilibrium and hence no current can flow across the junction as shown in figure (a

ECDV-50
 ELECTRONICDEVICES

a) Zero bias
b) Reverse Bias:
When reverse bias is applied,
the Fermi livel in the p-side
goes up relative to that in
the n-side. There are then some
energy states in the valance band
of p-side that are at the
same level as the allowed empty
states in the conduction
band of n-side to the n-side, giving
rise to reverse diode
current. The I-V curve stands to full from
zero current b) For small reverse bias
directly as shown in the figure (b).

c)Small Forward Bias:

When forward bias is applied across the diode,
the Fermi
level in the n-side goes upwards relative to that in 'the
n-
side so, there are some energy states in the conduction
N
band in the n-side which are at the same level as
the
allowed empty state in the valance band of p-side. Hence
electrons will tunnel from n-side to p-side, giving rise to
forward current as shown in figure (c). c) For small forward bias

d) Increased Forward Bias:

When forward bias in increased, tunnel current
increase since more available entry states are exposed
to the electrons. The tunnel current attain maximum
when the conduction band edge of n-side is in line
width the Fermi level in the p-side. Then
current d)
shunts falling as shown in figure (d). Increased forward bias

Energy bamd diagram of Tunnel diode

The following figure shows Energy-band diagram as well
as V-I Characteristics of
Tunnel diode of different biasing conditions.

ECDV-51
 POPULAR PUBLICATIONS

condition
forward bias
condition b) A slight
a) Zero bias

=
less
in which d) A higher forward bias with
condition
c)A forward bias tunneling current
transit curTent occur

e)Forward bias with higher value in

which dominating diffusion current

The fig. a clearly depicts that under zero bias, practically nocurrant flow in the diour
when slightly forward bias is being applied a small tunneling current flows in it.
takes
If forward bias voltage is slightly larger than maximum tunneling current flow ta
place because in this case, maximum number of electrons in eto
n region will be oppo
maximum number of empty states in f region.

ECDV-52
 ELECTRONIC DEVICES
With further inerease in forward
bias voltage,
it the number
ot electrons on n side will be tunneling current will decrease because in
Finally tunneling current will directly opposite empty states on P side.
be zero because there are no electrons
directly opposite to available on the n side is
The current voltage
empty states on p side.
characteristics of tunnel diode is
shown below

(a)

(c)
(b) (d) (e)
Some uses of tunnel diode-
i) They are used in low power
amplitiers.
ii) DLVA
iii) Microwave and RF power
moniters.
iv) High frequency triggers.
v) Zero bias detectors.
vi) Since they are more resistant
to nuclear radiation,tunnel diodes are used
applications like amplifiers for satellite communication. in space

2. a) Explain the working principle of a Zener

voltage device. diode and its use as a reference
b) What is the difference between step [WBUT 2007, 2016]
graded and linearly graded semiconductor
PN junction?
c) Define Diffusion capacitance and WBUT 2007, 2016, 2018]
Storage capacitance in PN junction.
Answer: WBUT 2007, 2016]
a) A zener diode is a silicon PN junction device, operated
in reverse breakdown region.
The equivalent circuit (shown below) shows
that a zener diode is equivalent to a battery
with voltage, V, in series with a resistance
r, called zener resistance. The zener resistance
is known as dynamic resistance or ac
resistance

Fig: zener diode and its equivalent circuit

ECDV-53
POPULAR PUBLICATIONS
shown below.
cteristics ofa zener diode is
The reverse-biased characte
Reverse bias with
Vz

cuTent

reverse voltage is increased reverse

figure, it is not much clear that, as the breakdown proces
From the
knee of the curve. At that point,
current is negligibly small up to essentially constant from the bottom of
the knee
stops. The breakdown voltage remains constant voltae
called regulating ability. Zener diode maintains a
This ability of diode is zener current.
across is terminals area over a range special of

Zener diode as voltage regulator

diode of a voltage regulator.
The following figure describes zener
S Rs

V(Regulator voltage)
Nz

Unregulated s
voltage

Fig zener diode ad voltage regulator

The input current, I, =

z

Where Vs =d.c input voltage to the regulator circuit

V, = zener voltage.
Voltage across zener diode terminals,

=Vz {,r,isnegligible)
Input current, Is = lz +I, or /2 = 1, -1

ECDV-54
 ELECTRONIC DEVICES
b) Linearly graded PN Junction
A PN Junction in which doping
concentration on either side of the metallurgical Junction
are approximated by a linear distribution
is called linearly graded PN Jn.
Step graded PN Junction
A uniformly doped PN Junction
in which one region of a semiconductor
doped with acceptor impurities is uniformly
and adjacent region is uniformly doped
impurities. The graded region can with donor
be describe by N, N, = G, where G =
which gives slope of the net impurity
-

grade constant
distribution.
c) The capacitance of a forward-biased
P-N junction due to minority carrier storage efect
is called Diffusion capacitance.
The excess minority carrier concentrations
at space charge edge generates capacitance-
known as Storage capacitance.

3. Prove that if donor ion concentration

is negligible compare
concentration then width of the
junction become w
to acceptor ion
={2eV/qNg]"",
with cross-sectional area A=0.001 A Si junction
cm' is formed with NA=10°Icm and No=10 "Icm.
Calculate contact potential and space
charge region width equilibrium
[es 11.8ed. WBUT
Answer: 2007
Electric field in space charge region is
detemined form Poisson's equation.
So we have dE J)2
dx
e(x)= space charge volume density
e Permittivity of semiconductor
. E = ds= eN
+C.[C=Integration constant
s
At space choose edge on the semiconductor, E

C E- , -x) = 0

E s

Sospace choose region width, a= =25,(, +]F

VReverse -
bias voltage.

io42K
Contact potential, = KiT, 10
In N 0259in

ECDV-55
POPULAR PUBLICATIONS

-2x11.8x8.85x 10" x,
Space choose region width = 1.6x10x10
discusS Witn basic principlee
ples
a Read diode and
Draw the basic structure of
a) operation negative differentiat
the of IMPATT diode. mechanism of the bulk ial
electron WBUT 2007]
D) Explain with transferred
diode and mention its application.
conductivity exhibited by Gunn
Answer: Short Answer Type Questions
a) Refer to Question No. 7of
periodic fluctuations
JB Gunn discovered
of
named after
b) Gunn-effect diodes are
arsenide (GaAs) specimen when applied voltage
gallium
current passing through n-type device.
critical value. A Gunn diode is a transfer electron
exceeds a certain

Transfer Electron Effect: a GaAs sample, due to high field conduction

When either a field or current is applied to
high mobility valley to high energy
low
transferred from low energy
band, electrons get
to this negative differential resistance
mobility valley of the conduction band. Due
phenomenon is called Transfer Electron effect.
develops in group III V materials. This
-

light mass, high mobility sub band with an

The principle involved is to transfer carriers of
mass, low mobility, higher energy
electric field so that carriers can transfer to a heavy
sub band as shown in the figurel.

Band Diagram: Upper

valley
Lower
valley

Conduction band

Valence band

Wave no.>
Fig: 1
GUNN Diode band diagram

at lower valley electrons have low energy

but high mobility.
at upper valley > electrons have
high energy but low
mobility.

ECDV-56
 ELECTRONIC DEVICES
Ridley-Watkins-Hilsum
Theory
The basic concept of RWH
bulk solid state I-V
theory is the differential
compound when either negative resistance developed
an electric field or a current in a
terminals of the sample.
Negative resistance is applied to the
and current controlled devices are classified into
modes. There two voltage controlled
J modes are shown in the figure
2.

Voltage -controlled E
mode
Current Controlled modeE
Fig: 2 Voltage and
current controlled mode
of GUNN diode
In the voltage controlled
mode, there will be multivalued
current-controlled mode, current density whereas
voltage can be multivalued. in
Mathematically, negative
resistance is represented as
a_dJ negative resistance
dv dE =-R
Modes of Operation
Gunn diodes are operated in
the following four modes,
a) Gunn oscillation mode namely
b) Stable amplification
mode
c) LSA oscillation mode
d) Bias circuit oscillation mode.
a) Gunn oscillation mode
This mode is defined in
the region where the product
about 10' cm/s and the product of doping multiplied
of frequency multiplied by length
by length is greater than is
b) Stable amplification 10 l em.
mode
This mode is defined
in the region where the
10' cm/s. product of frequency times
length is about
c) LSA oscillation
mode
This mode is defined
in the region where product
cm/s of frequency times length is above
10'
d) Bias Circuit
oscillation mode
This mode occurs
in a region where the
Oscillation mode product of frequency times
of Gunn length is to0 small.
In Gunn diode
diode, frequency of oscillation
is given by
f=deman where
eff
m Domain Velocity, Lete
Effective length.

ECDV-57
 possible «domain modes
PuBLICATIONS electrice ficld, threc
POPULAR
with the
velocity,
varies
Since clectron drift
are possible
namely
domain mode
(10'cm/s)
Transit time 10'em/s)
a)
domain mode
(10 cm/s < f.«

b)
Delayed 10'cm/s
2x
(/.>
mode ligure 3.
c)Qucnched domain shown in the
domain modes are
Various types of
de bias
b

bias
de Quenched mode

Transit tume mode

cbias
bias

GUNN Diode
Delayed mode 3 various
Modes of
Fig:

can serve as microwave

Application of GUNN
diode operation, Gunn diodes microwave
their low voltage (few-milliwatt)
I) By vitue of for very low powered
frequency generators
amateurs in Britain
(and
transmitters. being used by some radio
In the late 1970s they were
2) consisted
presumably elsewhere). published in journals. They typically mounted
transmitters were
3) Designs for
3 inch waveguide
into which the diode was
approximately that could
be
simply of an direct current power supply
A low voltage
(less than 12 volt) The waveguide was
used to drive the diode.
modulated appropriately was other end ideally
fed
form a resonant cavity and the
blocked at one end to
parabolic dish.
4) High power Gunn
diode used in continuous wave Doppler diode.
amplitier.
5) Used in Broad band linear

5.Briefly discuss the dependency of space change with doping

concentra
curren
Develop necessary mathematical expression. Prove the forward bias WBUT 200
exp(qV/kT-1) where the symbols have their significant meaning.
Answer: hantk
In PN junction the n region contains many more electrons in the conduction band fror
P region: the built in potential barrier prevents this large density of electroi cam
lowing into the P region. The built in potential maintains equilibrium between the
distributions on either side of the junction.

ECDV-58
 We have , -14| +|0»
ELECTRONIC DEVICES

In

,
n region the electron concentration

exp,E,)|
kT
in the conduction band is given
by

or,
n7, exp EE (i)
Potential in the n region
k
as ep =
En- E
Equation (i) may then be
written as = n, exp
kT2
n,
Settling n, = N, and solving for the potential, we obtain

Similarly
P +

where v, kT
We can calculate the minority çarrier
hole diffusion current density at
relation *=x, from the

,)=-elD,
The hole diffusion current density may
be written as

,x.)-eD, ®P.()
exp
,()
The hole current density for this forward -
bias condition is in the +x direction, which is
from the p to the n region.
Similarly the electron diffusion current density at
x = -x,, this may be written as

J)-(e0.) dx

The electron current density is also in the +x direction.

ECDV-59
 POPULARPUBLICATIONS

junction is the
The total current density in the pn
eD,PaeD,".| expT
J=J,(«,)+J.(-,)-|
a junction.
It is the ideal V- I relationship of pn

We may define a paranmeter

, as eD,PeDo
+
and J=1, then we can write

junction.
Derive expression of junction capacitance for an abrupt p-n WBUT 2009]
6. a) the
b) What do you mean by hyper-abrupt junction?
Answer:
a) Diode junction capacitance in the
its I-V curve. It conducts curront
Tdeal diode is completely characterized by is the same
and no current flows in the reverse direction. lts behavior
forward direction
mechanism is charge storage in the
independent of frequency. The first charge storage
regions adjacent to the depletion
depletion region of the P-N junction and in the neutral
is capacitance. The capacitance
region. The circuit implementation of stored charge
associated with the P-N junction depletion region is called junction
capacitance and is in
is important when a
parallel with the ideal diode (Q = C V). The junction capacitance
voltage
diode is reversed biased for two reasons. The first reason is that the reverse diode
is not in general constant. The second reason is that the reverse leakage current through
a

diode is very small and thus the current through the junction capacitance can be much
larger than the reverse leakage current. The capacitance of a P-N junction is a function of
the P-N junction's reverse voltage and it decreases as the reverse voltage increases
(distance between the charge increases C= c Ald). The jünction capacitance of a
reversed biased junction as a function of the reverse bias voltage is given by

CV)=- Co (1)

Diode reverse recovery

The second charge storage mechanism at a P-N junction is charge stored in the neutral
regions adjacent to the junction. The amount
of charge stored is proportional to
forward current and the proportionality constant is called the
transit time and has the un
of seconds.

Q=1T Is| e"ki

(2)
The transit time varies from us to about 10's of ns depending
on junction processing

ECDV-60
 ELECIRONIC DEVICES
b)p-n junction capacitance:
Basicaly two types of
capacitance due to capacitance are associated
the with a junction namely i)
does the lagging behinddipole in the transition region Junction
of voltage and ii) charge storage
Junction capacitance as current charges. capacitance
capacitance is dominantis dominant under reverse bias conditions
under forward and charge storage
biasing the junction.
Graded junction: Graded
sample. Mathematically Junction occurs when the impurity possible
for graded junction spreads out into the
N
The graded junction
-

N, = Gx [where
G= grade constant
profiles for linearly
below. graded, abrupt and hyper
abrupt case are shown
N Na)

Linearly graded, m=l

Abrupt, m=0

Hyperabrupt, m=-3/2

Fig: Graded Junction profiles

For an abrupt p-n junction,
the capacitance varies with the
In a graded junction, square root of the reverse bias.
capacitance can be written as,
C, V," were reverse bias voltage, V,
>> V
For a linearly graded junction,
n =
3
when n>, junction called hyper abrupt junction.
The donor distributed, N,(«) can be represented by the expression,
N, = (x) = 6x
where Ga constant and m = 0, 1
or
.We know that n= for p; junction
m+2
So,
n=for
2
abrupt junction andn= for linearity graded junction. For
hyper abrupt
junction, n=2.

7. Explain transferred electron mechanism with the help of RWH

the conditions for the occurrence of negative differential theory. What are
resistance in GUNN
diode? Write the applications of GUNN diode. What are the different
modes of
operations for GUNN oscillator? WBUT 2009
Answer:
Refer to Question No. 4(h) of Long Answer Type Questions.

8. a) Derive the expression for the current flowing across a p-n junction.
D Define diffusion capacitance and storage capacitance in p-n junction.
(WBUT 2010]

ECDV-61
 POPULARPUBLICATIONS

Answer: is shown m
ng
a) The eltect of bias at a p-n junction

V,-Vi

EEv
Evw

Reverse bias
Equilibrium Forward bias

electrostatic potential barrier and electric ficld within the

An applied voltage charges
transition region charges.
The electrostatic potential barrier at the junction
is lowered by a forward bias from ,
For a reverse bias, the
(-V.
the equilibrium potential V, to the smaller value

potential barier becomes(%+V,).

Reverse-Bias Breakdown
A p-n junction biased in reverse direction exhibits a small, essentially voltage
independent saturation current. This will continue until a critical reverse bias is reached
for which reverse breakdown occurs. (fig).

L Forward
Curtent

Reverse
Saturation
curre
Reverse breakdown current
Fig: Reverse breakdown
in a p-n Junction
ECDV-62
 Reverse breakdown
ELECTPOCDEVICS
electric ficld in the can occur by two mechanisms, cach
junction transition of which requires a
operative at low region. The first mechanism critical
voltages. If higher called 7ener cifect 1s
avalanche breakdown. voltage breakdown occurs,
1-V relation the mechanisn 1s
of p-n junction
diode is given bclow

where
i called the ideality
nature of material. factor.
= 1
for Ge and 2 for silicon.
It determines the
b)Refer to Question
No. 2(c) ofLong
Answer TypeQuestions.
9. a) Draw the
the operation ofbasic structure of a road
IMPATT diode and discuss the
b) Explain transferred diode. basic principles of
conductivity exhibited electron mechanism of
by Gunn diode the bulk negative differential
Answer: and mention its application.
a) Refer to Question WBUT 2010]
No. 7 of Short Answer
b) Refer to Question Type Questions.
No. 4 of Long Answer
Type Questions.
10. a) With the
at the junctionhelp of energy band
between a metal and diagram, describe formation
Schottky diode is of Schottky barrier
an n-type semi-conductor.
b) Describe the faster that a p-n junction diode. Explain why a
p-n junction. Also
origin of 'diffusion capacitance'
discuss their dependence and 'depletion
on the biasing capacitance' in a
condition of the diode.
Answer:
WBUT 2011]
a) Energy Band Diagram

Er

Ev Dep-
fcgion
a) Energy-Band Diagram of metal
and b) Ideal energy-band
semiconductor before contact diagram for metal
working semiconductor
Fig (a) clearly depicts energy-band working
diagram for a particular
junction before contact. The metal and semiconductor
vacuum level is considered
function and semiconductor as a reference level. Metal
work functions are mentioned work
as and o, respectively.
ECDV-63
 Fermi level in
semiconductor
PUBLICATIONS
become
me a constar
POPULAR contact,
Fermi level conductor flow ine
is
Before make
X.
asured
measu as To
metal. electrons tfrom Femi positive vely charged
aftinity is the created by
Electron that inequilibrium,
regions are
semiconductor was above
system in
thermal
ne states in thei
lower energy
donor atoms.
Schottky
metal.

arier, ,
Space

is
charge

measuredas,
, =(-x) at Builtiin potential,
ilt
barrier has nor
metal
Mathematically
, (d, -0)
semiconductor to
can move easily flow

,
as, = semiconductor,
V is measured applied to the situation, electron situation is known
positive voltage is remain constant. In thathad been reduced. Thusbefore is known as
increases while as barrier condition mentioned are shown below.
semiconductor into the metalSimilarly the conditions
trom Condition. the above two
Bias for
as Forward Condition. Band diagrams
Keverse Bias
-- E

0 under forward bias

reverse bias ldeal energy band
ldeal energy band under function voltage of
diode because effective
than P-n Junction
Schottky diode is faster
P-n Junction diode.
Schottky diode is less than
Schottky barrier diode is a majority carrier device. t
that
Moreover it must be said is associated with a forward
biased Schottky
diffusion concentration
signifies that no
diode is a higher frequency device than ordinary P-n Junction
diode. Hence Schottky
diode.
minority carrier storage time. Hence it can be used in Fast
In Schottky diode, there no
is

Switching Applications.
currei n
b) When a p-n Junction is reverse biased by a voltage, a small reverse saturation
fows from p to n. This reverse bias causes an increase in transition layer widtn a
charge of depletion layer. As a result, the voltaye across the transition layer increases.
If p diffusion current before applying reverse bias; then after reverse biasing a ne
equilibrium condition is reached with external reverse current I equal to (ls- lp)
Is Reverse Saturation Current.
As voltage across p-n junction changes, the charge stored in
depletion layer also chaS
The above thing is depicted in fig.

ECDV-64
 ELECTRONIC DEVICES

Q-Point
Charge stored in
depletion layer

Reverse voltage, Vr

The charge stored in depletion layer is, -q, = 4.NNpAW ip

(N + Np)
where A= Junction cross section area
and WdepDepletion layer width under reverse bias

Wdep
N, N
So depletion layer capacitance, C, =- dq,
dVrv,aa
CJo
C,

where,
CA2N, +N, )V.)
If a p-n Junction is forward biased then in steady state some excess minority carrier
charge is stored in p and n bulk regions. When the applied voltage changes, this stored
charge changes to a new steady state value. This charge storage phenomenon gives rise to
capacitive effect. This type of capacitance is called as diffusion capacitance.

Mathematically, C = |

where Mean transit time, I = Diode current at bias point. V, = Volt equivalent of
temperature.

11. Describe differentbreakdown mechanisms that may occur in a reverse biased

semi-conductor p-n junction diode. WBUT 2011]
Answer:
Refer to Question No. 10(b) of Long Answer Type Questions.
12. Explain how a Zener diode works as a voltage regulator. WBUT 2012]
Answer:
Zener diodes are widely used as voltage references and as shunt regulators to regulate
the
voltage across small circuits. When connected in parallel with a variable voltage source
ECDV-65
POIPULAR PUBLICATIONS aches the
voltage reaches the diode's
the
conducts when low impedadance of the liode
zener diode relatively
biased, a on, the
so that it is reverse
s rever
From that point
reverse breakdown voltage. diode at that vaiuc.
the
Kee s the voltage across

u
voltage, Un.N. is regulated
regulator, anO input
voltag
reference or voltage of diode D is stablable over a
In this circuit, a typical
UouT. The breakdown
the input voltage ma
dow n to a stable output
voltage even though
UouT relatively constant impedance of the diode
when
range and holds low
wId current a fairly wide range. Because of the circuit.
Tluctuate over limit current through the determined using
used to
ope ated like this. resistor R is flowing in the diode is
reference, the current
in the case of this simple across the resistor R;
the known voltage drop
Ohris law and Diode(U -UouT)/ Ra
conditions: reverse breakdown.
The value of R must satisfy two through D keeps D in
that the current
1. Rmust be small enough data sheet for D. For example, the
common
is given in the
The value of this current diode, has a recommended reverse current
BZX79C5V6 device, a 5.6 V 0.5 W zener Will be unregulated, and
insufficient current exists through D, then UouT
of mA. f
S
voltage (this differs to voltage regulator
tubes
less than.the nominal breakdown
voltage will be higher than nominal and could rise as high as UN).
where the output
any current through the external
When calculating R, allowance must be made for
load, not shown in this diagram, connected across Uou
enough that the current through D does not destroy the device. If
the
2 R
must be large
Va and its maximum power dissipation
current through D is Ip. its breakdown voltage
PMAN, then ,Y, < Phaw

A kad may be placed across the diode in this reference circuit, and as long as the zener
stays in reverse breakdown, the diode will provide a stable voltage source to the load.
Zener diodes in this configuration are often used as stable references for more advanced
voltige regulator circuits.
Shu it regulators are simple, but the requirements that the ballast resistor
be small enough
to avoid excessive voltage drop during worst-case operation (low
input voltage
concurrent with high load current) tends to leave a lot
of current flowing in the diooe
much of the time, making for a fairly wasteful regulator
with high quiescent pow
diss pation, only suitable for smaller loads.
These devices are also encountered, typically in
series with a base-emitter junction,
transistor stages where selective choice
of a device centered around "
zener point can be used to introduce the avalanche
compensating temperature
the transistor PN junction. An example co-efficient balancing
of this kind: of use would
amplifier used in a regulated power
supply circuit be a D e
feedback loop system.

ECDV-66
 ELECTRONICDEVICESs
13. a) Explain the working
principle of Zener Diode & its use as a reference voltage
device.
b) Calculate the ideality factor
(7) of a diode if the diode current increases from
0.40 mA to 10 mA when the
applied voltage increases from 0.38 V to 0.48 V at 300K.
Answer: WBUT 2013]
a) Refer to Question No. 12
of Long Answer Type Questions.
b) I-1(-1)
J=J,(e"hRT 1)
of, e'n kT=.
eV
PKT = log.
-2.3031os
nT
Ve
7-2.303log. 0.48
00532.3lo8. (26) = 0.5830
0.0253

14. a)
Prove that for an abrupt p-n junction transition
capacitance C, is proportional
to (V -V)3, where V, is the inbuilt potential
and V is applied potential.
b) The depletion layer capacitance
of a p-n junction under reverse bias
5.0 pF. If the built in voltage of the (-1.0V is
junction is 0.9V, calculate the junction
capacitance under 0.5V forward bias condition.
Answer: WBUT 2013]

a) The expression for C

The transition region width,

w. 24,NM equilibrium]
N,N,
The proper expression for transition region is

w- 2(,-) N,+N (with bias)

The value of Q is, Q = qAxN, =qAx,N,

N,
N +N,

ECDV-67
 POPULARPUBLICATIONS

N
*(N, +N,)
al xare
individual width. N, N
(NN W=A| 246 N, +N,
So charge on each side
of dipolar. = 44 N, + N,

4 24 NN
N, +N,|
Sojunction capacitance, a-2-V) to (%-V)
variable capacitance is proportional
So C, voltage
=5PF;K =0.9V;V,
=0.5; C, =?
b) V =-IV; Cp

C-2q
C2-(-V.)
NNp=10.89
N, +Np
PF

operation of a tunnel diode. Draw the l-yv

15. a) Describe briefly the
principle of
region.
characteristics and mention the -ve resistance
b) What is Thermal runway? WBUT 2013, 2017]
c) What is Photo Transistor?
Answer:
1 of Long Answer Type Questions.
a) Refer to Question No.
where an increase in temperature changes
the
b) Thermal runaway refers to a situation
conditions in a way that causes a further increase in
temperature, often leading to a
feedback.
destructive result. It is a kind of uncontrolled positive

c) Like diodes, all transistors are light-sensitive. Phototransistors

are designed specifically to take advantage of this fact. The
most-common variant is an NPN bipolar transistor with an
exposed base region. Here, light striking the base replaces what
would ordinarily be voltage applied to the base so, a
phototransistor amplifies variations in the light striking it. Note E
that phototransistors may or may not have a base lead if they do,
the base lead allows you to bias the phototransistors light response.

16. Describe the basic structure of Schottky diode

high frequency operation. and explain why it is suitable ro
Answer: WBUT 2013, 201
Refer to Question No. 17(b) Long
of Answer Type Questions5.

ECDV-68
 ELECTRONIC DEVICES
17. a) What is heterojunction?
b) Explain the carrier flow in WBUT 2014, 2017]
reverse bias condition. metal-n-type Schottky diode under forward bias and
c) What are the differences WBUT 2014]
between Ohmic contact and Schottky contact?
[WBUT 2014, 20171
Answer:
a) A heterojunction is the interface
that occurs between two layers or regions or
dissimilar crystalline semiconductors.
These semiconducting materials have unequal
band gaps as opposed to a homojunction. It
is often advantageous to engineer the
electronic energy bands in many solid state device
applications including semiconductor
lasers, solar cells and transistors. The combination
a device is called a heterostructure
of multiple heterojunctions together in
although the two terms are commonly used
interchangeably. The requirement that each material be
a semiconductor with unequal
band gaps is somewhat loose especially
on small length scals where electronic
properties depend on spatial properties.
Conduction Band (CB) -

Valence Band (VB)

Stradding Gap Staggered Gap Broken Gap
(type I) (type 1I) e

Ilm)

Fig: Three types of hecterojunction

b) Metal-to-semiconductor contacts are of great importance since they

are present in
every semiconductor device. They can behave either as a Schottky barrier or as
an ohmic
contact dependent on the characteristics of the interface.
The primary characteristics of a Schottky barrier is the Schottky barrier height,
denoted
by DB. The value of DB depends on the combination of metal and semiconductor.
The
barrier between a metal and semiconductor is naively predicted by the Schottky-Mott
rule
to be proportional to the difference of the metal-vacuum work function
and the
semiconductor-vacuum electron affinity. In practice, however, most metal-semiconductor
interfaces do not follow this rule to the predicted degree. Instead, the chemical
terminationof the semiconductor crystal against a metal creates electron states within its
band gap. The nature of these metal-induced gap states and their occupation by electrons
tends to pin the center of the band gap to the Fermi level, an effect known as Fermi level
pinning. Thus the heights of the Schottky barriers in metal-semiconductor contacts often
show little dependence on the value of the semiconductor or metal work functions, in
strong contrast to the Schottky-Mott rule. Different semiconductors exhibit this Fermi
level pinning to the different degrees, but a technological consequence is that ohmic
contacts are usually difficult to form in important semiconductors such as silicon and
gallium arsenide. Non-ohmic contacts present a parasitic resistance to current flow that
consumes energy and lowers device performance.

ECDV-69
 POPULAR PUBLICATIONS tor its recti.
junction, used a low forw
metal-semiconductor when
single suitable kind of dide Also, becaus
because of
A Schottky diode is a most power supply.
often the DC
diodes can chieve greater
achi
properties. Schotky diodes are high
efficiency
hioh
Schottky
appropriate to rectify
in a
voltage drop is desired, such as mechanism,
conduction making them
tncir majority-carrier diodes,
switching speeds than p-n p- junction Figure. It consists of a netal
men
in
junction is showncontact, that
frequency signals. a contact such
metal-semiconductor
The structure of a ideal Ohmic
emiconductor. An semiconductor, made to the other side of the
is
contacting a piece of the and curTent is also shown in
metal and applied voltage
potential exists between the the
The sign
onvention of Ohmic
semiconductor. semiconductor
/contact
Figure. metal

cathode
anode

n-type

Xd

() convention of a
sign
Fig: Structure and
metal-semiconductor junction
carriers.
junction is mainly due to majority
metal-semiconductor from the semiconductor
The current across a mechanisms exist: diffusion of carriers
Three distinctly different across the Schottky barrier and quantum-
emission of carriers the driving
into the metal, thermionic
barrier. The diffusion theory assumes that
mechanical tunneling through
the
depletion layer. The thermionic emission theory
over the length of the those, which have an
energy
force is distributed energetic carriers,
postulates that only interface,
on the other hand conduction band energy at the metal-semiconductor takes
the
equal to or larger than Quantum-mechanical tunneling through the barrier
flow. through thin
contribute to the current allowing them to penetrate
wave-nature of the electrons, exist.
into account the a combination of all three mechanisms could
junction, making it the dominant
barriers. In a given only one limits the current,
that
However, typically one finds
current mechanism. emission currents can be written
in
diffusion and thermionic
reveals that the
The analysis
the following form:

J, = qN, exp

ECDV-70
 ELECTRONIC DEVICES
This expression states that the
current is the product of the electronic charge, 9. a
velocity, V, and the density
of available carriers in the semiconductor located next to the
interface. The velocity equals the mobility
multiplied with the field at the interface for the
diffusion current and the Richardson
velocity for the thermionic emission current. T he
minus one term ensures that the
current is zero if no voltage is upplied as in thermal
equilibrium any motion of carriers is
balanced by a motion of carriers in the opposite
direction.
Diffusion current
This analysis assumes that the
depletion layer is large compared to the mean free path, so
that the concepts of drift and diffusion
are valid. The resulting current density equals:
J, =TDN244-V,)N4exD
The current therefore depends
exponentially on the applied voltage, V,, and the barrier
height, fB. The prefactor can more easily
be understood if one rewrites it as a function of
the electric field at the metal-semiconductor
interface, max:
max 246-V.N
Yielding:

, =94, N, exp
So that the prefactor equals the drift current
at the metal-semiconductor interface, which
for zero
Thermionic emission
The thermionic emission theory assumes that electrons,
which have an energy larger than
the top of the barrier, will cross the barrier provided they move towards
the barrier. The
actual shape of the barrier is hereby ignored. The current can be expressed
as:
ASATe»(e",-1)
where is the Richardson constant and fB is the Schottky barrier height.
The expression for the current due to thermionic emission can also be written as
a
function of the average velocity with which the electrons at the interface approach the
barrier. This velocity is referred to as the Richardson velocity given by:

VR2m
So that the current density becomes:

,qVN, exp

Tunneling
The tunneling current is obtained from the product of the carrier charge, velocity and
density. The velocity equals the Richardson velocity, the velocity with which on average

ECDV-71
 POPULARPUBLICATIONS
density equals
the density of
of available
carrier
The probability, Q, yielding:
the carriers the barrier.
electrons n. r multiplied withthe tunneling
J qvne obtained rom:
Where the tunneling probability is

=exp
fa, to
-
and the electric field equals fp/L. exponentially on the barrier
height, fB. to the
the 3n
current therefore depends
nneling
power.
no potential exists
between the metal
Ohmic contact, a contact such that
ocal
Semiconductor, is made to the other side of the semiconductor.
An ohmic contaet
line
between two conductors that has a ear
HO-rectiying junction: an electrical junction
resistance onmic contacts are used
current-voltage (1-V) curve as with Ohm's law. Low Ised
with0
to allow charge to flow easily in both directions between the two conductors,
to voltage thresholds.
locking due to rectification or excess power dissipation due a
Dy Contrast, a junction or contact that does not demonstrate linear 1-V curve is called
non-ohmic.
A Schotky barrier refers to a metal-semiconductor contact having a large barrier height
(i.e. 4, > kT) and low doping concentration that is less than the density of states in the
conduction band or valence band. It is a rectifying contact.

18. a) Derive expressions for Built-in potential.

WBUT 2015
Answer:
The built-in potential in semiconductor equals the potential
region in thermal equilibrium. Since thermal equilibrium across the depletion
constant throughout the p-n diode, the internal
implies that the fermi energy is
between the fermi energies of each region. potential must equal the difference
,In
=V,n+, n
b) Define the diffusion capacitance
of p-n junction
diode and derive
Answer:
its expression.
[WBUT 2015]
the expression for the capacitance
space-charge region, across the junction,
respectively. For and the variation
junctions, which are
approximated closely
this we will
consider two
of the field in n
junction, which results in practice. types of ideali
from the alloying technique, These are (i) the abrupt or s
results from the crystal-growing
technique. and (i) the
Abrupt junction graded junction, hich
hown in
Fig 1(b) is the charge
the p-side and the n-side density of
ofthe transition a step junction under on
region close the assumption t

ECDV-72
to the junction,
the charge i
 ELECIRONICDEVICEs
a e, ani eNa resctively.
For simplicity, the actual charge density is idealized as

ohane density

(6)

dealized net
hange density

(c)
Electrostatic
hole potential

(d)

Bectric field (e)

max

Fig: The profiles of charge density, potential,

and electric
field in an abrupt junction
Assuming one-dimensional geometry, the
Poisson equation in the depletion region is
given by

-(N-N) .(1)
where & and p are the semiconductor dielectric permittivity
and the volume charge
density respectively. For x, <x <0, Eq. (1) can be written as

2)
Integrating Eq. (2), we get

E
.(3)
The boundary condition restricts us that at r = *p, Eo = 0 which implies the
assumption
that the voitage drops in the bulk of the semiconductor are negligible. Thus, substitut
ing C, = x,eN./c in Eq. G) yields

ECDV-73
POPULAR PUBLICATIONS

.(4)
dV eN,
slope
-E dx
(+x,) is a linear plot with a negative
distance

,
that the electric field versus
mt oS
Integrating Eq. (4) gives (S)
* since the choice of the reference for
as shown in Fig. 1(d),
WeCmay choose V = atx = 0 0
Hence, Eq. (5) can be wntten as
the potential is arbitrary.
(6)
V-eN
*p Eq. (6) is
Atx
--eN,
=
(7)
V 26
Similarly, at x =X»
(8)
2
Thus, the total voltage Vr is given by
(9)
the
difference
is the between the contact potential and
It may be noted that in
Eq. (9). V negative
total space-charge neutrality requires that the positive and

where A is the
,
applied voltage. The
charge-density areas must be equal.
=eAN = eAN,x,
junction area.
Mathematically, we can write
. (10)
Hence, Eq. (9) can be expressed in terms of
cither x, or x,

(11)

depletion region widths in the p-1ype and n-type are

Thus, from Eq. (11) the

2 N .. (12a)
eN, N, +N.)

26 VN, . (126)
N, N,
*eNcan be determined from the Eq. (4):
+

The maximum field

Bo
dV eN_eN (13)
dx

ECDV-74
 BLECTRONICDEVICES
Since there is a voltage-dependent
charge associated with the depletion region, tHis
indicates the existence of a junction
defined as:
capacitance, C, The C, can be mathematucatiy

C, dQ ds,
dv dx, dv (14)
But from Eq. (10)
d, dv

dQ
= eANa
d (15)
And from Eq. (12a)

2N,V
dv,
Hence, the junction capacitance is
given by
-
2 eN.(N, + N.)J eN,(N, +N)
2&N
.(16)

+Na) .(17)
The expression for capacitance
derived above is referred
also known as junction or space-charge capacitanceto as the transition capacitance
reverse-biased junction. It should be and exists primarily at the
noted that physics of transition capacitance
diode is totally different from that of a
of the well known parallel plate capacitor
electrical science despite their striking similarity. of basic

The junction capacitance is proportional

to V3 in the step-junction case, while
it is
proportional to V in the graded-junction case. The voltage-variable-capacitance
property of the p-n junction is utilized to maximum
advantage in several practical
applications. One such application is as a voltage-tunea
element in resonant circuits;
other applications are in the field-effect transistor.
The nonlinear voltage dependence
the junction capacitance also finds application in of
harmonic generation and in parametric
amplification. A p-n junction designed for use as a
voltage-variable-capacitance is
called a varactor, or sometimes a varicap. The capacitance versus
voltage curve of a
typical p-n junction is shown in Fig. 2.

ECDV-75
 POPULARPUBLICATIONS

(pE)

300

200

100

-S -10-12-14-16

Applied reverse voltageV

function of the applied
Fig. 2: Plot of the junction capacitance as a
reverse potential for the abrupt p-n junction
cm and N, = 8x 10
C For a silicon one-sided abrupt junction with N = 2x10"
4V (T
Gmcalculate the junction capacitance at zero bias and rovorsed blas of 2015] WBUT
300K)
Answer:
Inbuilt potential for the junction, "r im{4p)=0.026 x 34.1 = 0.889
N cm
For Silicon the value of intrinsic concentration n, at 300K has been taken as 1.5x10"
In general expression for junction capacitance

C 4
where 6 Permittivity of the Silicon
=
A = Junction Area
W Depletion Width
C" = (1)
So, Capacitance per unit area

The depletion width can be expressed as

W=2%+V)N, +N,) *
eNN
According to problem N, >> Np, therefore W can be approximated for this one sided
1/2

abrupt junction as
=26,+V)
eN
So, from Eqn. (1) the junction capacitance for one-sided junction can be expressed a
/2
C
etyN
2(+V.) (2)

ECDV-76
 ELECTRONIC DEVICES

From Eqn. (2) zero bias condition

C (16x10")(11.8»8854x108x10 ) /2
C2) 2(0.889)
2.74x10 F/m
The Junction capacitance with 4
volt reverse is
e6,Np 6x10(18x8854xl0 *)(8x10")|
2(0.889+4) =1.17x 10 F/m2

19. Explain working principle of

Answer:
Schottky Diode. WBUT 2015]
Refer 1o Question No. 17(b) of Long
Answer Type Questions.
20. With the help of energy
band diagram,
diode. What do you mean by negative explain the l-V characteristics of a tunnel
tunnelin9 phenomena? Mention any two resistance? What are the conditions for
can be used as oscillator. Justify. applications of tunnel diode. Tunnel diode
Answer: WBUT 20181
1", 2nd, 3r, 4th Part: Refer to Question No.
1of Long Answer Type Questions.
sth Part:
The tunnel diode helps in generating a very
high frequency signal of nearly 10GHz. A
practical tunnel diode circuit may consist
of a switch S, a resistor R and a supply source
V, connected to a tank circuit through
a tunnel diode D.
Working:
The value of resistor selected should be in such way
a that it biases the tunnel diode in the
midway of the negative resistance region. The
figure below shows the practical tunnel
diode oscillator circuit.
Tank circuit
Ri *~--

V out

In this circuit, the resistor R sets proper biasing for

T
the diode and the resistor R2 sets
proper current level for the tank circuit. The
parallel combination of resistor R, inductor
L and
capacitor C form a tank circuit, which resonates at the selected frequency.
When the switch S is clgsed, the circuit current
rises immediately towards the constant
Value, whose value is determined by the
value of resistor R and the diode resistance.
1owever, as the voltage drop across the tunnel diode Vp exceeds
Vp, the
the peak-point voltage
tunnel diode is driven into negative resistance region.

ECDV-77
 OPULAR PUBLICATIONS
voltageVp becomes equal he
till the voltage Vpdrives the
starts decreasing. increase in the
current tends to inc.de
In this region, the curme
point, a further circuit
voltage this
Ey point V,. At
into positive resistance region. As a result of
this, the
across the resistor R which will
voltage drop
This increase in circu will increase the
reduce the voltage VD

21. Write short notes on the following wBUT 2006, 2010, 2014, 2012
WBUT 2007
a) Schottky Barrier Diode
b) IMPATT diode
:
WBUT 2007, 2009, 2015, 2016
c) Tunnel Diode WBUT 2007, 2010, 2014
2017
d) Voltage regulator circuit WBUT 2008, 2010, 2014,
e)Varactor diode WBUT 2009
) Ohmic contact WBUT 2011]
g) Gunn diode WBUT 2014]
h) Avalanche and Zener mechanisms WBUT 2016
i) Diode Switching [WBUT 2016
i) TRIAC WBUT 2016
k)Diode Capacitance
Answer:
a) Schottky Barrier Diode:
A Schottkey diode or contact is a metal
semiconductor diode or contact having similar
metal is deposited directly on the
characteristic to a p-n junction. When the
fabrication structure is
semiconductor surface that produces the schottkey contact. The
Metal (Al or Au)
shown below.

n-type
semiconductor
Fig: Schottky contact
The direct metal-senmiconductor contact produces a contact potential barrier known as
Schottky barrier. This barrier produces the rectifying behavior. Thus the Schottky barrier
diode is designed.
A metal-semiconductor rectifying contact has the current-voltage characteristic similar to
apn junction diode. A rectifying metal-semiconductor contact is referred to as a Schottky
diode
If aluminium which is an acceptor impurity in silicon, is attached to n-type silicon as a
lead, the n-region near the surface where aluminium is deposited
must made by highly
ype (ie n') to achieve an ohomic contact If aluminium is directly
deposited on n-type
silicon, a rectifying contact is obtained. In Fig: (a), the
contact A is rectifying and the
contact B is ahmic, Producing a Schotky diode where the contact
A is the anode.
The circuit symbol ofa Schottky diode is shown in Fig
(b). The current transport in ue
Schottky diode is determined by electrons, s0 that
this diode is a majority carrier
Such diodes can be incorporaled easily in integrated devi
circuits.

ECDV-78
 ELECIRONICDEV CES

(a)
Fig: (a) A Schottky (b)
diode (b) its círcuit symbol
b) IMPATT diode:
Refer to Question
No. 7 of Short
Answer Type Questions
Advantages and disadvantages
of IMPATT Diode:
They operate at frequencies
between about 3 and 100
their high power capability.
power radar systems
These diodes are used GHz or more. A main advantage is
to alarms. A major in a variety of applications from
level of phase noise drawback of using IMPATT diodes low
they generate. This is the liigh
these diodes make excellent results from the avalanche process.
microwave generators for Nevertheless
many applications.
Tunnel Diode: Refer to Question No. 1 of Long Answer Type Questions.
d) Voltage regulator
circuit:
Voltage regulator
The following figure describes
zener diode of a voltage regulator.
Rs

VL(Regulator voltage)

Unregulated Vs
voltage

Fig: zener diode ad voltage regulator

The input
current, I, =sk
Where Vs
=d.c input voltage to the regulator circuit V, = zener voltage.
Voltage across
zener diodeterminals, V, =V2
+I,d
=Vis
i=V,/R
negligible)

nputcurrent, Is = 1, +l, or I2 =/s

-l
ECDV-79
POPULARPUBLICATIONS
or. Basicaly it is a
capacitor.
e) Varactor diode: dependent, variable
voltage sed on its transition
Varactor diode is a semicor operation is
mode of
reverse biased junction diod where by, T where
capacitance is given
Mathematically, the junction W is the
tance. area of P-N Junction, e
material, A is the
vity of the semiconductor region increased that
width of space- charge region. space charge
reverse bias potential, width of transition capacitance, C
n the increase of reverse bias, the
terms of
s ransition capacitance, CT. In
K
is given by, C V, +Vy
where K= constant
temperature,
V = Volt equivalent
and
V=Reverse bias applied in volts,
diffusedjunctions].
alloyed junction)
tor
The schematic symbol and
a simple equivalent
3

circuit for a varactor diode

is shown in fig.
are given in

capacitance with reverse bias voltage

ig. The variation of

s
Equivalent circuit

Symbol mechanically
possessing voltage-controlled capacitance have replaced
Varactor diodes automobile radios.
capacitors in many applications such as television receivers and
tuned
an inductor gives a resonant tank
circuit. These are used
diode in parallel with
A varactor
in frequency modulator,
parametric amplifiers etc.

Reverse bias voltage

Ohmic contact: Refer to Question

No. 1() of Short Answer Type Questions.
Type Questions.
g) Gunn diode: Refer to Question No. 41) of Long Answer

ECDV-80
 ELECTRONICDEYICESS
h) Avalanche and Zener
Avalanche Breakdown mechanisms:
Avalanche breakdown occurs
region is large, an electron at higher voltages.
If the electric field E in the transition
kinetic energy entering from the
to cause an ionizing collision p side may be accelerated to high enougn
results in carrier multiplication, with the lattice. A single such
the original electron and interaction
swept to the n side of generated clectron are botn
the junction and
is avalanche since each generated hole is swept to the p side.
incoming carrier can This process
cariers. initiate the creation of a large
The band structure is
number or
shown in fig.
Ec

---
E

Eva
Zener breakdown Fig: Avalanche Breakdown
Zener effect occurs when
tunneling of electrons occur
conduction band which from p-side valence band
causes reverse current flow to n-side
Basic requirements for from n to p.
tunneling current are a
separated from a large number large number of electrons
of empty states by a narrow barrier of finite that are
the tunneling probability height. Since
depends upon barrier- width,
following figure describes doping should be high.
the above phenomenon. The
Ec

tunneling
Er -Eca
Ev
P
Evn

(a)
(6)
Fig: Zener breakdown
Given 12V zener diode, = 150S2,
R R= Ik2
Minimum zener current is
nearly zero.
Maximum zenercurrent= 20mnA
Loadcurrent I= 12V/IkQ= 12mA

ECDV-81
POPULARPUBLICATIONS
12mA
is = (12mA +0)14 x 150= 1.8V
Thu
miimum allowable total current (1) R = Va= IR = 12 x 10
TCOTCsponding voltage drop across 13.8V
VR12 + 1.8= decomes
Thus minimum value of V is, Vm
then total current (I)
i.e., 20mA
current becomes maximum
Zner
(20+12) = 32mA and VR= 32 x 10x
150=4.8V
Therefore Vmas=4.8+12 = 16.8V
is 13.8V and 16.8V.
So the operating range of the input voltage

i)Diode Switching:
reverse
Junction Diode Switching Times:
a p-n junction to steady Torward or
response of
ar we have considered the
bias. Junction diodes are used in switching
a
R

applications where it is made to carry out

A VR
transition from one bias state to another.
simple circuit for the above purpose is shown
below (fig 1).
A forward current, Ig, is initially made to flow
through the p-n junction. At time t = 0, reverse Fig 1: Circuit for diode transient
through the diode. The
current »flows function of time and the current
corresponding variation in the junction voltage as a
transient are shown in figure 2. (a) and (b).
(Voltage)
I (current) V

t
(ime) (ume)

VR

(a) (b)
Fig 2.:(a) Junction current and (b) Voltage variation
with time for a p-n junction
) TRIAC
Triac is a three terminal device that can conduct in either direction when triggered eithe
by a positive or negative pulse irrespective of polarity of the voltage across its ma
Lerminals.
Behaviour of triac is nothing both two SCR°s connected in paraliel but in opposit
directions with a common gale terminal. Symbol and equivalent circuits are show
below

ECDV-82
 ELECTRONICDEVICES
MT2 MT2

A SCRI
Z SCR2

G
-
MTI
Symbol

Fig: 1
MTI
Operations of Triac Equivalent circuit
Four modes of operation,
gate terminals are
depending upon polarity
possible in Triac namely of voltage across main terminals and
a) MT2 is positive
and G is positive
b) MT2 is negative
and G is positive
c) MT2 is positive and G
is negative
d) Both MT2 and G is
negative
V-I Characteristics
of Triac
The relationshipbetween Triac current and voltage
depict V=I characteristics applied
of Triac variation is shown below.across its two main terminals

MT2 of gate positive

w-r-t MTI1
Current

Voltage

Voltage

Curent
MT2 of gate negative
W-r-t MT
Fig 2: V-I Characteristics of Triac
Applications
Tiac is applicable for the following
c) Heater control
cases e.g. a) Phase control b) Motor speed
etc. control

ECDV-83
POPULARPUBLICATIONS

k) Diode Capacitance:
Iransitional
Diffusion capacitance and
divided into two group ie
Is DTuson capacitance tends anddominate the capacCitance two in
a forward

bailed pPN Junction.

bailed
PN Junction under F-B conditions,

Diffusion capacitance
.+, = T,J, +T,J, = TJ
n type silicon and
are the life time of holes in
Cdv where T, and T,

ciectrons in p type silicon respectively F = mean Transit time.

PN Junction under Revese bias
Depletion capacitance
At steady state, I = I, =1,

Depiction layer width- .+)=W

C,
Depletion capacitance C, : for abrupt J

2
N+N, JV.)

ECDV-84
 ELECTRONIC DEVICES

BIPOLAR JUNCTION TRANSISTOR

Chapter at a Glance
Introduction:
Transistor as its name implies is
a multifunction semiconductor
gain, voltage gain and signal device. It is capable of current
power gain. The basic action transistor
one terminal by applying of is control of current at
voltage across other two
Bipolar transistor is a voltage terminals of the deViCe.
controlled current source. Basically in
Junctions are connected back bipolar transistor, two pn
to back each other. It is basically a
electrons and holes are involved bipolar device as both
in current conduction.
Transistor has three terminals
namely emitter, base and collector.
common emitter, common So it may be used as
collector and common base mode.
Transistors can be operated in
three modes i.e. saturation (when
forward biased); cut off (when both both junctions are
junctions are reverse biased) and active
emitter-base junction is forward biased and mode (when
collector base junction is reverse biased).
Current Expressions: The emitter current in forward
biased mode can be written as,
Ic =lco-alg ,Where, Ico is the reverse
saturation current, Ie is the collector current
and Ig
is the emitter current. So a is
expressed as, a = - o. The quantity a represents the
total fraction of the emitter current contributed
by the carriers injected into the
reaching the collector. Since lE and le are opposite base and
as far as their signs are concerned,
always positive. Generally a lies within 0.95 to 0.995. a is
a is not a constant but varies with
the emitter current IE, the collector to base voltage VCB,
and the temperature.
Early effect: In the operating region of a transistor or for normal operation
of the transistor,
the emitter-base junction is forward-biased. So the emitter current
variation with emitter-to-
base voltage will be similar to the forward characteristic of a p-n
junction diode. An increase
in the magnitude of the collector to base voltage (VcB) causes
the emitter current to increase
for a fixed VEB. When | VcB| increases, the depletion region in
the collector-base junction
widens and reduces the base width. This is known as the early effect.

Multiple Choice Type Questions

1.
BJT is WBUT 2006, 2009]
a) a voltage controlled device b) current controlled device
a
c) a temperature controlled device d) none of these
Answer: (b)
2. In n-p-n BJT electrons are energized in WBUT 2008]
a) forward biased junction b) reverse biased junction
c) bulk region d) both the junctions
Answer: (d)

ECDV-85-
POPULARPUBLICATIONS wi
docreaelng, tho current gain
load Hno lo WBUT 2009]
mlddlo of the
movenslstor at the d) of the load ling
move the Q-point o) nowhero
a) down b) up
Answer: (¢)
WBUT 2009
4. The output voltage of a CE amplifler le
b) Invortod
a) amplified d) all of theso
o) 180 out of phaso with tho input
Answer: (a)
[WBUT 2010]
5. Thedoping lovel of omittor roglon of a translstoris
a)greator than colloctor and base reglone
b) less than collector and baso rogions
collector region
G)less than base reglon but groater than collector rogion
d) greater than base reglon but less than
Answer: (c)
WBUT 2011
6. A BJT used configuration offers
in CE
a) low input impedance and high output impedance
b) high input impedance and low output impedance
c)low input and output impedances
d) high input and output impedancos
Answer: (b)
7. A bipolarjunction transistor, when used as a switch, operates in WBUT 2011
a) out-off and active region b) active and saturation region
c) cut-off and saturation region d) all of these
Answer: (c)

for CE model
8. If WBUT 2012
hcommon 1 k.ohm, hre =
50 then for
collector model he. hfe will be
a) 1 k.ohm, 50 b) 1 k.ohm,51
c) 1/51 k.ohm, 50 d) 1/51. k.ohm, -51
Answer: (6)

9. The leakage current I flows through WBUT 2013]

a) base and emitter terminals b) emitter and collector terminals
c) base and collector terminals d) emitter, base and collector terminals
Answer: (C)

10. To turn OFF an SCR, it is necessary to reduce its current to less

WBUT 2013, 2017
a) trigger current b) holding current
c) breakover current d) none of these
Answer: (a)
ECDV-86
 ELECTRONICDEVICES
11. In a BJT, the
base region should be very narrow to minimize
a) drift current
the WBUT 2013)
c) recombination b) diffusion current
current
Answer: (c) d) tunneling current

12. A transistor
configuration with the lowest current
a) common base gain WBUT 20141
c) common collector b) common emitter
Answer: (d) d) emitter-follower

When a transistor is
13.
a) cut-off region used as switch its operation
is confined to WBUT 2015)
c) active region b) saturation region
Answer: (d) d) both (a) and (b)

14. Atransistor connected in CB

a) high input resistance configuration has
and WBUT 2015)
b) low input resistance low output resistance
and high output resistance
c) low input resistance and
low output resistance
d) high input resistance
and high output resistance
Answer: (a)

15. In case of BJT, the

base width should be narrow to minimize
a) drift current [WBUT 2017]
b) diffusion current
c) recombination current
d) tunneling current
Answer: (a)

16. Atransistor configuration having highest current gain

a) Common base [WBUT 2017
b) Common collector
c) Common emitter d) Emitter follower
Answer: (c)

17. Cut-off frequency is the frequency at which the magnitudde

a) of the CE
WBUT 2018]
current gain is unity b) Of the CB current gain is
unity
c) Of the CC current gain is unity d) None of these
Answer: (a)

18.
Inverse active mode is the condition in which WBUT 2018]
a) B-E is forward biased and B-C junction is reverse biased
b) B-E is reverse biased and B-C junction is forward biased
c) B-E is forward biased and B-C junction is forward biased
d) B-E is reverse biased and B-C junction ls reverse biased
Answer: (b)

ECDV-87
 POPULAR PUBLICATIONS
9ucstions
Answer Type
LShort a
relationship botwetween Ico and
BJT? Dorlve WBUT 2006, 2008, 20121
1. What ls punch through broakdown in
cao and discuss thoir offects on temporaturo. effective base width
Answer: is increased, the
junction cpletion region covers
As the reverse bias of thc collector collector junction, the depl
the penetrates the
decreases. At a eertain rever bias of to zero. As the collector voitage
eflective base width a result, an excessively
C ase reducing the emitter junction is lowered. s
C potential barrier at the hrougn.
T

phenomenon is called Punch

This is mnainly due to the flow
rge emitter current Nows.
B-C junction current)
ne current, 1mo (normal reverse biased B-C space charge region into the base.
Or inority carrier holes from the
collector across and BE
base passive with respect to the emitter
moves
ne tlow of holes into the base
biased. Forward biascd BE junction produces
the current
Junction becomes forward
ChO

common- emitter current gain)

or cKo Blnol=
1-a
CBo iS temperature dependent.

in early effect. WBUT 2010

2. What is early effect? Define punch through
Answer:
1 part: plot of the input current /, against input
The CE input characteristics constitute the
to both
voltage with output voltage Ver as parameter since the emitter is common
device. For a constant ", the effective base widh
the input' and output section of the
is because width of depletion region at collector
decreases with increasing|ee This
emitter junction increases. This is called Early Effect.

2nd Part:
As the reverse bias of the collector junction is increased, the effective base wId
decreases(the Early Effect). At a certain reverse bias of the collector junction.
depletion region covers the base,reducing the effective base width to zero.As the collec
voltage penetrates the base,the potential barrier at the emitter junction is lowered. A
result, an excessively large emitter current flows.This phenomenon is called pn
through or reach-through,and puts an upper limit to the reverse collector voltage. Pun
through is different from avalanche breakdown of the reverse-biased collector junctioror
aparticular transistor,the collector voltage limit is dictated by punch-through
breakdown, whichever takes place at a lower voltage.

ECDV-88
 ELECTRONICDEVICES
3. What is meant by d.c.
characteristics? What operating
is load line? point or Q point in the context of
Why is transistor
biasing necessary
transistor
Answer:
WBUT 2013, 2017]
1 Part: Operating Point
Load line: It is a and Load Line
graphical way to find
is described by its
characteristic curves.the device currents and voltages when the device
locus of all The load line solves the purpose
such points on the as it gives the
corresponding output curve, where the
can be obtained. device can be operated and a

Rc

R Vcc

Fig 1: A common emitter amplifier

Here, Rc is the resistor
at the collector; Rß is the
respective currents are shown resistance at the base terminal.
by ic and ig with two voltage The
sources for proper biasing.

c(mA) 80 uA

70 A
60 uA
20
50
A
40 uA

B 30 uA
O
20 uA

10
A
lu-0 pA
VE
CEst
CEmay c.0)
cutoff

By applying KVL which is Fig 2: Region of operation of a BJT

ePer-R
And this can be written as

iR R
ECDV-89
POPULAR PUBLICATIONS the in VS.
x-axis is Vcc. On
and that on the equation. Suitable change in
The intercept on the y-a3y-axis is VrcR, line for the above by the line is called d.c.
straight intersection points
Stem, we obtain
a
coordinate syste etc. The racteristics. GenerallyQ point is
characteristics
ucn as VBB, Rp and
operating point or Q point in the context
transistor
of
transistor
characteristics and mid of load line.

chosen at the middle of the

is use to set the Q point. Before the
enabla
2d Part: because by dc
biasing
proper biasing which
Transistor biasing is essary essential to set
amplifier or switch it
transistor is use as
transistor to work properly. current in
effect modifies the input
effect? Explain how the
early
transistor? WBUT 2013, 2016, 2017
.what is early of an n-p-n
case of CB and CE configuration Answer Type
Answer: Type & 2(a) of Long
Answer
Refer to Question No. 2 of Short
Questions.
applications. two
5. a) What is SCR? Point out its
major
briefly describe the basic operation of
b)By using two transistors analogy, [WBUT 2014]
terminals SCR.
Answer: semiconductor-controlled rectifier is a
four-layer solid
rectifier or
a) A silicon-controlled name silicon controlled rectifier is General Electric's
device. The
state current controlling
trade nanme for a type of thyristor. conduct current only in one direction as
opposed
i.c. can
SCRs are unidirectional devices can flow through them in either direction.
bidirectional i.e. current
to TRIACs which are by currents going into the gate as opposed to
normally only
SCRs can be triggered normally by either a positive or a negative
current
TRIACs which can be triggered
applied to its gate electrode.

b) Construction: (SCR) consists of four layers of semiconductors, whicn

The Silicon Control Rectifier It has three junctions, labeled J1, J2, and J3 and three
structures.
form NPNP or PNPN connected to the P-Type material of a PN
terminal of an SCR is
terminals. The anode while the gate of ne
terminal is connected to the N-Type layer,
structure, and the cathode cathodt
Control Rectifier SCR is connected to the P-Type material nearest to the
Silicon materia
SCR consists of four layers of alternating P and N type semiconductor
An
semiconductor, to which the proper dopants are added. I
Silicon is used as the intrinsic po
are either difused or alloyed. The planar construction is used for low
junctions
SCRs. The mesa type construction is used for high power SCRs. Inare this case, junction
method and then the outer two layers alloyed to l,
is obtained by the diffusion
properly st
the PNPN pellet is required to handle large currents. It is o1
to provide greatcr mechanical strength. One
with ungsten or molybdenuim plates
SInK
to a copper stud, which is threaded for attachment of hea
plates is hard soldered

ECDV-90
 ELECTRONICDEVICES
The doping of PNPN will
depend
similar to those of the thyratron. on the application of SCR, sinceits characteristics ar
Today, the term thyristor applies to the
multilayer devices that exhibit larger family o
bistable state-change behavior, which
ON or OFF. is, switching either
The operation of a SCR
and other thyristors can be understood
tightly coupled bipolar junction in terms of a pair of
transistors, arranged to cause the self-latching
action:
Anode
Anode

Gate

Gate
Cathode
Cathode
6.What is power transistor?
What are the special features of power
Compare with small signal BJT? transistor?
Answer: WBUT 2015
1" Part:
Power transistors are transistors
that are used in high-power amplifiers
supplies. Power transistors are suited and power
for applications where a lot of power
current and voltage. The collector is being used-
of the transistor is connected to a metal
as a heat sink to dissipate excess power. base that acts

2nd
Part:
Power bipolar transistor possessed
1. high blocking voltage capability in OFF state and
2. high current capability in ON state.
3d Part:
BIT is a 3 layer 2 junction semiconductor
device. lt has 3 leads named as
Collector and Base. It is used in circuits as a switch or Emitter,
an alnplifier.
Power BJT is different from BJT in
construction. It has additional layer named
"drift layer". It is used in power electronic circuits. as the

LLong Answer 'Type guestions

1.Using appropriate circuit and diagram explain the use of a BJT in CE
amplifier, mode as an
[wBUT 2009]
Answer:
Common-emiter (CE) mode: When the emiiter terminal is common to both the input
ånd the output circuits, the mode is called the common-emitter mode
of the ransistor.
igure shows this type of configuration.

ECDV-91
POPULAR PUBLICATIONS

Vec

Ves

V E
C

b)

E common-cmitter configuration
symbols for transistor
Fig: Notation and b) pnp
a) npn transistor

Current Expressions biased mode can be written

as Ilco-al,
The emitter current in forward
the collector current
and I the emitter
Where, Io is the reverse
saturation current, I
current. So a is expressed as a= -
contributed by the
the total fraction of the
emitter current
The quantity a represents
and reaching the collector.
carriers injected into the base
be
nanoamperes, their vahue can always
current is of the order of
The reverse saturation current. Thus the expression for a reduces
too-
compared to the collector
neglected as
base
Ic/lE
circuit curent transfer ratio or the current gain for a common
The small signal shot as the ratio of the change in the collector
by a. t is defined
configuration is denoted
emitter current at constant collector to base voltage.
current to the change in the
a'=-A4|
represent the change of collector and base current.
A/
Here AI and
mooc
a transistor operated in the common emitter
The maximum current gain of
to the Da
denoted by the parameter. It is defined as the ratio of the collector current
current.

ECDV-92
 ELECTRONIC DEVICES
Majority
carriers

Depletion region

Fig: Transistor
with emitter junction
forward biased and
collector junction open

Since the emitter

junction is connected
makes the emitter
diffuses to the base
base region forward to the positive pole of the battery VEE, Which
bias, the majority carriers
region (n-type). (holes) from the
forward biased p-n The fig. depicts that p-side
junction with collector it is very much clear that
the hole direction base open circuited, for a
that is from p-side a forward current flows
emitter current IE. In (emitter) to n-side (base) and hence in
the base region, the termed as the
which has a large holes from the p-side
probability of meeting acts as minority carriers,
electron and hole form an electron in the base.
a covalent bond. The In such a case both
base region are supplied electrons and holes that the
externally by the VEE through have been lost in the
the base lead.
There are two cases:
a) When the collector
side is open circuited:
In such a case only
the emitter current lE flows
source VEE from emitter to base
and to voltage
b) When the collector
side is closed:
In such a case recombination
occurs in the base
current lE minority PIus lE majoriry thus creating the recombination
Thus,

and
lElE majority
lE minority

Ic=lc majority
The recombination current lc minority
in the closed circuited emitter-base
region, which was termed
asEminority, is nothing but called as the base current la.
Thus applying Kirchhoff's current rule in the collector terminal,
Iatle= lE

Operating Point and Load Line

Load line: It is a graphical way to find the device currents and voltages
IS described
when the device
by its characteristic curves.

ECDV-93
POPULAR PU8LIGATIONS

Ve

amplitier
common emitter the base terminal. The
Fig A resistance at
biasing.
the collector; Ra is the
voltage
sources tor proper
Here, Re is the resistor at ic and ig with two
currents are shown by
ve (mA)

la=0 uA
VCE

cutoft
CEmax r 0)

Fig: Region of operation of a BJT

By applying KVL
which is Vee =ce-icR,
And this can be written
as
i,R R, VBE
y-axis is Vcc/R and that on the N-axis is Vcc. On the ig VS.
The intercept on the change
coordinate system, we obtain a straight line for the above equation. Suitable
parameters such as VBB, R and etc.

ECDV-94
 ELECTRONICDEVICES
2. a) What is early
effect? Explain
BJT in CB configuration. how it influences the input characteristics
b) Draw output ot a
different the characteristics
regions in the characteristicsof a BJT used in CB configuration.
Answer: and explain them. Indicato
a) In the operating WBUT 2011, 2017]
region of a transistor
emitter-base junction is or for normal operation
forward-biased. of the transistor, the
base voltage will be So the emitter current variation
similar to the with emitter-to-
increase in the magnitude forward characteristic
of the collector to base of p-n junction diode. An
a
to increase a voltage
for fixed VEB. When Vcu increases,
(VNcR) causes
the emitter current
base junction widens the depletion region in the colleetor-
and reduces the base
width. This is known as the
early etlect.
Saturation
region

6mA
Active
region
Iu-5mA
Iu-4mA

I3mAA

Va

Fig 1: Graphical representation of Early Voltage

Base width modulation by collector current
In BJT, the base width is a function of Base-Collector Voltage. As Base-Collector
bias voltage increased, Base collector space charge reverse
region width increase ultimately
reduces base width thickness. So a base width reduction will
cause the gradient in
minority carrier concentration to increase which ultimately increases diffusion
current.
This effect is known as base width modulation. The collector
current and collector
emitter voltage variation is shown in the following figure.

with collector emitter voltage

Fig 2: Variation of collector current
to zero collector current, current
t the collector current characteristics is extrapolated
ntersect the voltage axis at a point which is defined as Early voltage.
ECDV-95
POPULAR PUBLICATIONS

From the figure we may write, d go

0
dVer Ve+a
where 80 output conductance
Va Vox positive quantities
characteristics ror common
b) aracteristic curves known as the input and the output
aSe and common-emitter modes are of practical use and
importance

Common Base mode:

input and output sections of the
nce inthis mode, the base is common to both the
transistor, the input characteristic for CB
mode as shown in figure 3, constitutes the s0
plot of input current Ie against input voltage
VEB with output voltage Vca as parameter.
30

Since, the emitter-base junction is forward

biased in normal operation; the input 10L
characteristics are similar to that of a
forward biased -n
diode. For a fixed VEBe
0.I 0.2 0.3
increases with increase of|VcB When
Emitter-base voltage, V»(V)
Vca increases, the width of the depletion Fig: 3 Input characteristics in CB mode
region at the collector base junction
width. The change of the effective base
increases, thereby reducing the effective base,
Effect. The decrease of the effective
width by the collector voltage is termed as Early
enhances the concentration gradient of holes in the base region. There is a
base width
minimum voltage called Threshold voltage, V, below which I is very small.

Input characteristics:
against the input voltage of the transistor in a particular
The plot of the input current operation
configuration, with the output voltage as parameter for a particular mode of
a
for that mode.
gives the input characteristics

Output Charucteristics: current

Similarly a plot for the output current against the output voltage with the input
parameter gives the output characteristics.
a four distinct regions:
The output characteristic can be divided into
The active region,
)
region,
ii) The saturation
active region and
ii) The inverse
iv) Cutoff region.

ECDV-96
 ELECTRONCDEVICES

Active rregion

e 50 mA

0
e 40 mA

le 30 mAA

le20 mA

0
10 mA

lc O mA

Cutoff region

VcH (V)
Fig: 4 Output characteristics of CB p-n-p transistor
3. Describe operation of a p-n p-n-structure on the basis of two-transistor
analogy.
[WBUT 2011]
Answer:

PNP

G
NPN

Fig: Equivalent circuit

The basic structure of SCR can be divided into 3-layer structure as shown below. The
upper 3-layer structure is a PNP transistor whereas lower is one an NPN transistor.

4.Derive the equation for the different current components in a BJT by Ebers-Moll
model. WBUT 2013, 20171
Answer:
Ebber-MolM models
A transistor consists of two coupled pn junctions. Transistors
are basically constructed
with a thin base region. In an npn transistor,
current components are emitter current, base
components are emitter-base voltage and
Current and collector current. The two voltage
collector-base voltage.
above discussion, the following points are to be considered.
On the basis of the

ECDV.97
 POPULARPUBLICATIONS
are cmitter.
back to back. There diodes
a) In this model twvo diodes are connected
trans
ase junction and collector-base junction of tne token care of.
) In this model, two controlled current S
tasic Ebber-Moll equivalent circuit is shown in he
following:
he

Fig 1: Basie Ebber-Molls equivalent circuit

From KCL we may write
+, +le =0
The collector current,
a,l-
where a = common base current gain in forward-bias mode
So
al +les: les = reverse-bias Base-collector junction current and
e
If base-collector junction is forward biased function

,exp
Ia,lsexp
So we can write,

eVm
or, (e
where a, = common base current gain for inverse active mode. The above equation is
called Ebber-Moll equation.

a) Describe punch-through effect in BJT.

5.
WBUT 2015]
Answer:
As the reverse bias of the collector junction is increased, the effective base width
decreases. At a certain reverse bias ot the collector
junction, the region covers
he base reducing the effective base width to zero. As the collectordepletion
voltage penetrates tne
ECDV-98
 ELECTRONIC DEVICES
se.
base. The potential barrier at the
emitter junction is lowered.
large emitter current flows. This phenomenon As a result, an excessivey
fimit to the reverse collector voltage.
is called Punch Through and puts an upper

For an ideal p-n-p transistor, the current components

I3mA, In0.01m4,.14, =2.99mA and =0.001mA.areDetermine given by
() the emitter
efficiency 7. (10) the base transport
factor a,, (ii) the common-base current gain
a, and (iv)
Answer:
WBUT 2015
From the given data we can write the
emitter current for p-n-p transistor

And collector current

) The emitter efficiency y =. 3

tp+ 3+0.01u.y6
(i)The base transport factor a, == 99
=0.996
(i) The common-base current gain

aa,-=+l a,299+0. 3+0.01

= 0.994

(iv)Here co 0.001 mA =l 4A
c)
Explain working principle of PNPN transistor. WBUT 2015]
Answer:
Anode, A

P
N
Gate 2
Pa
G
G
N

K
o K, Cathode
b) Symbol
a) Construction Fig: 1
n Power
Electronics field, sCR is one of the most important semiconductor device,
nich is used as a controlled switch to perform a variety of functions e.g. rectification, dc
whic
0 ac inversion
and power contro.
ECDV-99
 structure
ure. It has three PN
PNPN cathode
node and gate
anode,
POPULARPUBLICATIONS forming a called
layers terminals above.
semiconducto are three figure
SCR consists of four There the
Junctions namely amd
symbol
J.
J4. 1ne
J,J, and SCRare
of
shown in
applied
voltape
ge across
truction and polarity of to cathode, SCR is
The
upon the respect
depending positive, with The Biasing Structure is
The Bia
Biasing of SCR
biased in two
modes
anou reverse bias.
SCR can be When
terminals. is in
anode and cathode otherwise
forward biased,
Said to be in
shown below.

P
N

- P
N2

Reverse Biasing
Forward Biasing Fig:2

Circuit
SCR Equivalent shown here. structure as shown
here. The
circuit is 3-layer
The equivalent SCR can be
divided into transistor.
basic structure of whereas lower is one an NPN
The transistor
is a PNP
upper 3-layer structure

PNP

Fig: Equivalent circuit

K
Fig3

notes on the following:

6. Write short
2009J
characteristics WBUT
a) BJT
Model WBUT 20151
b) Ebres-Moll 2015
c) SCR
WBUT 2016,

ECDV-100
 ELECTRONIC DEVICESs
Answer:
a)BJT characteristics:
Transistor Characteristics
curves known as the input
Characteristic
and the output characteristics for common-Dasc
and common-emitter modes are
of practical use and importance.

Common Emitter mode:

The CE input characteristics constitute the
plot of
the input current against input voltage VaE
with output voltage VCE as parameter
since the
emitter is common to both the input and output
section of the device. For a constant
RE, the
effective base width decreases with
increasingVC This is because width of Base-emitter voltage, VsE(V)
depletion region at collector emitter junction Fig: Input characteristics in CE mode
increases. This is called Early Effect.

Common Base mode: Refer to Question No. 2(b) of Long Answer Type Questions.

Definitions of transistor states

Transistor state Base-Emitter Junction Base-Collector Junction
Forward active Forward (VBE 2 V,) Reverse ( BcSV,)
Cut-off Reverse (E SV,) Reverse (: SV,)
Forward
Saturation Forward (E 2V) (2V,)
These four BJT states or operating modes correspond to the three possible
ways we can
bias the transistor junctions:
The active region is the region normally
employed for linear (undistorted) amplifiers. In
particular in the active region the
collector-base junction is reverse-biased, while the
In the reverse active region the base-emitter
base-emitter junction is forward biased.
collector region is forward biased.
Junction is reverse biased and the basé

Operating Point and Load Line voltages when the device

graphical way to find the device currents and
Load line: It is a purpose as it gives the
characteristic curves. The load line solves the
Is described by its can be operated and a
on the curve, where the device
Ocus of all such points
Corresponding output can be obtained.

ECDV-101
POPULAR PUBLICATIONS

Re

Vim

Fig: A common emitter

amplifier

e (mA)

Cmax

Vce
CEmax cc.0)
cutoft

Fig: Region of operation of a BJT

By applying KVL which is v = Vee -iR,

And this can be written as i= Ve
R
The intercept on the y-axis is Vcc/R and that on the x-axis is Vec.
On the is vs. VBE
coordinate system, we obtain a straight line for the above equation.
Suitable change in
parameters such as VBB, Rp and etc.

b) Ebres-Moll Model: Refer to Question No. 4 of Long Answer

Type Questions.
c) SCR: Refer to Question No. 5 of ShortAnswer Type Questions.

ECDV-102
 ELECTRONIC DEVICESs

MOSFET
Chapter at a Glance
MOSFET: Metal Oxide Semiconductor
improved version of field Field Effect Transistor (MOSFET) is basically an
effect transistor. It is
totally insulated by insulating similar to JFET except that its gate region
layer and is isolated from channel is
semiconductor layer at oxide-semiconductor region. The propery o
interface is most important in MOSFET. Fiela
input changes the type of
conductivity i.e. say from a
is produced by an applied p-type or n-type, of this layer. The tiela
voltage across oxide
.Basic Structure of MOSFET: layer.
SOURCE
GATE(-) DRAIN

Metal clectrode
SiO

Induced
p-channel

n-substrate

Fig. p-channel MOSFET

Energy-band Diagram of MOS Capacitor: The energy band diagram of a MOS capacitor is
shown in Figure:

ale Oxide

a) For positive gate

Gate Oxide E

Induced postive space charge region

b) For negative gate bias

ECDV-103
 POPULAR
PUBLICATIONS

Gate
E

Es

Inversion Laser of holes

)Large negative gate bias is
are tentary MOS or CMOS: In CMOS technology, both pMOS and nMOS transistors
abricated in the CMOS technology. Of late CMOS technology totally overpower Bipolar
matche nology. CMOS is a logic family that uses n-channel and p-channel MOSFETS in
nea
e
or complimentary pairs. In
this family, p-channel MOSFET IS uSed as pull-up load
tor a n-channel MOSFET pull down device. It possesses the lowest power dissipation
nghest packing density in comparison with all the other logic families.
OSe margin: Noise margin of a digital. gate or circuit describes the behaviour of the logic
e under noisy conditions. The noise margin for high logic levels IS given by,
NM4 =Vou-Vu
and noise margin for low logic
levels is given by, NM,
For VpD 5V we can write;
=
'u-oL
NM, = NM, = Vpo12
Capacitance-Voltage Relation for MOS Capacitor:
ofan The capacitance-voltage characteristics
n-channel MOS capacitor is shown in Figure below.

Strong inversion

Depletiod

Weak inversion

Weak
accumulation

Fig. C-Vrelation for an n channel MOS Capacitor

Multiple Choice Type Questions

1. In n-channel MOSFET, source and drain are doped
with WBUT 2006, 200)
a) n-type impurity
b) p-type impurity
c Source with p-type and drain' with n-type
impurity
d) none of these
Answer: (b)

ECDV-104
 2. JFET normally works ELECTRONICDEVICES
a) Cut-off region in alan
c) Ohmic region [WBUT 2007]
b) Saturation region
Answer: (c) d) Breakdown
region
In a P-type MOSFET
in accumulation
a) downwards b) sideways rogion, the band bends
Answer: (c) (WBUT 2007]
c) upwards d) none of these
4. When the drain saturation
current is less
than ldss a JFET acts like
a) bipolar transistor
b) current source WBUT 2007]
Answer: (c) c) resistor d) battery
Strong inversion occurred
5.
a)
Where and
Answer: (b)
b)
in N-MOSFET
=20,
are surface and Fermi
for condition
c) D =0
potential respectively.
WBUT 2008, 2018]
d) < ,
6. A D-MOSFET can operate
in the
a)
depletion mode only WBUT 2009, 2018]
c) depletion mode or enhancement b) enhancement mode only
Answer: (c) mode d) low impedance mode
7. lon implantation is done
a) at lower temperature WBUT 2010]
compared to diffusion
at higher temperature compared to diffusion
b)
c) at most same temperature as diffusion
d) none of these
Answer: (a)

8.
Flat band condition in an MOS capacitor occurs when
a) =
Answer: (a)
0 b) >0 c) <0 , d)
WBUT 20101

9.
Inversion layer in an MOS device can be created by WBUT 2010]
a) doping b) impact ionization c) tunneling d) electric field
Answer: (d)

10. If
and . denotes respectively the surface and Fermi potential, strong
in an n-channel MOSFET when WBUT 2011)
ersion takes place
a) b) o < c) o, = d) o=2
=0
Answer: (b)

ECDV-1055
POPULAR PUBLICATIONS
phototransistors are
Bipolar WBUT 2012
11. Compared to Field offoct phototransistor,
*red
sonsitive and slowor
b) more
a) more sensitive and faster sonsitive and faster
d) less
C)less sensitive and slower
Answer: (C)
WBUT 2012]
12. Consider the following statements py
voltage of a MOSFET can be increased
threshold
1. Using thinner Gate oxide
2. Reducing the Substrate concentration
3. Increasing the Substrate concentration
Of these corroct
a) (3) alone is correect b) (1) and (2) are
d) (2) alone is
correct
c) (1) and (3) are correct
Answer: (b)
WBUT 2013]
13. The function of the SiO, layer in MOSFETs is to provide
a) high input impedance
b) high output impedance
c) flow of current carries within channel
d) both (a) and (b)
Answer: (c)

14. Strong inversion takes place In an n-channel MOSFET when WBUT 2013]
a)
Answer: (b)
=0 b)
s )=20 d) Dp

15. Consider the following statements: WBUT 2014]

The threshold voltage of MOSFET can be Ihcreased by
1. Using a thinner gate oxide
2. Reducing the substrate concentration
3. Increasing the substrate concentratlon
3 alone correct b) 1 and 2 correct
c) 1 and 3 correct d) 2 alone correct
Answer: (c)

16. Compared to field effect phototransistors, bl-polar phototransistors are

WBUT 2014
more sensitive and faster
a) a b) more sensitive and slower
c) less sensitive and slower d) less sensltlve and faster
Answer: (¢)

17. Above pinch off voltage in a JFET the drain current WBUT 2015]
a) decreases b) increases sharply
remains constant
b) d) both (a) and (b)
Answer: (c)

ECDV-106
 18. f V is ELECTRONICDEVICES
thevoltage applied
MOS capacitor
then V < 0 to the metal with respect to p-type
a accumulation b) depletion
corresponds to semiconductorn
Auswer: (a) c)inversion d) strong WBUT 2015]
inversion
19. Flat-Band voltage of n-channel
a) positive enhancement type MOSFET
o) positive or is WBUT 2016]
negative b) negative
Auswer: (a) d) zero
20. Which one of
the following is
a) MOSFET
b) IGBT
not a voltage controlled
Auswer: (o) c) BJT
device? [WBUT 2016]
d) JFET
21. Pinch-off voltage
a) channel width
of FET depends
on
o) applied voltage b) doping concentration
WBUT 2016]
Answer: (d)) d) both of (a) and (b) of channel

22. For design of high speed

electronic system
the preferred one should be
a) Si n-Mos WBUT 2016]
GaAs n-MOS
o) b) Si p-MOs
Aaswer: (c) d) GaAs p-MOS

23. Above Pinch

off voltage in a JEFT the current
a) decreases WBUT 20171
c) increases b) becomes saturated
sharply d) none of these
Answer: (d)

Short Answer Type Questions

1. What do you mean by Pinch-off
situation. condition in JFET? Briefly
describe the
WBUT 2011]
Answer:
The condition in which the channel
region is being completely filled up by
gate to channel space charge conditions is known as reverse biased
Pinch off condition.
in Pinch off condition, drain
current is essentially zero as the depletion region
Source and drain terminals. In this condition, gate isolates
junction space charge region extends
Completely through the channel. As a result the channel is completely
depleted of free
carrier

Determine the probablity of occupancy of a state that is located at 0.359 ov

0Ove &, at T» 300 K. WBUT 2016]

ECDV-107
 POPULARPUBLICATIONS

Answer:
()
+exp 35

AT eNp 0259

AtT-27°C,KT= 0259
eap(-13.514)
0.9999986481
I.000001 3519
[WBUT 2018)
3.What do mean by Plnch-off condition In JFET? Brlofly doscribo t.
Answer:
Pinch-ofT Effect: l-0

Source Dran

N-1ype channel

Gate When Vow>V» the channel

closes "pinched off"

N-channel JFET Biasing Circuit for Pinched-off Condition

The JFET with N-channel structure is shown above. At primarily if the gate voltage is
zero, then the channel resistance is also zero and the conduction of the channel is high. If
the gate voltage (i.e. negative voltage) increases to above zero, then the resistance of the
channel also increases and the small amount of current will flows through the channel.
If we apply a large amount of negative voltage at the gate terminal, then the channel
totally blocks the low of current through it. In this condition, there is no current flow
through the channel and now the JFET acts as a perfect resistor.
The state of JFET in which the channel closes is called "pinched-off" and the voltage
applied at gate in that situation is called "pinched-off voltage (Vp)". At the pinched-of
condition the gate voltage (YGs) controls the channel current. The P-channel JFET
operation is same as the N-channel JFET with some variations, such as the channel
current is positive because or the conduction due to holes and it is needed the reverse
voltage.
polarity to apply gate
ECDV-108
 ELECTRONICDEVICESS

Long Answer Type Questions

1. a) Sketch the cross-sectional
view of a p-channel MOSFET
with proper labels.
b) Define WBUT 2006, 2015]
)flatband voltage and
i) capacitance of MOS
c) Derive and expression fordevices
the threshold voltage
of an ideal MOSFET.
WBUT 2006]
a) What do you mean by MOS OR,
b) Draw the C -
capacitor?
V dependence
curve and specify the three different region in
cgraph.
Define fiat band
voltage with
the
respect to MOS devices.
Answer: WBUT 2016]
a) Basic Structure of MOSFET
SOURCE
GATE( DRAAIN

Metal electrode
SiO

Induced
p-channe

n-substr ate

Fig: p-channel MOSFET

The basic structure of p-channel MOSFET is shown above.
Itconsists of a lightly doped n-type semiconductor
substrate on which two heavily doped
P-region are grown.
The pt region acts as source and drain.
Above the structure, a thin layer of silicon
dioxide (SiO,) is grown. Metal contacts are made. The
metal contact on the insulating
SiO, is called the Gate.
The metallic layer, silicon dioxide layer and the
semiconductor channel forms a parallel
plale capacitor where the Si0, layer is the dielectric.
-channel MOSFET is similar in structure. It has a lightly doped p+ substrate and
heavily
aoped nt region. The induced channel is of n-type.

by ti)
Flat band voltuge
e
no space
gate voltage tha must be applied to create the lat bond condition in which there
charge region in the semiconductor under the oxide is ealled Flat band voltage
is

Flat band
voltage is expressed as,
ECDV-109
 POPULAR PUBLIGATIONS

polysilicon gate and silieon

between
where Ms=Work function ditference area, Theshold
oxide
capacitance /
ox=Oxide fixed charge:
adjusting implantation impurities.
Gate
shown in
an n-chanel MOS Capacitor is
CItance-voltage characteristies of
Fig.
Stong mversa

Depletybn

inversion
Wk

Weak
accumulaton

Fig: C-V relation for an n channel MOS Capacitor

accunmulatiom
The variation depends on whether the semiconductor surfäce is in
depletion or inversion. The general expression for capacitance and voltage is,

C dV
If we look at the electrical equivalent circuit of a MOS capacitor or MOSFET, it is the
series combination of a fixed, voltage independent gate oxide (insulator) capacitance and
a voltage-dependent semiconductor capacitance such that the overall MOS capacitanoe
becomes voltage dependent. The MOS structure appears almost like a parallel plate
capacitor, dominated by insulator properties C, = €,/d.
As the voltage becomes negative, the semiconductor surface is depleted. Thus a depletion
layer capacitance, C is added in series with C, and C, where e Senmiconduct

permittivity, w = width of depletion layer. Hence the total capacitance, C

C,+C
The capacitance decreases as w grows until final inversion is reached at /,. Since u
charge increases as Square root of surface potential, D, the depletion capacitance

obviously decrease as / which is as like as the depletion

eapacitanee of a P
junction.

ECDV-110
 ELECTRONIC DEVICES
Threshold voltage
The
voltage that is needed to invert
Mathematically the charge carrier is called
threshold voltage, threshold voitage
V, may be written as,
,---2,
C
where
latband voltage.
=-,
0,/C
=work function
=Charge accumulated
potential difference.
at the depletion region.
Q/C, = Interface charge
E-6,)/g
In aP-channel device, negative threshold
supply must be looser voltage means that the negative voltage
than V, in order to achieve that we
strong inversion.
2. a) Sketch the energy band
diagram in an MOS capacitor with
in accumulation, depletion and an n-type substrate
b) Define flat band and
inversion modes.
threshold voltage with respect to MOS devices.
c) Derive an expression
for threshold voltage of an ideal
Answer: MoSFET. WBUT 2008]
a) Energy band diagram in an
MOS capacitor with an n type substrate in
depletion and inversion modes: accumulation,

E
E

(a) Energy Band diagram with n type substrate (b) Accumulation

Conditions:
E For Accumulation:
VGBVFB
E
Q'c>0
E
Ys <0

(c) Weak Inversion

ECDV-111
 POPULAR PUBLICATIONS

and Inversion
For Depletion
VaB> VFB

Qc<0
Ys>0

(d) Moderate Inversion

--

(e) Strong Inversion

b) Refer to Question No. I of Long Answer Type Questions.

c Refer to Question No. I of Long Answer Type Questions.

3. Why the JFET is called a field effect transistor? At complete pinch-off condition
of the channel in JEFT how the channel still fiows? How a CMOS is used as an
inverter? Why is n-channel MOSFET preferred to p-channel one? A MOSFET made
by p-Si as substrate with N, = 10/cm and a Si0, layer having thickness 10mm.
Calculate the threshold voltage and the minimum capacitance at ideal condition.
=
Use Foude =3.86,. =11.86, and N, 1.5x100 /cm'. WBUT 2008]
Answer:
The field effect transistor is a semiconductor device with the output current controlled by
an electric field. It follows that for a given drain to source voltage, the drain current is
a

function of a gate to source voltage. The name field effect is used for the device because
the transverse field produced by the gate gives the effect of controlling the drain current.
For small values of drain voltage, as it increases the drain current through the channel
also proportionally increases. But at the same time a voltage drop builds up along the
channel resistance. It reverses biases the gate p-n junction, consequently a depletion
region forms within the channel and reduces the channel width. If the gate is reverse
biased, the above effect becomes more pronounced. As drain voltage increases, the
depletion region spreads more and the channel becomes narrower. Ultimately, at a certain
voltage, called pinch off volfage the drain current becomes almost constant and
independent of drain voltage. Ihe channel cannot be completely closed and drain current
cannot be zero.
ECDV-112
 ELECTRONICDEYICES
CMOS inverter:
The simplest form of gain stage
is
are cu 1fthe bias of M,is the CMOS operation;n; both parasitic bipolar transistors
less than its V7,
the current in the circuit will be negligible DD

the perating point ill be very and

close to VpD
Under this condition,
the input transistor P channel
operates in the sub threshold
hile other is in or in saturation
active. As input(V) output (Vou
input
mput ransistor exists the
V increases the
sub-threshold and
egins to condu However the output n
channet
remain close to pD up to voltage
the point for which
GND
the current in M, transistor approaches
the CMOS inerter
saturation current of
M2. Both transistors are in saturation.
Finally when the 1/P is
such that the current in
M, tends to be larger than
the saturation current in M2, the
o/P voltage becomes so low as to push M,
into triode region. The o/p voltage drops
down close to ground.
n channel MOSFET is preferred
to p channel one because in n channel MOSFET
faster switching due to greater mobility we get
of electrons.
Given N =10°/cm r=10mm e,axide3.8e, e,m11.8e,
N=1.5x10°/cm N, =10° /cm
Calculate
A Ca at ideal condition

C +4+26,
3.8xI.6x Lg10 = 6.08x10-" =6.08x10 pF
10xJ

=N,N
r=245,N_v2x1.6x10-°x11.8x1.6x10x10
Cax 6.08x10
2x1.6x11.8x1.6x107.114xI9=12784x 10
6.08x10
6.08x10
a- (max) where max) eN,Ar

ECDV-113
 POPULARPUBLICATIONS

an applied positave
gate volta
diagram of the MOS system with
we get VG =AVand +Ad, = Vn t0 *P*
At thresold.
we can define V
=N 2 +
surce potential is
d = 2, at be written
K, can
as
=Vl+
nt
where is the voltage across the oxide at this threshold inversio

Finally,
-&v.r- x
the threshold voltage can be writen as
(e. (mas)-«)
ax)_ CaR s+2
C
or
K- (%(max)-%)
2
From here ViN
((max).v,,+20,
Ca
So the threshold voltage is a function of semiconductor doping, oxide charge Qs and
oxide thickness.

4.aDiscuss the
n-channel JFET.
basic principle of operation and -Va characteristics of

b) Derive the expression of pinch-off voltage for JFET.

) Compare the properties of BJT and FET. How do you use JFET as VVR?
WBUT 2009
Answer:
a) Enhancement MOSFET:
In an n-type enhancement MOSFET, if we apply a negative voltage to the gate, due to
capacitive action a positive charge will be induced in the n-type semiconductor.
soURCE GATE DRAIN

P*

n-substrate

Fig: Enhancement MOSFET

There positive charges form the inversion layer in the n-type substrate. The charges art
minority carriers and are contined to a thin region called the channel.

ECDV-114
 ELECTRONICDEVICES
If a positive charge is applied
the induced channel carry to the source w.r.t.
negative gate voltage. current from source the drain, the positive charge carTiers
to drain. The drain current is
enhanced oy
Depletion MOSFET
In depletion MOSFET,
a portion of
with the same type of the substrate between source
impurity as that and drain is
application of the oxide of the formation of source and the drain diffused
layer. before the
SOUR
URCE
()GATE DRAIN

n+
n
Inducedn-
channel

p-substrate

Fig: Depletion MOSFET

When a positive voltage is applied

to the drain w.r.t. source, a drain current
flows for zero
gate-to-source (as 0) voltage. When gate
is negative, positive charges are induced
the diffused n-channel conductivity as in
a portion of the channel is depleted
drain current falls as Vas is made more negative. of cariers. The
Field effect transistor (FET) is a unipolar transistor.
The current conduction is only due to
majority carrier. FET is a voltage controlled device,
i.e., the output current is controlled
by electric field, hence the nai Fiel d Transistor. FET is basically a resistor
value is controlled by the potential applied to the control whose
terminal. The conducting region
1S called
channel which may be either p type or n type.
Junction Field Effect Transistor (JFET) is classified into n channel and
p channel JFET.
The structure of FET is very simple. In an n-channel JFET, an n-type
silicon bar, referred
to as the channel has two smaller pieces of p-type
silicon material diffused on the
opposite sides of its middle part, forming p-n junctions. The two p-n junctions forming
diodes or gates are connected internally and a common terminal called gate terminal.
he diagram of an n-channel and p-channel JFET are shown in the figure.

ECDV-115
 POPULAR PUBLICATIONS

9 Drain, D

P-ype Gates 1 Drain, D

Gate, G

CGat

Sonee, S
Source, S
Fig p-channel
Fig: n-channel JFET
enter the bar.
ource (S) is the terminal through which the majority carriersleave
carriers the bar.
Drain (D is the terminal through which the majority
heavily doped with impurities.
ate (G) s the region on the two sides of the bar

The symbol of n-channel and p-channel FET is shown below.

D

S p-channel JFET
n-channel JFET

Fig: Symbol of n-channel & p-channel JFET

ECDV-116
 ELBCIAN DEVICES
Operation of ET
Theoperation principle
of JFET can
be explained by the following

Vps Fig: (a) - Fig: (b)

With Vas= 0; applied voltage
When negative gate to source
Vs causes a current to flow from drain to source.
voltage is applied, the depletion
junction widens and channel layer of the gate channel
becomes narrow. So, channel
decreases for a given value of resistance is increased and i
Vs. Because of small value of Vs,
uniform and the device
acts as a voltage variable resistance. the depletion layer is
As value
depletion layer widens until it occupies of
(in the negative direction) Vis is increased
This value of Vas is
called the Pinch off Voltage (V,). the whole channel.
As Vs appears
along channel length, voltage increases as we move
from source to drain. As a along the channel
result, depletion layer becomes non-uniform.
varies along channel length and is highest Reverse bias
at drain end and the depletion layer is
drain end. Hence channel resistance widest at
varies along the channel and (- Vzs) characteristic
curve becomes non-linear. The variation
of channel with along length of channel is
shown in fig.

drain
Source

Gale

Operation ofn-channel FET:

he operation of n-channel JFET is being considered by the following discussions.

ECDV-117
 POPULAR PUBLICATIONS junctions are equal
around the pn
Case : regions
depletion
When x = 0 and V =0,
thickness and symmetrical (Fig). to
terminal D where
teminal S to flow of. is
Cuse I1: from Due
trons flow D to S.
channel fromresistance
When Vos=Positive, the as we move from
through channel
conventional drain curTent /, flows
ain current. across the is a uniform
vOltage drop
voltagee drop there
Current, there is an uniform terminal S. Hence depletion
terminal S. terminal D to
to D than to S. So.
a
terminal D to move from tying closer
across the channel resistance- points
the channel at +V
ayer penetrates more deeply intoare formed (shown in r
wdge-shaped depletion regions
+V

Von

Fig: JFET with

Small-ve
Fig: JFET with no bias Gate Source Bias
increases
increased from zero, I,
As Vns is gradually
Ohmic relationship
proportionally as per Ohm's law. The
continues till Vas reaches a certain
between 2s and 1
called pinch-off voltage, V, where drain
critical value,
its maximum value called
current becomes constant at

Case IlI:
Vas is decreased from zero, a stage
When Vps = 0 and In this
regions touch each other (shown in figure above).
comes when the two depletion
be cut off.
region, the channel is said to

Case IV:
as increased; values of pinch off voltage as well 8
When Vas is negative and is
decreased.
breakdown voltage are
controls drain current, JFET is called a voltage controlled device.
Since gate voltage
ECDV-118
 ELECTRONCDEVICES
Transfer Characteristics
The transfer characteristics
i.e. variation
shown in Fig. The transfer characteristics of I
with V for a constant value of
Vs 5
approximately follows the
equation
Vs(off)

0 l(mA)
JFET Parameters
AC Drain Resistance,r -s-
is the ac resistance between
It
pinch off region. It is given
drain and source terminals
by, when JFET is operating in ine
Change in Vzs
Change in Ip lForconstant
Vcs
ft is also named as dynamic drain
resistance.

Transconductance, g
8is basically the slope of change of I, and change in Vs with constant
Vs. It is
given by,
Change in
8mChange in Vas
p
Iroronsant
Vs

Transconductance
From Shockley equation we have the expression of drain current,

Differentiating both sides we have,

dl
2 -2/
of,

when
8
ls, 2 pSS
VGS=0, g 8mo 8moF-

ECDV-119
 POPULAR PUBLICATIONS

we haves
From the above equations

Amplficaton Fuctor, u
Change in Px
Change in Ps,onant
channel
DC Drain Resistance, Rs resistance ofthe
R is called Static or Ohmic

RVs/»
Advuntages of JFET
JFET are
The main advantages of
impedance
a) High input
b) Low noise
c) Small size response
d) High frequency

Disadvantages bandwidth product

a) Small gain to damage in
handling them.
Greater susceptibility
b) it we
voltage, and by suitably varying
by the gate voltage becomes
drain current is controlled only calculation of the pinch-off
b) The
amplification of an ac signal. The
can obtain
analysis is made from Fig
rather simple if the depletion region (W) under a biased condition is
expression for the width of the
The
given by Eq (1).
+N
2e(-P),
N.N
Where,
the dielectric constant of the material,
cis potential,
V, is the contact
voltage,
V is the applied charge,
is the magnitude of electronic
q
concentration of the acceptor ions in the p-type gate, and
is the
N,
of the donor ions in the n-type bar.
N, is the concentration
ECDV-120
 Channcl lhalt width is measured ELECTRONICDEVICES
channnel under no bias from centre
h width
of the channel line in this figure.
a the actual width of the
is a functim
ofx, Le.,
h(x) and W(x)
at a distance x from
1 the source terminal and
depletion region represent the corresponding
at the sides
of the channel. widtn or ue
Wx)=a-h(a)
(2)
G

Geometry of a JFET
under a biased condition
From this relation giving
the width of the depletion
from the source (at the region, its value at a distance
drain terminal) can be calculated L away
as:
W{r=1)=2E(-Y)
As the width of the depletion region
cannot be negative, so:
/2
(r=1)-2-Y
Np
The condition
of the pinch-off is
W(r=L)=a-h(x=L)=0
Poisson equation for the depletion region in the n-type bar is: -N,
The barrier electric field is: F = -
dV
dy
integrating the Poisson equation of we get:
or,
dy
-(y-W)
Of,
-Fddy (y-w)

ECDV-121
 POPULAR PUBLICATIONS

Jav
Or,
-w}o
or,
Vo)--*-2w)
2e reduced to:
= pinch-off voltage; the equation is
" )=V,
Vow)=(- 2ww)
, 26

2e
w-2w)

w=a, Substituting the value of

At pinch-off condition h(x) = 0; therefore, from Eq. (2),

w, Eq. (c) is modified as: V, = N

2&
with the drain and the gate
The pinch-off voltage is a positive number and its relation
voltage is given by: V, = -Yan (pinch-off) = -Vg +»
It is important to note that in the above analysis we
assumed that the equilibrium contact
voltage is zero.

1s Part: FET
BJT
1. Electrons and holes are two types of
1. Either electron or hole is required here.

carrier. 2. Movement of carriers are done by drift

2. Movement of carrier is made by diffusion
process. process.
is comparative| 3. Switching speed is more.
3. Switching speed of BJT
low.

2nd Part: to
transistor (FET) is a unipolar transistor. The current conduction is only due
Field effect controlled
carrier. FET is a voltage controlled device; i.e., the output current is
majority whose
field, hence the name Field Effect Transistor. FET is basically a resistor
by electric
potential applied to the control terminal.
value is controlled by the

ECDV-122
 ELECTRONIC DEVICES
The diagram of an n-channel and p-channel
JFET are shown in the following figure.
Drain, D

p-type Gates

Gate, G
T

Source, S

Fig: n-channel JFET

Source (S) is the terminal through which the majority carriers
enter the bar.
Drain (D is the terminal through which the
majority carriers leave the bar.
The Channel conductivity can be controlled by controlling the applied voltage so JFET is
called Voltage Variable Resistor or VVR.

5. a) Briefly describe the operation of CMOS inverter. What are the advantages of
CMOS?
b) With the help of suitable diagram find out the expression of
threshold voltage
for ideal NMOS.
o Find the maximum width of the depletion region for an MOS capacitor on p-type
Si with N= 10 cm WBUT 2009]
Answer:
a) In CMOS technology, both pMOS and nMOS transistors are fabricated in the CMOS
technology. Of late CMOS technology totally overpower Bipolar Junction technology.
CMOS is a logic family that uses n-channel and p-channel MOSFETs in matched or
Complimentary pairs. In this family, p-channel MOSFET is used as pull-up load device
for a n-channel
MOSFET pull down device. It possesses the lowest power dissipation and
nighest packing density in comparison with all the other logic families.
CMOS inverter
is a building block for digital circuit design. The following Fig describes
CMOS inverter, schematic and its logic symbol.

ECDV-123
 POPULAR PUBLICAIIONS

VEx-5V

Vw5V

A
Input
Input. Outpu
Output

Fig: CMOS Inverter

When the input terminal is
ne inveter performs the logic operation of A to A.
connected .
und, the
input terminal
output is pulled to 5V through
pulled
p-channel transistor. When the
to ground through n-channel
connected toVpp, the output is
MOSFET.
trom DD to
portant advantage of CMOS inverter is that its output voltage swings
is found families. The static power dissipation of CMOS
round that not in other logic
to give equal sourcing and
er Is practically zero and the inverter can be sized
sinking capabilities.

DC Characteristics
The trans fer characteristics of CMOS inverter is shown in the following figure.
Vpo Ref. 2 Ref. 3
Ref.
I
M2 OFF
o M2 ON MIBoth ON MI ON
OFF

VoH

Vin

Input Vo, output

VoL
B
VSL

transfer characteristics that in region I, M2 is ON and MI is OFF.

It has been found from
are ON but in region 3, M2 is OFF and M1 ON.
is
In region 2, both VoH and the minimum output low
maximum output "High voltage iIs labeled
The transfer curve equaling
Points A and B on this curve are defined by slope of
voltage, Vo.
and low voltages are denoted by
V and
Similarly the input high
-1.

ECDV-124
 ELECTRONICDEVICES
Noise Margin
Noise margin
of a digital gate or circuit
noisy conditions. The describes the behaviour
noise margin for of the logic gate unaer
and noise margin for low high logic levels is given by,
logic levels is NM4 =
VoHH
given by, NM, =VL-VoL
Inverter Switching Point
The transfer characteristics
of CMOS inverter
figure, the point, C Is is shown in the following
called switching point
voltage.
Output Reg.1 Reg.
Fig.
and voltage at this point is called In ts
switching
Reg. 3
2

Slope=1
(output=Input)

Vc

Inregion 2 both inverters are in saturation Input

region and current in each transistors
equal. So we can write, are

and m -K,-,}
As Ips ps

ie -V.) -v»-V,-.,
Va+o-Van
So
Vs,=-

Advantages of CMOps
CMOS operates in both positive and Negative cycle where as MOS operates only in one
halfcycles so CMOS uses the power in both the half cycles efficiently.
D)
Refer to Question No. 1 of Long Answer Type Questions.

ECDV-125
POPULAR PUBLICATIONS Poisson's equation
e in
solve
junction. We
c)Analysis of MOS Capacitor one-sidedn'p
analysis is similar to t fa
the p region.
d P(x)
dx
nditions gives
For depletion p, = -4N boundary condi
appropriate
imposing
twice and
grating Poisson's equation

=v.
cive inversion
where p

the criterion is
26s

ng=Na
or , =2w, =2-In
maximum, at effective
inversion (low
reaches a
region width saturates, i.e.
C epletion
frequency).
46,kT In

d
- 25,2s-25=1N
qNAN, N,
dmax
= 10*° cm to find out
Now substitute N,
capacitor with an n-type substrate
in

6. a)Sketch the energy band diagram of MOS

modes.
accumulation, depletion and inversionan MOS capacitor? How does it vary with
b) Whatis the total
capacitance of
voltage? threshold voltage of an ideal MOSFET. WBUT 2010]
for
c) Derive an expression
Answer:
a) Refer to Question o.
2(a) of Long Answer Type Questions.

Long Answer Type Questions.

b) Refer to Question No. 1(6) of
1(¢) of Long Answer Type Questions
c)Refer to Question No.
both
7. Sketch the transfer characteristics of a depletion MOSFET operated in 2011]
depletion mode and enhancement mode. WBUT
Answer:
n-Channel MOSFET
The electrical behavior of MOs system under external bias is shown in the following
fig. 1.

ECDV-126
 ELECIKONIC DEVICE

O0000660000006 des
p type i sutnraet

(a)
Vy9 (smaly

onde
V0

p type S4 susbtract

(b) V Depletion
egon

Vo 0snally

----
Ec Onide
o ooo o oo oo ooo o o0 0
** --

V
p type Si subtract
**++++
(C) Dpletion
-0 Tegon
Fig. I n-Channel MOSFET

Considering fig 1
(a) it has been observed that when a negative voltage [Vg < 0] have
en applied to the metal gate, the holes in p-type substrate are attracted to the silicon
oxide interface. Since holes are the majority carrier in p-type substrate, the majority
rier concentration near the surface becomes larger than equilibrium hole concentratíon
surface.
Substrate. This is known as carrier accumulation on the
a
hen small positive voltage has been applied to metal gate, surface gets depleted of the
ority carriers and is left with immobile ions. A depletion region is created near the
Tace. This is
the depletion case.

ECDV-127
 POPULAR PUBLICATIONS downward
bend even more and
applied, bands mes smaller than Fermi
In fig (c). when latge
1
positive
uge positive
voltage
voltage is
15

ntrinsic level, E, at the surface crosses(electrons)

fer
level
ie.,
at the
E
surface is
Through
s
larger than holes
larger holes. The
this nversion
inversion lau
layer,
Ievel and number of minority carriers case.
is known ds
Inversion
terminals of MOS system.
Surtace becomes n-type. This two
the current takes place between
conduction
of JEET & explain Determine the
8. a) Draw the V-I characteristic 2.5mA.
b) Draw FET small signal model. Amp & las [WBUT 2012, 2017
= 4.5v, lass 10mA
nsconductancP
Answer:
a)
Io(mA)
Breakdown
Ohmic Saturaion Regian
20
Vas0
Icss -

15 Vas-Iv

Vas-2 Io
10
Vas-3v Drain
Vrs
ate
Vas-4
Source
Pinch-off Regon Vss
Vos () 0
VP

the Gate controls the current flowing between the Drain and
The voltage Vos applied to voltage applied between the Gate and the
Source
Vas refers to the
the Source terminals. Because
Vps refers to the voltage applied between the Drain and the Source.
while controlled. device, "NO current flows
into
Transistor is a voltage
a Junction Field Effect the device equals the Drain
current
the gate!"then the Source current ( Is ) flowing out of
Is ).
flowing into it and therefore ( Io= regions of
characteristics curves example shown above, shows the four different
The
given as:
operation for a JFET and these are and
Region - When Vas = 0 the depletion layer of the channel is very small
Ohmic
voltage controlled resistor.
the JFET acts like a voltage
Cut-off Region This is also known as the pinch-off region were the Gateresistaner
Vos is sufficient to
cause the JFET to act as an open circuit as the channel
is at maximum.
is controlle
Saturation or Active Region - The JFET becomes a good conductor and
by the Gate-Source
voltage, (Vos) while the Drain-Source voltage, (VDs) has littieo
no effect.
ECDV-128
 ELECTRONIC DEVICES
Breakdown Region- The
voltage between
enough to causes ne JFET's the Drain and the Source, (Vps) 1s gh
maximum current.
resistive channel to "
break down and pass uncontrou
haracteristics curves tor a P-channel
ase junction field effect transistor are the same as
those above, except that the Drain current
ID decreases with an increasing
Source voltage, VGs. positIe daate-
he Drain current is
Zero when VGs = Vp. For normal
mewhere.between
son p and o. Then we can calculate the operation, Vas is biased to DE
bias Doint in the saturation or active region as
Drain current, Ip for any gve
follows:
Drain current in the active egion.

Note that the value of the Drain current will be between zero
and Ioss (maximum current). By (pinch-oft)
knowing the Drain current Ip and the Drain-Source
voltage Vps the resistance of the channel (lb) is
given as:
Drain-Source channel resistance.

8m
Where: gm is the "transconductance gain" since the JFET is a voltage controlled
device
and which represents the rate of change of the Drain current with respect
to the change in
Gate-Source voltage.

b) Srmall signal model of FET

G oD

Vgs

)Transconductance, 8m
8, is basically the slope of change of 1p and change in Ves with constant Vps. It is
given by,

Change in p
F

Change in Vos lFor constant ns

V, =Vsar

ransconductance,
8m

ECDV-129
 POPUAR PUBLICATIONS

Fort tramsconductance Vos -0m transcondtctarce g.

210 4 Am3
45
ch
SExlain inversion in case of NMOS. What is channe
band Dending& channel
length modulation? WBUT 2012,
201
Answer
1f the ate
voltage, V, hecomes fmore psitive than
,
band bending result
ults. With
this,
condutivity of the channel channel current MOstEls, having sueh
characieristics are increases and also ch
known type MOSFET
In enhancement as Enhancement
mo MOSFETs a voltage drop across the oxide induces a conductie.
cHarini between the source and drain contacts via the tield effect. The term
emet
acds
mode" refers to the increase of conductivity with increase in oxide field
carriers to the channel, also referred to as the inversion layer. I he channel
n eiectrons (called an nMOSFET or nMOS), or holes (called a pMOSFET can
or
opposite in type to the substrate, so nMOS is made with a p-type substrate,
and
Os with an n-type substrate. In
the less common depletion mode MOSFET, detailed
aier o, the channel consists of cariers in a surface impurity layer of
substrte, and conductivity is decreased by application of a field opposite type to the
from this surface layer. that depletes carriers

Chans el length modulation

Source 9Gate Dran

Fig Cross section ofa MOSFET

operating in the saturation
region
One of several short-channel effects in MOSFET
CLM) is a shortening of the length scaling, channel
of the inverted channel length modulation
bias for large drain biases. The result region with increase in dran
a reduction of
of CLM is an increase
output resistance. Channel in current with drain bias and
transistors, not just MOSFETs. length modulation occurs
in all field eftect
To understand the effect, first
the notion ofpinch-off
channed is formed by of the channel is introduced. Ihe
attraction of carriers to the
channel is nearly a constant gate, and the current drawn through
independent of drain tn
near the drain, the voltage in
aie and drain jointly determine the saturation mode. However
flowing in a channei, beyond the electrie field pattern. Instead o
pinch-off point the
made possible because the drain carriers flow
and the gale both in a subsurface paet
control the
current. In the figure at
ECDV-130
 ELECIRONIC DEVICE
the channel is indicated by a dashed
dhched
4proacheed. leaving a gap of line
uninverted silicon and becomes weaker as the drain is
between the end of
qyerand the drain (the pinch-offregion) oftthe formed inversion
drain voltage increases,
As the its control over
the current extends further toward the
source, so so the uninverted region
expands toward the source,
nel region, the etfect called channel-length shortening the length of the
tional to length, shortening
proportic modulation. Because resistance
rrent with increase in the channel decreases
crease in curre its resistance, causing an
drain bias for a MOSFET operat
eee is more pronounced the shorter the source-to-drain ating in saturation. The
nction, and the thicker the oxide insulator. separation, the deeper the drain
he weak inversion region, the influence of the drain analogous to channel-lerngn
Alation leads to poorer device turn
modula
off behavior known as drain-induced Darrn
wering, a drain induced lowering
of threshold voltage.
ln bipolar
devices a similar increase in current is
Ane seen with increased collector voltage
to base-narrowing, known as the Early effect.
rent has led to use of the term "Early effect" for The similarity in effect upon the
MOSFETs as well, as an alternative
me for "channel-length modulation".

10. Write down the names of different steps in IC fabrication. Explain

photolithography.
WBUT 2012]
Answer:
part:
The fabrication'of integrated circuits consists of the following process steps:
Lithography: The process for pattern definition by applying thin uniform layer of
viscous liquid (phot0-resist) on the wafer surface. The photo-resist is hardened by
baking and then selectively removed by projection of light through a reticle
containing mask information.
Etching: Selectively removing unwanted material from the surface of the wafer. The
pattern of the photo-resist is transferred to the wafer by means of etching agents.
Deposition: Films of the various materials are applied on the wafer. For this purpose
mostly two kind of processes are used, physical vapor deposition (PVD) and
chemical vapor deposition (CVD).
Chemical Mechanical Polishing: A planarization technique by applying a chemical
Slury with etchant agents to the wafer surface.
'Oxidation: In the oxidation process oxygen (dry oxidation) or HO (wet oxidation)
nolecules convert silicon layers on top of the wafer to silicon
dioxide.
impurities into
l0 Implantation: Most widely used technique to introduce dopant
electrical field and
Semiconductor. The ionized particles are accelerated through an
argeted at the semiconductor wafer.
step following ion implantation is used to anneal
usion: A diffusion
bombardment-induced lattice defects.

r"Part: Long Answer Type Questions

E
Refer to Question No. 15(a) of
ECDV-1311
 POPULAR PUBLICATIONS
understand the
gate conntrol
11.a) Explain how helps to
the junction theory compared to the cham
over the
the channel current.
D)Justify the reason of high doping of the
gate WBUT 2012,
nannel
2014)
doping.
is onlv
Answer:
The current conduction curro
a) Field effect transistor transistor. output
(FET)is a unipolar device, i.e., the is
basicall
to majority carrier. FET is a voltage controlled Transistor. FET IS
Effect T
controlled by electric field, hence the name Field applied to the control terminal.
or whose value is controlled by the potential type.
either p type or n
ucting region is called channel which may
Field Effect Transistor (JFET)
e
classified into n channel and
p channel JFET
an n-type silicon bar, referred
nction
structure of
ne structure
The Eransistor (JFET) is classiied
of FET is very simple. In an cna
T material diffuse
used on the
p-type silicon
to as the channel has
two smaller pieces of 1
ne w P ions forming
of its middle part, forming p-n junctions.
Sides
aiodes or gates are connected internally and a common terminal callea gate terminal
is

brought out.

b) MOSFET MOS capacitor. The energy bands in the

part of the is
ain adjacent to oxide-semiconductor interface band
depending upon voltage
nuctor
appiea across MOS capacitor. The position of the
conduction and valence bands relative
TO rermi level at the interface is a function of MOS capacitor voltage.
ne semiconductor surface at oxide-semiconductor interface can be inverted trom p-type
or n-type by applying a positive gate voltage or form n-type to p-type by applying a
adjacent
negative gate voltage. Thus an inversion layer of mobile charge can be created
to the oxide. The basic MOS field action is the modulation of the inverse charge density
or channel conductance by the gate voltage.
The current in a MOSFET is due to the flow of carrier in the inversion layer between the
source and drain terminals. The inversion layer charge density and channel conductance
are controlled by the gate voltage which means the channel current is also controlled by
the gate voltage.
When the transistor is biased in the nonsaturation region |spssan )), the inversion
charge extends completcly across the channel form source to drain terminals.
When the transistor is biased in saturation region|VN> Vps sat). the inversion charge
density is pinched off near drain terminals and the ideai drain current is only a funetion of
gate to source voltage.
The MOSFET is actually a four terminal device, with the substrate or body being the
fourth terminal. As the magnitude of the reverse bias source to substrate voltage
increases, magnitude of threshold voltage increases. The substrate bias effect is important
in integrated circuits in which source and substrate are not electrically tied together.

ECDV-132
 ELECTRONICDEVICES
The threshold voltage is
the applied gate voltage required
point which is the condition
at which the to reach the thresho1a inv
to the semiconducior inversion charge density
doping is equal in mag
band voltage, semiconductor concentration. The threshold voitage is a function or
High dopitng ot gate or use
doping concentration iat
and oxide thickness.
of high k dialectic increases
the switching speed of MOsEl.
12. Why is the depletion
region
increase of ps why complete tapered near the drain end of a JFET? With the
Derive an expression for pinch-off at the drain
pinch-off
end does not take placer
find out an expression voltage of a JFET. From Shockley's
for the slope of equation,
Derive an expression
for equivalent the transfer characteristic of a JFET.
Answer: capacitance for a MOS capacitor. WBUT 2013)
1 part:
Operation of JFET
The operation principle
of JFET can be explained
by the following.
G

Vps Fig: (a)

Fig. JFET biasing Fig: (b)
With Vas=0; applied voltage VDs
causes a current toflow from drain to source.
When negative gate to source
voltage is applied, the depletion layer
junction widens and channel becomes narrow. of the gate channel
As a result, channel
and i decreases for a given resistance is increased
value of Vps. Because of small value
ayer is uniform and of Vas, the depletion
the device acts as a voltage variable resistance.
increased (in the negative direction) As value
depletion layer widens until it occupies of Ves is
channel. This value of the whole
As Vns appears
Vs is called the Pinch off Voltage (Vp).
along channel length, voltage increases as we move
along
from source to drain.
As a result, depletion layer becomes non-uniform. the channel
varies along channel length and is Reverse bias
highest at drain end and the depletion layer
drain end. Hence channel resistance is widest at
varies along the channel and (la- Vps)
characteristic

ECDV-133
 POPULARPUBLICATIONS

along lengtn or channel is

Curve becomes channel with
non-linear. The variation of
shown in figure
JFET channel.

drain

Source

Gate
Fig. JFET Channel
Operation of n-channel FET
Kefer to Question No 2 (b) of Long Answer Type Questions.
2nd
part:
Refer to Previous question (Operation of n-channet FET) and the jollowing
portion,
Basically internal pinch-off voltage is not gate-to-source voltage for achieving pinch-off.
ne gate-to-source-voltage required for pinch-off condition is caled pinch-off voltage.lt
is the actual voltage for making device to turnoft.

3rd part:
The condition at which gate junction space charge region extends completely through the
channel so that channel is totaly depleted of free carriers is called Pinch-off voltage.
In gate of MOS transistor, the space charge width is given by,

w2-aeNd
w=

where V, = Built in potential barrier, Vas= Gate to source voltage.

At pinch-off condition, w=channel thickness betweenp' gate region and substrate = a
(Suppose). At this time, potential across p n junction is called internal Pinch-off voltage,
Vpo

So, 2,
eNd J
ea Nd where Vo
So, Vo26s = Pinch-off voltage (Internal)

ECDV-134
 ELECTRONIC DEVICES

4 part:
Transfer Characteristics
The transfer characteristics i.e. variation of
with Vos for a constant value I
of Vps is shown in
Fig 1. The transfer characteristics
approximately lD (mA)
follows the equation

Fig. 1
Transfer characteristics of JFEET
sthpart:
Capacitance-Voltage Relation
for MOS
The capacitance-voltage characteristics Capacitor
of an n-channel MOS capacitor is shown in
Fig.l
Strong inversion

Depletion

Weak inversion

Weak
accumulation

1C-V relation for an n channel MOS Capacitor

Fig.
The variation depends on whether
the semiconductor surface is in
depletion or inversion. The general
expression for capacitance and voltage accumulation,
is,
C ddV
If we look at the electrical equivalent
circuit of a MOS capacitor or MOSFET,
series combination
of a fixed, voltage independent it is the
a
gate oxide (insulator) capacitance
voltage-dependent semiconductor capacitance and
such that the overall MOS
becomes voltage dependent. The MOS structure capacitance
appears almost like a parallel
capacitor, dominated by insulator properties plate
C, =E,/d.
As the voltage becomes negative,
the semiconductor surface is depleted.
Thus a depletion
layer capacitance,
C,is added in series with C, and C, =whereSemiconductor
W
Es=
permittivity, w = width of depletion layer. Hence the total capacitance,
cCGC
C.C
ECDV-135
 POPULARPUBLIÇATIONS

he capacitance decreases as w grows until

final
inversion is reached at
potential, Ds the
depletion
. Since
nce

etion capacitance will

t
the

charge increases as Square root of surface

the depletion capacitance of a p-n
p.
like as
obviously decrease as 1/,, which is as
junction.

Calculation of threshold voltage inversion point is

calle
achieve the threshold
must be applied to distribution througn MOS device
Threshold volt t
,OTage. The following figure shows change
at threshold inversion ap-type semiconductor substance.
point for
Ptype
Metal Oxide Semiconductor

Qm Qs

Fig: 2 Charge distribution in an MOS capacitor

From change conservation law it can be written that, +s =p(max)
Where (max)=eN,x
The energy-band diagram ul a MOS structure with positive applied gate bias is shown
below.

EFi

Fig: Energy band diagram through

MOS structure
with positive applied
gate bias
ECDV-1366
 ELECTRONICDEVICES
From the above diagram
we may

At
V=
threshold
AVox +Ad=Vor write,
+o, +
point, V,

layer change.
=V where V = Threshold voltage that
creates electron inversion
The surface potential is =
d 20,,
V=VaxT20 +
VoT QmCox
where Cor = Oxide capacitance/area.
So it can be written that,
VaT
(mav)-
So mas) +24
COx Cox

-0 (max-a4+24
Threshold voltage,
= Cox +Vn +26
13. Draw the V-I characteristic of JFET and
explain it. Draw FET small signal
A JFET has V,=4.5V, amp model.
I =1Om and =2.5mA. Determine the
transconductance.
Answer: WBUT 2014
rPart: Refer to Question No. 12(4" Part) ofLong Answer Type
Questions.
Part: Refer to Question No. 7 (b) & (¢) of Long Answer Type Questions.

3 Part:

V,
>I-Vos/V,=1/2
Vas/V- %
Vos-2.25Volt
Change in Ip mAmp
= -1. lmi lim ho
b Change in Vus lro coestant -2.25Vol
s
14. a) What is flat band voltage in case of ideal MOSFET? wBUT 2015)
Answer:
efer to Question No. I of Long Answer 1ype Questions.
ECDV-137
 POPULARPUBLICATIONS
MOSFET depends on
b) How and voltage K, in case of real WBUT 2015]
why threshold voltage ' #hickness?
Semiconductor doping, oxide charge ana ox
Answer:
er to Question No. I of Long Answer Type Questionb
following parameters:
c) An ideal p-channel MOSFET has
W= = 350A and V = -0.8OP. If transistor
S00cm* IV-s, L=1.5um, l..
at
V =
0.5V, then calculate value of
Operating in non-saturation region WBUT 2015]
Transconductance g?
Answer:
C arain current equation of PMOS in non-saturated region
(Linear region) 1S given as

,C w forVs S
p

l2-Vm)s-Va
and VasasV)
Therefore,

8m aVGs
L
(15x10)(3x10)3.9x8.854x10.0.5) =0.296 mA/V
(1.5 x10)(350 x 100

d) What is the effect of reduction in channel length as drain voltage is increased in

MOSFET characteristics? WBUT 2015
Answer:
Refer to Question No. I of Long Answer Type Questions.
15. Write short notes on the following:
a) Photolithography WBUT 2006, 2007, 2008, 2009, 2010, 2018]
b) MOS Capacitance WBUT 2009, 2015, 2018]
c) Channel length modulation [WBUT 2017]
d) CMOS Inverter WBUT 2018]
Answer:
a) Photolithography:
Selective removal of the insulator layer of Sio, to form openings through which
impurities can be difrused is called photolithography. During the photolithographic
process the wafer is coated with a uniform film of a photosensitive emulsion. Á large
black-and-white layout of the desired pattem openings is made and then reduced
hotooraphically. This negative of the required dimensions is placed as mask over the
a
photoresist.
By exposure of ultraviolet light through the mask, the photoresist becomes polymerized
ECDV-138
 ELECIRONIC DEVICES
the transarent
wwd by using a eions chemical
of the mask. The
mask is now removed, ana
mpolymerized known as trichloroethylene is
n in Figure (a). portions of the photoresist that dissol
The emulsion film and leaves the surface pattern as
chip is immersed in an etching which was not
removed in devivelopment is now fixed.
the areas through which solution of hvdrofluoric acid, which removes
dopants are
nst portions of the SiO,
which are protectedto be diftused.
id as shown in Figure (6) After diffusion by the photoresist are unaffected by the
stripped) with a chemical of impurities, the resist mask is removeu
solvent (such as
hot H,so,). A negative photoresist
e process described above. Posithve is used
photoresists are
tion of the polymer iS washed away and also used in which the exposcu
thus retains the unexposed material.
Utraviolet
Polymerized
Mask photoresist

Photoresist
wNNNee N
SiO
Silicon chip vw w

(a) (b)
Fig: Photolithography process
(a) Masking and exposure to UV radiation (b) Development and
etching
The making of a photographic mask involves complicated
and expensive processes. After
the circuit layout has been determined a large-scale drawing
is made showing the
locations of thè openings to be etched in the Si0, for a particular process step.

b) MOS Capacitance
Refer to Question No. 1(b) of Long Answer Type Questions.
) Channel length modulation:
efer to Question No. 9 of Long Answer Type Questions.
CMOS Inverter:
efer to Question No. 5(a) of Long Answer Type Questions.

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OPTO-ELECTRONICS

Chapter at a Glance
opposite field.
An absor on: Theeciromagnetic
absorption of a field is the addition of
energy is transformed to
an
other torms of energy for
radiance, which is
CAdmple, to heat. It is squarc of the absolute
the square
proportional to variation of the
TOt equal to the coPOportional particular in photon counting
uare of the variation of a relative radiance, in
CNperiments. The absorption called allenmuation
of light during wave propagation often
is
waves does not
remains of the order of lhv lc, so that absorption of
rdiance intensity (linear absorption). Using lasers, the medium changes
its
neir
insparency dependently on the intensity of waves going through, and the nonlincar
absorption, or amplification occurs.
eractions among electrons, holes. phonons, photons, and other particles are required toA
van on of energy and crystal momentum (i.e. conservation of total K-vector).
photon with an energy near semiconductor band gap has almost zero momentum. An
mportant process is called radiative recombination, where an electron in the conduction band
nniniates a hole in the valence band, releasing the excess energy as a photon. lf the electron
1s near the bottom of the conduction
band and the hole is near the top of the valence band (as
S usually the case), this process is possible in a direct band gap semiconductor, but
Impossible in an indirect band gap one, because conservation of crystal momentum would be
VIolated. For radiative recombination to occur in an indirect band gap material, the process
must also involve the absorption or emission of a phonon, where the phonon momentum
equals the difference between the electron and hole momentum. (lt can also, instead, involve
a crystallographic defect, which performs essentially the same role). The involvement of the
phonon makes this process much less likely to occur in a given span of time, which is why
radiative recombination is far slower in indirect band gap materials than direct band gap ones.
This is why light-emitting and laser diodes are almost always made of direct band gap
materials, and not indirect band gap ones like silicon.
LED: A light-emitting diode (LED) is a semiconductor light source. LEDs are used as
indicator lamps in many devices and are increasingly used for other lighting.
When a light-emitting diode is forward biased (switched on), electrons are able to recombine
with electron holes within the device, releasing energy in the form of photons. This effect is
called electroluminescence and the colour or the light (corresponding to the energy of the
photon) is determined by the energy gap of the semiconductor. An LED is often small in area
(less than mm), and integrated optical components may be used to shape its radiation
1

pattern. LEDs. present many advantages over incandescent light sources including lower
energy consumption, longer litetime, improved robustness, smaller size, faster switching, and
greater durability and reliability. LEDs powerful enough for room lighting are relatively
expensive and require more precise current and heat management than compact fluorescent
output.
lamp sources of comparable
The laser diode: The laser diode 1s a laser where the active medium is a semiconductor
similar to that found in a light emitting diode. The most common type of laser diode is formed
from a p-n junction and powered by injected electric current. The former devices are
cometimes referred to as injection laser diodes to distinguish them from optically pumpcd
ECDV-140
 ELECTRONICDEVICES
laser diode is formed
wafer. The crystal is doped by
to produce doping_a very thin layer on the surface ystal
other, ulting in a p-n junction, and
and n-lype
n-type_region of a
region
oeDiode:
Tunnel
or
The tunnel diode diode
and a p-type region, one above
tn
negative rresistance is a negative-resistance
The is created gave-resistance semiconductor
by the semiconductor p-n junction diode.
already discussed in the section tunnel effect
of Zener diode. of the ele
electrons in the p-n junction as

Multiple Choice
Type Questions
1. the barrier potential is increased
junction will in any
any p-n
junction then the width of the
a) remain unaltered
Hincrease proportional WBUT 2006]
to square root
c) Increase linearly of the potential
d decrease proportional to
square of the potential
Answer: (b)

2 When PN junction is forward bias, forward

diffusion current
a) current is dominated by [WBUT 2007]
c) drift or diffusion current b) drift current

Answer: (a)
d) displacement current

.Which of the following has a

negative resistance region?
a) Zener diode b) Tunnel diode WBUT 2008]
c) Photo diode d) LED
Answer: (b)

4. Reverse saturation current of p-n junction diode is

a) diffusion current WBUT 2008]
b) drift current
c) displacement
current d) none of these
Answer: (b)

S.
Which metal is suitable for ohmic contact with p-type silicon?
a) Fe
[WBUT 2008]
b) Cu c)AI d) Au
Answer:
(c)
6.
Is p-n junction diode forward current. Diffusion capacitance is
proportional to
[WBUT 2008]
b) c) T
d)
Answer:
(a)
Solar cell operates [WBUT 2010]
in
31st quadrant of I-V chart b) 4th quadrant of 1-V
1-V
chart
2nd quadrant of l-V chart d) 3rd quadrant of chart
Answer:
(b)

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8. Avalanche or WBUT 2010

breakdown wn primarily dep
depends on the phenomenon
mpact
c) particle
ioni
zation b) field ionization
Answer: (a) collision d) impurity doping

2nphotodiode, E-H incident photo should

be? pairs are generated, when energy of WBUT 2010]
a) hf < Eg b) hf>
d) hf>> Eg
Answer: (b) Eg

10. Solar cell operates WBUT 2010, 2013]

in
a) 1st quadrant
of 1-V b) 4th quadrant of I-V chart
c) 2nd quadrant of I-V chart
chart d) 3rd quadrant of -V chart
Answer: (b)
on the phenomenon of WEUT 2010)
Avalanche
a) impact
breakdown primarily depends
ionization
ionization b) field
c) particle collision d) impurity doping
Answer: (a)
12. Photodiode operates in WBUT 2017]
a) reverse bias b) forward bias c) without bias d) none of these
Answer: (d)

13. If V, is reverse bias voltage, then transition capacitance (C) for

hyper abrupt
p-n junction diode is proportional to [MODEL QUESTION]

a) b) ) d) V,
Answer: (d)

14. An avalanche photo diode works on [MODEL QUESTIONI

a) High Forward bias
b) High Forward bias and impact ionization
c) High reverse current
d) All of these
Answer: (b)
15. Fill factor is the realizable power factor of [MODEL QUESTIONI
LED
b) c) P-I-N diode d) solar cell
a) Laser
Answer: (d)
done [MODEL QUESTION
16. lon implantation is compared to diffusion
a) at lower temperature
b) at higher
temperature compared to diffusion
temperature as diffusion
c) almost at same
d) none of these
Answer: (a) ECDV-142
 ELECTRONIC DEVICES
Short Answer Type
is tovoltaic effect? Questions
1. What
Answer
WBUT 2008, 2010, 2015, 2018]
The hasic physical process
through which
etricity is called photovoltaic a photovoltaic cell
ioht is conmposed ot effect . converts
nverts sunlight
photon
erent anount or energy that which is a packet of solar energy. These photons contai
ditterent
photons strikes a PV cell,
correspond to different
they may be reflected wavelength of solar specru
lgh. The absorbed photons generate or absorbed or theyy may pass sight
o an electron in an atom ot electricity. The energy
the semi conductor of a photon is transi
escape from its normal device. With this energy, electron is
hocome part of the current
position associated with
a single atom in the semi conductor aoio
in an electrical
circuit.
evices based on this eftect device as
power sources in remote terrestrial locations
for satellites and other space applications. and
Photo voltages powered calculators and other
consumer electronic products are widely
available.
The basic requirement for the photo voltaic
effect are 1) absorption of photons through
the creation of electronie pairs in a semiconductor
2) separation of the electrical rule so
that their recombination is inhibited and electric field within
the semiconductor is altered
and 3) collection of electrons and holes separately by
each two current collecting
electrodes so that current can be induced to flow in a circuit external to semi
conductor
itself.

2 Explain the working principle of Solar cells. WBUT 2008, 2010]

OR,
Write down the operating principle of solar cell. WBUT 20151
OR,
Explain the operation of a Solar Cell. WBUT 2018]
Answer:
Type Questions.
Refer to Question No. 1(1" Part) of Long Answer
WBUT 2008, 2010]
.Calculate the Conversion Efficiency of Solar Cell?
Answer:
Answer Type Questions.
eler to Question No. 1(2"d Part) of Long
expression for short circuit current and open
What is fill factor? What is the WBUT 2009, 2014]
reuit voltage for the solar cell? OR,
voltage for the
a) What
is fill factor? circuit current and open circuit [WBUT 2016]
Deri vethe expression for short
B
ar cell.

ECDV-143
 POPULARPuBLICATIONS
as
cell. It is kn
known
Answer: solar
1" part: from a
realizable
power
Fill Factor of Photovoltaic cellasure of
. is a me
Ratio of .to Yo below and is a
figure [Iy
fill factor. It is defined as, rr in the measured from the
1Vac graph as shown Vac Can be maxXimum power
from the IV and
Fill factor can be measured
solar cell. The
lse
region i the IV graph of the
measure of reliable power from
a
shaded on the
the
sults and
corresponding cross section
graph from the experim and Voe
Vm are the lm» Vms sea
rectangle; where Im and measure
Solar cell. Thus from the
graph we can

Vm oc
rectangle of solar cell
Fig: The Maximum power
photon power into electrical
which directly converts
The solar cell is a p n junction diode
solar cell is a p-n junction device With no
The
power and delivers this power to a load.
voltage directly applied across the junction. satellite and space vehicles and
used for the power supply of
These kinds of devices are
also the power supply of calculator.
1 of Long Answer Type Questions.
2nd Part: Refer to Question No.
4. Explain how an LED works as a source of light. WBUT 2012, 2018]
Answer:
Operation ofLEDs
The LED consists of a chip of semiconducting material doped with impurities to create
ap-njunction. As in other diodes, current flows easily from the p-side, or anode, to the n-
side, or cathode, but not in the reverse direction. Charge-carriers-electrons and holes-
flow into the junction from.electrodes with different voltages. When an electron meets a
hole, it falls into a lowerenergy level, and releases energy in the form of a photon.
The wavelength of the light emitted, and thus its color depends on the band gap energy of
the materials forming the p-n junction.Ihe materials used for the LED have
a direct band
gap with energies corresponding to near-inirared, visible, or near-ultraviolet
ED development began with intrared and red devices made light.
Aduances in materials science have with gallium arsenide.
enabled making devices
with ever-shorter
wavelengths, emitting light in a variety of colors.

ECDV-144
 ELECTRONICDEVICES

P-type
n-type

hole
O
ele ctron

light
000 conduction band
-
.Fermi level
band gap
OO000000 (forbidden band)
valence band
LEDs are usually built on an n-type substrate, with
an electrode attached to the p-type
layer deposited on its surtace. P-type substrates, while less common, occur as well. Many
commercial LEDs, especially GaN/InGaN, also
use sapphire substrate.
Most materials used for LED production have very high refractive indices. This means
that much light will be reflected back into the material at the material/ air surface
interface. Thus, light extraction in LEDs is an important aspect
of LED production,
subject to much research and development.

5. For the photovoltaic cell calculate the power output for different values of the
load resistance Ru. What is the optimum value of R? [MODEL QUESTION]1
Answer:
The table indicates the Power versus R, chart
R mA)
0.145
V(V)_ P(W)

8002 0.14 0.12 15.4

3.4K 0.10 0.35 34
1OK 0.04 0.42 16.4
The optimum value of R.3.4K.
P VI= 0.35Vx0.10mA =35 W. The hyperbola intersects the characteristics at one
point.
Maximum power is generated at one point only.

Long Answer 1ype Questions

1.Explain the principle of operation of a solar cell with conversion efficiency and
WBUT 2007
define 'photovoltaic emf.

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 POPULARPUBLIGATIONS

Answer:
1 Part:
Working Principle
The solar cell photon power into electrical
is ap
Junction diode which directly converts
a p-n junction device with no
power to a load. The solar cell is
Voltage directly
voltage directly applied across
the junction.
t us of devices are for the power supply of satellite and space vehicles and
alsa
also the power supply
used
of calculator.
Pjunction solar cell with resistive load is shown in figure

E ficld

L -I

R
Incident photon illumination create electron-hole pairs in the space charge region that
will swept out producing photon current in reverse
The net p-n junction current,
I bias direction.

As the diode becomes forward biased, magnitude

of electric field in space charge region
decreases but does not go to zero or change direction.
The photo current is always in the
reverse bias direction.
The l-V characteristic is shown in the figure.

OC
2n Part:
Conversion Efflciency
The conversion efliciency of a solar cell is desired as
the ratio
to incident optical power
of output electrical power

-x100%-x1009%
in

ECDV-146
 ELECTRONICDEVICES

r
The atio
is called Fill factor
and is a measure of reliable power from a
solar cel.
The curternt-voltage characteristic
is shown in the
device can be maximized by figureThe power delivered by the
maximizing the area under the curve in
maximizing the product figure or oy
(e x Voc). By properly choosing the load resistor, the output
power can be achieved. In
dark region, thermally generated
junction constitute reverse minority carriers across te
saturation current.
The efficiency ofa solar cell can

where
be written as,

and 1, are the voltage and

=a = FF

current at the point of maximum power and

the incidentoptical power. n s

Thus to realize a solar cell with high efficiency,

it is not only necessary to have high Vo
and Ise but also a high FF.
Solar cells are used as on board satellites
to recharge their batteries. Since their sizes are
small, a large number of cells are required
to make charging. Presently GaAs is used for
better efficiency and better thermal stability.

3rd
Part:
Photovoltaic emf
Generation of voltage from light energy is being done by photovoltaic effect.

2. a) What is photovoltaic effect? WBUT 2007, 2010, 2016, 2018]

b) Write down the basic operating principle of solar cell. Derive the expression for
Voc WBUT 2007, 2010, 2016, 2018]
Answer:
a) Refer to Question No. I of Short Answer Type Questions.

b) Refer to Question No. 1 of Long Answer Type Questions.

3. a) Briefly explain the working principles of a photodiode and draw its
characteristics curves at different illumination level. What is photovoltaic effect?
b) Discuss how a photodiode can deliver power to an external load.
c) Explain the construction ofa solar cell. What is fill factor? WBUT 2012]
Answer:
a) When a reverse biased p-n junction diode is illuminated with light,extra electron-hole
pairs are generated in p- and n- regions.As a result,the minority carrier concentration
Changes significantly but the majority carrier concentration does not change much. The
is found to vary
BCnerated minority carriers increase the reverse current. he diode current
I

almost linearly with the light flux.This is the basic principle of operation of a
photodiode.

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 POPULAR PUBLICATIONS

Characteristics

Equivalent circuit lo Dark curtent

Rs Photocurent
ICs Diode capacitance
current
RD I Noise
Serics resistance
R
R Load resistance

ideal Diode
U.(E)

E
R
Photovoltaic
Es Photovoltaic mode (Solar
mode Cell)

RLR
Es
Light intensity LE)
E E< E»< E4< Es

Photovoltaic effect: Refer to Question No. I of Short Answer Type Questions.

b) For the photodiode to deliver power to an external load it has
to be operated in the fourth quadrant, i.e., the junction is forward
biased.
When a forward biased p-n junction diode is illuminated with
V
light,photons are absorbed and electron hole pairs are produced
in p- and n- regions.The electrons and the holes that are
generated over a short distance from the junction can reach the
depletion region of width W by diffusion.The electron-hole pairs
are then separated under the action of the strong barrier field
existing across the depletion region .The electrons of the p-side
can slide down the barrier potential to reach the n-side whereas the holes in the n-side can
move towards the p-side.

c)1 Part: Refer to Question No. 5(b) of Long Answer Type Questions.
2 Part: Refer to Quesfion No. 41 Part) of Short Answer Type Questions.

4. a) With VI characteristic curve explain how solar cell delivers power to external
load.
b) What are fill factor and conversion efficiency of solar cell. WBUT 20131
Answer:
a) Refer to Question No. 3(b) of Long Answer
Type Questions.

b)
1s Part: Refer to Question No. 4(" Part) of Short Answer Type Questions.
2nd
Refer to Question No. 1(2 Part) ofLong Answer Type Questions.
Part:
ECDV-148
 ELECTRONIC DEVIES
Write a short notes on the following:
a) P--N photo diode
b) Solar cells WBUT 2006, 2009, 2011, 2017]1
c) Photo transistor WBUT, 2008, 2011, 2017]
A)
Optical absorption in
semiconductor WBUT 2015]
e) Semiconductor Laser [MODEL QUESTION
Answer: [MODEL QUESTION
a) P--N photo diode:
A photodiode is a p-n
junction or P-1-N
strikes the diode, it cxCites structure. When a photon of sufficient energy
an electron thereby
charged clectron hole. If creating a mobile electron and a positively
the absorption occurs in
carriers are swept trom the junction's depletion region,
the junction by the these
produced photocurrent. built-in field of the depletion region that
Photodiodes can be used
under either zero bias (photovoltaic
(photoconductive mode). In mode) or reverse bias
zero bias, light falling on
the device, leading to forward the diode causes a current across
bias which in turn induces
direction to the photocurrent. "dark current" in the opposite
This is called the photovoltaic
solar cells-in fact a solar cell effect, and is the basis for
Reverse bias induces only little
is just a large number of big photodiodes.
current (known as saturation or back current)
direction. But a more important along its
effect of reverse bias is widening the depletion
(therefore expanding the reaction of layer
volume) and strengthening the photocurent.
other hand, the photovoltaic mode tends On the
to exhibit less electronic noise.
Avalanche photodiodes have a similar structure,
but they are operated with much higher
reverse bias. This allows each photo-genera
carrier to be multiplied by avalanche
breakdown, resulting in internal gain within the photodiode,
which increases the effective
responsivity of the device.

Materials for photo detector diode:

The material used to make a photodiode is critical to defining its
properties, because only
photons with sufficient energy to excite electrons across the material's
bandgap wil
produce significant photocurrents
Materials commonly used to produce photodiodes include:
Material
Silicon (Si)
Germanium (Ge)
Indium gallium arsenide (InGaAs)
Lead sulfide (PbS)
Because of their greater band gap, silicon-bused photodiodes generate less noise than
germanium-based photodiodes.
P-N junctions, almost
dnCe transistors and IC's are made of semiconductors, and contain
Yery active component is potentially a photodiode. Many
components, especially those
it illuminated, due to the induced
Stve to small currents, will not work corectly
so they are placed in an opaque
Potocurrents. In most components this is not desired,

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 POPULAR PUBLICATIONS
energy
X-rays or other high en
housing. Since housings opaque to photo-currents.
are not completely due to induced
radiation, these can still nmalfunction
cause many ICs to Ti
Features:
Chical performance parameters of a photodiode inci
Responsivity: power, typically expressed
in A/W
photocurrent to incident light
crated
when used
used iin photoconductive mode.
Dark current: operated in
photodiode the absence of light, when it 1s
through the in
includes phótocurrent generated by background
duci ve mode. The dark current
rad
radiation and the saturation current of the semiconductor junce
Noise-equivalent power (NEP):
input optical power to generate photocurrent, equal to tne rms noIse
imum related characteristic detectivity (D)
is the inverse of
T n aI hertz bandwidth. The
NEP, 1/NEP; and the specific detectivity is the detectivity normalized
to the area (A) of
detectable input power of a
the photodetector. The NEP is roughly the minimum
photodiode.
Applications:
as compact disc players,
Fnotodiodes are used in consumer electronics devices such
DVD player and televisions.
smoke detectors, and the receivers for remote controls in
as detectors for
They are also widely used in various medical applications, such
computed tomography.

Advantages:
Excellent linearity of output current as a function of incident light.
Spectral
1.
other
response from 190 nm to 1100 nm (silicon), longer wavelengths with
semiconductor materials
2. Low noise
3. Low cost
4. Compact and light weight
5. Long lifetime
typically 80%
6. High quantum efficiency,
7. No high voltage required
Disadvantages:
. Small area
photodiodes, but their gain is typically 102-
2. No internal gain (except avalanche
photomultiplier)
103 compared to up to 108 for the
3. Much lower overall sensitivity
is slower.
4. Response time for many designs

ECDV-150
 ELECTRONICDEVICES
b) Solar cells:
The photovoltaic
diode or solar
energy probiems. cell is an important
it is also
known technological device
diode which converts as solar energy for overcoming
solar energy into converter; it is basically a
The energ electrical energy. p-njuncuon
reacning the earth's
radiation, which covers surface from
a spectral the sun is primarily
energy into electrical range of 0.2
to electromagin
energy is called 0.3 micrometre. The conversion
photoelectric effect. or tnis
Construction and
working principle:
A photovoltaic diode
essentially consists
with a glass window
on the top. Surface of a silicon p-n junction diode usually
that the incident light layer of the p-material packagea
(photons) can penetrate and is made extremely so
in Fig. 1. reach the p-n junction easily, thin
as shown
Top Ant-reflection
contai
ncident Coatng
iç

P-Si

Back contact

Fig: 1 Structure of a solar

When these photons cell
collide with the valence electrons,
energy so that they they impart in them sufficient
gain enough energy to leave the parent atoms. In
electrons and holes are this way, free
generated on both sides of the
constitutes a current (minority junction. Consequently, their
current). This current is directly flow
illumination (lumen/m* or mW/m*). proportional to the
This, in general depends on the
being illuminated.
The open circuit voltage Voc is a functionsize of the surface
Consequently, power output of a solar of illumination.
cell depends on the level of sunlight
Power cells are
also available in the form of a flat strip so as to illumination.
Surfaceareas. cover sufficiently large

Im

7777
Maximum power
rectangle (P)

LLLA Vm

Fig: 2. 1-V characteristics of an illuminated solar cell

showing the point of maximum power
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Current-voltage
The curent characteristics curve passes
voltage characteristic is seen that the
Characteristic shown in Fig. 2. It
is show
is
gn the
rough the fo
fourth quadrant and hence the device can den
aiso sce that V« is the ad under open-circuit
nons of the diode,
and
,
maximum voltage obtainabic
is the maximum curt
a h the load
maximized by maximizing8
under short-
circuit conditions. The power b
delivered
ne area under the curve (see Fig. 3) by the device
or by maximizing the product (e X Vo). By properly
choosing the l
the load resistor, output power can Dea the absence of light,
Thermally generated minority
across
nctitute the reverse sauralo
current. carriers the junction
Tomaximize power, we need to maximize both Iie and Voc
tnep- E (FF) isis defined
and n-side of the junction heavily doped. The fill factor defined as FF
FF
P
where Pm is the maximum power output of the solar cell. For a well-designed
3O1ar cell the FF usually lies between 0.7 and 0.8. The efficiency of a solar cell can be
written as7=nm
P
FF"L = where V, and are the voltage and the current at the
P
point of maximum power, and Pm is the incident optical power
Thus, to realize a solar cell with high efficiency, it is not only necessary to have high V
and but also a high FF. Solar cells with 15% efficiency are commercially available.
Top finger contact

Fig: 3 Top finger contact with anti-reflecting coating

The surface of the solar cell is coated with anti-reflecting coating imaterials such as SiO
TiO and Ta,0, to obtain better conversion efticiency as shown in Fig. 3 Today the solar
cell, a non-conventional source of energy of the 21* century, has become popular in
remote villages and in rural areas. Solar cells are used on board the satellites to recharge
their batteries. Since their sizes are small, a large number of cells are required for
charging; therefore, series parallel cell combinations are employed for this purpose. Si
and Ge are the most widely used semiconductor materials for solar cell but nowadays
thermal stability.
GaAs is used for better efficiency and better

ECDV-152
 ELECTRONIC DEVICES
c) Photo transistor:
A phototransistor
is a light-sensitive
a photobipolar transistor, transistor. A common
type of phototransistor, cad
encased in a transparent is in essence a bipolar
case so that light transistor
collector junction. It was can reach the
Bell Labs in
invented by Dr. John N. Shive
base
1948.The electrons at
nhotons in the that are generated
base-collector junction by
base, and are injected
this photodiode into the
transistor's current current is amplified
gain f (or by the
leads are used and
h). If the base and collector
Fig: Photo transistor
the emitter is
photodiode. While phototransistors left unconnected, the phototransistor
have a higher responsivity becomes a
to detect low levels of for light they are not abie
light any better than
significantly longer response photodiodes. Phototransistors
times. Field-effect phototransistors, also have
FETs, are light-sensitive also known as photo
field-etfect transistors.
The diagram is shown below.
d) Optical absorption
in semiconductor:
The absorption of a field is
the addition of an opposite
In Physics, absorption field.
of electromagnetic radiation
opposite field which is requires the generation of
the field which has the opposite the
use quantum electrodynamics, coefficient in the same mode.
that is photons, the set of normal To
photons must contain modes used to define the
the mode of emission of the absorbing
Interactions among electrons, system.
holes, phonons, photons, and
satisfy conservation other particles are required to
A
of energy and crystal momentum (i.e.
conservation of total k-vector).
photon with an energy near a semiconductor.band
gap has almost zero
important process is called
radiative recombination, where an electron inmomentum. An
band annihilates a
hole in the valence band, releasing the the conduction
the electron is excess energy as a photon. If
near the bottom of the conduction band and the
valence band (as is hole is near the top of the
usually the case), this process is possible in
semiconductor, but impossible in an a direct band gap
indirect band gap one, because conservation
crystal momentum would
be violated. For radiative recombination to occur of
band gap material, in an indirect
the process must also involve the aborption or emission
where the phonon of a phonon.
momentum equals the difference between the electron
momentum. (It can also, instead, and hole
involve a crystallographic defect, which performs
ssentially the same role). The involvement of the phonon makes
this process much less
IKely to occur in a given span of time,
which 1s why radiative recombination is far
OWer in indirect band gap materials than direct band gap ones.
This is why light-
ing and laser diodes are almost always made of direct band gap materials, and not
ndirect band gap ones like silicon.
C Tact that radiative recombination is slow in indirect band gap materials
also means
under most circumstances, radiative recombination will be a small proportion of
daccombinations, with most recombination being non-radiati ve, taking place at point
or at grain boundaries. However, if the excited electrons are prevented form
S ng these recombination places, they have no choice but to eventually fall back into

ECDV-153
 slocation
a dislo
POPULAR PUBLICATIONS creating
be done by and
beneneath the
This can above energv
recombination. loop. the planes which raises tre
the valence band by radíatíve the negative pressure, cartor pass this
loop in the material. At the edge of elecironS
creating ae result that the
"dislocation disk" are pulled apart, crea
d
cOnduction hoSubstantially, with
the

cdge. to thar
semiconductor similar from a
c) Semiconductor Laser: active medium is a
2ser
diode is formed
sometimes
The laser diode is a laser where
the common type offormer devices are
The most The pumped laser
found in a light.emitting diode. electric crrent. optically
injected from
p-1junction and powered by diodes to distinguish them
referred to as injection laser fer. The
crystal wafe
a
the surface ofone above the other
diodes. very thin layer on region,
A laser diode is formed by dopinga Vpe_region and a p-Dpe
n-
crystal is doped to produce and semiconductor p- Juncüon
resulting in a p-n junction, or diode. classification of charge
form a subset off the larger causes the two species of
diodes laser diode of the p-n junction
Cr
uCrorward electrical bias across the
- be injected" from opposite sides
electrons form the n-
and electrons to p-doped, and
carrier holes region. Holes are injected from the charge carriers, foms as a
depletion any
LC semiconductor. (A depletion region, devoid of n- and p-type semiconductors
doped,
difference in electrical potential between charge injection in powering
result of the use of
are in physical contact). Due to the "injection lasers or
"injection
wherever they termed
lasers is sometimes may also be
most diode lasers, this class of lasers are semiconductor devices, they
laser diode" (ILD). As
diode
designation distinguishes diode lasers from
lasers. Either
classified as semiconductor
solid-stale lasers. lasers is the use of optical pumping. Optically
powering some diode semiconductor chip as the gain media,
Another method of use a lI-V
Lasers (OPSL) several
Pumped Semiconductor laser) as the pump source. OPSL offer
another diode from
and another laser (oftenparticularly in wavelength selection and lack of interference
advantages over ILDs,
structures. recombine or
internal electrode are present in the same region, they may
and a hole
When an electron spontaneous emission - i.e., the electron may
re-occupy
"annihilate" with the result being difference
state of the hole, emitting a photon with energy equal to the
the energy states invoived. (In a conventional
semiconductor junction
electron and hole
between the carried away
energy released from the recombination of electrons and holes is
diode, the as photons.) Spontaneous emission gives
lattice vibrations, rather han
as phonons, i.e., threshold similar properties to an LED. Spontaneous
the laser diode below lasing
sources ot
is necessary to initiate laser oscillation. but it is one among several
emission oscillating.
inefticiency once the laser is conventiona!
difference between the photon-emittung semiconductor laser and
The junction diodes lies in the use of a
phonon-emitting (non-light-emitung) semiconductor
physical and atomic structure confers the
different type of semiconductor, one whose so-called
hese photon-emitting semiconductors are the
possibility for photon emission.
ECDV-154
 ELECTRONICDEVICES
direct band gap semiconductors.
single-element semiconductors, The properties of silicon and germanium,
have band gaps that which are
low photon emission and are
all do not align in the way needed to
not considered "direct". materials, the so-callca
ompound semiconductors,
have virtually identical
Other
ermanium but use alternating crystalline structures as silicon or
arrangements of two different atomic species in
checkerboard-like pattern to break
the symmetry. The transition
between the materiais in
a
the alternating pattern creates
the critical "direct bandgap"
indium phosphide, gallium property. Gallium arsenide
antimonide, and galliun nitride
semiconductor materials that are all examples of compound
can be used to create junction
diodes
In the absence
of stimulated emission (e.g., lasing) conditions, that emit light.
coexist in proximity to one electrons and holes may
another, without recombining, for
"upper-state lifetime" or "recombination a certain time, termed the
time" (about a nanosecond for typical
laser materials), before they
recombine. Then a nearby photon with diode
recombination energy can cause energy equal to the
recombination by stimulated emission.
another photon of the same frequency, This generates
traveling in the same direction, with the same
polarization and phase as the first
photon. This means that stimulated emission
gain in an optical wave causes
(of the correct wavelength) in the injection region,
increases as the number of electrons and the gain
and holes injected across the junction
spontaneous and stimulated emission increases. The
processes are vastly more efticient in
bandgap semiconductors than in indirect direct
bandgap semiconductor; therefore silicon is
a common material for laser diodes. not
Some important properties of laser
diodes are determined by the geometry
cavity. Generally, in the vertical of the o otical
direction, the light is contained in a very
the structure supports only thin layer, and
a single optical mode in the direction perpendicular
layers. In the lateral direction, to the
if the waveguide is wide compared to the waveguide
wide compared to the wavelength is
of light, then the waveguide can support
lateral optical modes, and multiple
the laser is known as "multimode". These laterally
lasers are adequate in cases where one multi-mode
needs a very large amount of power, but not
small diffraction-limited
beam; for example in printing, activating chemicals, a
other types or pumping
of lasers.
In applications where a small focused beam is' needed, the waveguide
narrow, on must be made
the order of the optical wavelength. This way, only a single lateral mode is
Supported and one ends up with a diffraction-limited beam. Such single spatial mode
Evices are used for optical storage, laser pointers, and fiber optics.
ne wavelength emitted is a function of the band-gap of the semiconductor
and the
nodes of the optical cavity. In general, the maximum gain will occur for
photons with
Yslightly above
aTge most strongly.
the band-gap energy, and the modes nearest the gain peak will
If the diode is driven strongly enough, additional side modes may
large. Some laser diodes, such as most visible lasers, operate at a single wavelength,
that wavelength is unstable and changes due to fluctuations in curent or temperature.

Write down advantages and disadvantages of LEDs. [MODEL QUESTION

ECDV-155
 EOPULARPUBLICATIONS

Auswer:
Adntages of LEDDs
Lov
OW operating voltage, consumption make LEDS compatible with
electronic e,current and poc
current power
ectonie driva
drive cireuits.
vibration and allow them to be
Lsad in high resistance to mechanical shock and
used in severe environment
conditions.
ensure a longer operating lite line, thereby improving the overall reliability and
lowerine t
iowering the maintenance costs of equipment.
have low inherent noise levels and also high immunity to externialy generaled
LtDs
noise
LEDS exhibit linearity of radiant power output with forward current over a wide
range.

Limitations of LEDs
emperature dependence of radiant output power and wavelength.
Senstivity to damages by over voltage or over current.
3. Theonetical overall efficiency is not achieved except in special cooled or pulsed
conditions.

Operation of LEDs
The dominant operating process for LEDs is spontaneous emission. A photon of
appropriate energy can be absorbed by a semiconductor, creating an EHP in the process.
This is called optical absorption. Let us consider Fig. 2.10 (a) which depicts two energy
leveis in a semiconductor E, and E; where E, corresponds to the ground state and E to the
excited state. At room temperature, most of the electrons are in ground state.
When a photon of frequency greater than, or equal to, vi2 = (E; - E,Vh is incident on the
system, an electron in the ground state absorbs it and goes to the excited state: Howeve,
the excited state is unstable. So, after a short time, without any. external stimulus, the
electron comes back to the ground state emiting a photon of energy hv/2. The emitted
wavelength å is given by à =where E, is the band gapof the semiconductor.
E
This process is referred to as spontancous emission and schematically represented
is in

Fig. (iXb).
-
(E-E)
hvu
E (b)
(a)
Fig. (i): (a) Schematic showing the basic process of absorption
and (b) emission
are used
fraredLEDS are used in fibre-optic communication systems where silica fibres
optical signal over long distances. An important application of infrared LED
to guide the
ECDV-156
 ELECTRONIC DEVICES
is inopto-1S0lators where an
input electrical signal
enerated and subsequently is applied to the LED. LIgnt
detected by a photodiode
signal as a current and converted back to an
flowing through a load ciecnca
transmission at the speed of light resistor. Opto-isolators allow signa
and are electrically isolated. In this context, it may
noted that the emitted wavelength De
2 is given by
he
E
where E Is the band gap of the semiconductor. The probability of direct (radiative)
transition is high in direct band gap
semiconductors. Hence, GaAs1,P, (y <0.45) is
for light emission in the wavelength used
range of 627-870 nm. For y> 0.45, the material has
an indirect band gap. So, special
recombination centres have to be introduced to facilitate
radiative recombination. Incorporation
of nitrogen results in the formation of such a
recombination centre. It introduces an electron
trap level very close to the bottom of the
conduction band and greatly enhances the
probability of radiative recombination. In
general, red LEDs are fabricated on GaAs
substrates while orange, green, and yellow
LEDs are fabricated on GaP substrates on which
a graded GaAs,P, layer is grown by
epitaxy. In optical communications, to take advantage
of the I.3-um and 1.55-um low-
loss windows in optical fibers, InGaAsP substrates
are used.
At a low forward voltage, the LED
current is dominated by the non-radiative
recombination current, mostly due to surface recombination. At higher forward voltages,
the radiative diffusion current dominates and light is emitted as
the injected minority-
caiers recombine with the majority-carriers through a radiative-recombination process
Finally, at very high forward voltages, the series resistance limits the current. Figure
(i)
shows the symbol of an LED.

Fig. (ii): The symbol of an LED

ECDV-157
POPULARPUBLIÇATIONS

INTEGRATED CIRCUIT

Chapter at a Glance
on insulator (SOI) is
Process: The accomplishment of implantation to form silicon
t
MOX n form Si^N4 in a process
called SIMNI or
nign energy implant of is called SIMOX
to
by performing hi
a
form SiO, in a process that
Cergy implant ofO' to or nc Cireuit,
The SIMOx
O r5
process is advantageous for the following reasons: increased specd
ncreased radiation hardness and increased packing density
pattem of geometric shapes on
Lithography is the process of transferring
oBraphy:
to a thin layer of radiation sensitive material know as
resist covering whole surfaces of
dsk
the semiconductor substrate.

Multiple Choice Type Questions

[MODEL QUESTION]
1. CMOS technology is used in developing
a) Microprocessor b) Microcontroller
Digital logic circuits
c) d) All of the mentioned
Answer: (d)
[MODEL QUESTION]
2. CMOS has
high noise margin
a) b) high packing density
c) high power dissipation d) high complexity
Answer: (6)
[MODEL QUESTION]
3. Oxidation process is carried out using
a) hydrozen
b) low purity oxygen
d) nitrogen
c) sulphur
Answer: (6)
Short Answer Type Questions
of Lithography in fabrication of VLSI chips?
1. What is the function [MODEL QUESTION]

Answer: patern ot geometric shapes on a mask to a thin

Lithography is the process of transierring the
of radiation sensitive material know as resist covering whole surfaces of
laver
semiconductor substrate.

What is the function of Lithography in fabrication of VLSI chips?

2. [MODEL QUESTION

Answer: ransrerng panern o geometric shapes on a mask to a thin

Lithoeraphy is the proces oI of the
radiation sensitive material Khow as resist covering whole surfaces
laver of
semiconductor substrate.
ECDV-158
 ELECTRONICDEVICES
3.Why Si02 is very useful
in IC fabrication?
Answer: [MODEL QUESTION]
siO, is used for the
following applications.
i) For acting as
mask for dopant
ii) For providing diffusion into silicon.
surface passivation
ii) For isolating one device
iv) For acting as gate. from other in
Integrated Circuit.
v)For providing electrical isolation.
4. What is Optical Lithography?
Answer: [MODEL QUESTION]
Formation of patterns
utilizing prOximity or / images in a photoresist due to visible or ultraviolet
projection printing radiatior by
is called Optical Lithography.
5. What is lon Lithography?
Answer: [MODEL QUESTION]
lon Lithography systems are
masked beam system.
of two types namely scanning
focussed beam systems and
When an ion beam is
used to expose resist, higher
resolution
of it is in the repairing of masks for is being obtained.
The main application
the ion sources
may be in the form of field ionization lithography. In this technique,
strong electric field source. lons are produced
and near a pointed tungsten tip, in the
lignified material surrounding source of material is a gas
tip. or a
6. Classify different kinds of ICs.
Answer: [MODEL QUESTION]
Integrated circuits are classified
into Semiconductor IC and Film IC based
scheme. on fabrication
Depending on scheme of deposition and thickness of deposited films, film ICs
divided into are further
thick film and thin film ICs.
7.What
is hybrid IC? [MODEL QUESTION]
Answer:
ybrid circuit IC (HIC) is a kind of microcircuit that represents a combination
of passive
ICments and discrete active elements disposed on a common insulating
substrate.
.What are the features of thin film ICs? [MODEL QUESTION]
Answer:
h features of thin film ICs are
Resistors
)
and capacitors of high precision values are formed from it.
Deposition of this kind of film are being done at a much faster rate.
A low rate of film growth allows easy control of film thickness.
.Wat are the advantages of lon implantation mechanism? [MODEL QUESTION

ECDV-159
POPULAR PUBLICATIONS

Answer: makes it versatile tool

implantation process
The controllability and repr oducibility of ion can be removed by
that it causes
tor yielding finer-scale devices. The lattice damag
USing rapid thermal processing with minimal ditrus
MODEL QUESTION
10. What is SIMOX process?
Answer: or by
on insulator (SO1) done
is
silicon
plishment of implantation nto form a process
called SIMNI or by
erf
performing a high energy implant of to form SiN in that
th: is called SIMOX.
SiOz In a pro
Pertorming a high energy implant of O' to form reasons: increased speed of the
process is advantageous for the following
A
circuit, increased radiation hardness and increased
packing denisiuy
[MODEL QUESTIONJ
11. What are the fast diffusants in silicon?
Answer: form deep level traps and
uroup I and VIII elements are fast diffusants in silicon. They
currents.
affect minority-carrier life time and junction leakage
[MODEL QUESTIONJ
12. What is channeling?
Answer: by minimizing lattice damage is
inside the target
The mechanism for placing ions deep
called channeling.
making this a useful technique.
There are so many practical problems for order of 1° wafer tilt and beam
Channeled ion profile is sensitive to charges in the
surface films.
divergence and ions are scattered by amorphous

LLong Answer Type Questions

crystal, crystal is measured at seed end with the help
o

1. For phosphorus doped

0.9 mm. If (V/) ratio is 202 for 0.8 solidified
Four-Probe method, having spacing ofexpected range. [MODEL QUESTION]
find out feed end doping and
fraction,
Answer:
We know, resistivity, p=|2D
0,09).2-cm
p=(20x2x3. 15x
Moreover we know,
5x104 from plot of resistivity concentration]
[Obtained
C 0.35x(1-0)
o0.35-1

= 1.42x 10 atoms/cm
1.42x10"(1-0.8)-=3.23x105 atoms/ec
Cy=0.8x

ECDV-160
 QUESTION 2014
Group-A
(Multiple Choice Type Questions)

Answer any ten questions:

1.

PIN diode has

a) p andn layers separated by I layer b) p+ and n+ layers separated by| layer
c) p-andn-layers separated by I
layer d) either (b) or (c)

i) Under high electric fields, in a semiconductor

with increasing electric field
a) The mobility of charge carriers
decrease b) the mobility of charge carriers increase
c) velocity of carriers
saturate d) both (a) and (c)
ii) Compared to field effect phototransistors,
bi-polar phototransistors are
a) a more sensitive and faster b) more sensitive and slower
c) less sensitive and slower d) less sensitive and faster

iv) Consider the following statements:

The threshold voltage of MOSFET can be increased by
1. Using a thinner gate oxide
2. Reducing the substrate concentration
3. Increasing the substrate concentration

a) 3 alone correct b) 1 and 2 correct

c) 1 and 3 correct d) 2 alone correct

v)Effective mass of electron depends on

b) band gap
a) curvature of band
c) doping concentration d) temperature

vi) Photodetector diodeis

b) square law device
a) triangular device
d) both (a) and (b)
c) linear device

VI) Hall voltage is proportional to

b) magnetic field
a) velocity
d) both (a) and (b) perpendicular to velocity
c)both (a) and (b) parallel to velocity
semiconductor depends on
concentration of a given
intrinsic carrier b)temperature
a) bandgap d) none of these
C) bandgap and temperature
 POPULAR PUBLICATIONS

Schottky barrer diode is

between the metal and the semiconductor of a
t
a the difference between the metal work function and semiconductor electron aftinity
work function
c) the diffo Deween the metal work function and semiconductor
difference between work function
the metal electron affinity and semiconductor
d) the
Crence between the metal electron affinity and semiconductor elecr
X)A trensistor
configuration with the lowest current gain
a) common base b) common emitter
c) common collector emitter-follower
d)
xi) Varactor diodes are commonly
used
a) as voltage controlled
capacitance b) as a constant current source
c) as voltage multiplier
d) as a constant voltage source
XIl) DiTrusion constant of holes and electrons are in ratio 4:1. Then the mobility of holes and
electro ns will be in the ratio
a) 4:1 b) 16:1
c) 1:4 d) 1:16

Group B
(Short Answer Type Questions)

2. Describe briefly the basic structure of a Schottky diode and explain why it is suitable in high
frequency operation.
See Topic: P-N JUNCTION, Short Answer Type Question No. 2.

3. With E-K diagram, explain why LED emits light but PN junction rectifier doesn't.
See Topic: P-N JUNCTION, Short Answer Type Question No. I(2d Part).

4. What is fill factor? What is the expression for short circuit current and open circuit voltage for
solar cell?
See Topic: OPTO-ELECTRONICS, Short Answer Type Question No. 4.

5. a) VWhat isSCR? Point out its major applications.

b) By using two transistors analogy, brietly describe the basic operation of two terminais SCR.
a)&bi See Topic: BIPOLAR JUNCTION TRANSISTOR, Short Answer Type Question No. 5.

6 What is the mass action law tor tne cafner concentration in a semiconductor? Write down the
abical exoression for Fermi Dirac probability function [(E)] and plot
f(E) vs ElEF
for three different temperatures 7= 0K, 300K, 2000K and explain it
ENERGY BANDS & CURRENT CARRIERS IN SEMICONDUCTORS, Short Answer
See Topic:
15.
Type Question No.
ECDV-162
 ELECIRONIC DEYICES

Group-C
(Long Answer Type
Questions)

7 a) What is heterojunction?
olain
Explai the carrier flow in metal-n-type Schottky
) diode under forward bias and reverse bias
condition.
Mhat are the differences between Ohmic contact
and Schottky contact?
Topic
nic: P-N JUNCTION Long Answer Type
See Question No. 17(a), (b) & (¢).

a What is meant by direct and indirect semiconductors?

HExplain with the help of a neat diagram and give
example of each category.

dShow that for intrinsic semiconductors, the energy of the Fermi level,
E, = where

E.,E, are energy of the conduction and valence bands respectively.

Se Topic: ENERGY BANDS & CURRENT CARRIERS IN SEMICONDUCTORS, Long Answer
Type Question No. 4(a), (b) & (c).

9. Draw the V-I characteristic of JFET and explain it. Draw FET small signal model. A JFET has
,4.SV, p =10m amp and I 2.5mA. Determine the transconductance.
See Topic: MOSFET, Long Answer Type Question No. 13.

10. a) Explain how the junction theory helps to understand the gate control over the channe
Current.

) Justify the reason of high doping of the gate compared to the channel doping
Se Topic: MOSFET, Long Answer Type Question No. 11.
11. Write short notes on any three of the following:
a) Varactor diode
b) Miller
indices
c)Voltage regulator circuit
d) Schottky
barrier diode
e) Avalanche and zener mechanism.
No. 21(e).
e opic: P-N JUNCTION, Long Answer Type Question
CARRIERS IN SEMICONDUCTORS, Long Answer
See Topic: ENERGY BANDS & CURRENT
ype
Question No. 8(a).

eelepic: Topic: P-N JUNCTION, Long Answer Type Question No. 21(d).
P-N JUNCTION, Long Answer Type
Question No. 21(u).
e)
SeeTopie: Question No, 21(h).
TION, Long Answer Type
P-N JUNCTI

ECDV-163
POPULARPUBLICATIONS

QUESTION 2015

Group-A
(Multiple Cholce Type Questlons)

Answer any ten questions

1.
ootential
wnen a positive voltage is applied to a p-n junction structure tho barrer
a) increases b) decreases
c) remains same d) none of theso

i) Electron transition in In-direct band gap semiconductor Invoives

a) a change of momentum of electron b) dependence on band gap
c) no change of momentum of electron d) none of these

ii) Effective electron mass depends on

a) curvature of band b) band gap
c) doping concentration d) temperature

iv) Instrinsic carrier concentratlon of a given semlconductor depends on

a) band gap b) temperature
c) bandgap and temperature d) none of these

v)Metal n-type semiconductor form ohmic contact if

a) PP 6)
PP
c) PP d) none of these

vi) In Schottky barrier diode, the current mechanism is due to

a) minority carrier b) majorlty carrier
c) both (a) and (b) d) none of these

vii) When a transistor ls used as switch its operatlon is confined to

a) cut-off region b) saturation region
c) active region d) both (a) & (b)
vii) Above pinch off votage In a JFET the drain current
a) decreases b) increases sharply
c) remains constant d) both ()& (b)

ECDV-164
 voltage applied ELECTRONICDEVICES
to the metal with
nen V<0 Coresponds to respect top-type
p-t
semiconductor in a MOS capacitor
a) accumulation
c)inversion b) depletion
d) strong inversion
nacitance of varactor
Capad diode can
a) doping
be changed
by varying
c) size of the diode b) biasing
d) all of these
A ransistor
connected in CB
configuration
a) high input resistance has
and low output
b) low input resistance resistance
and high output
clow input resistance and resistance
low output
d) high input resistance resistance
and high output
resistance
Quadrant of 1-V plot relevant
to operation of
a) 1st solar cell is
c) 3rd b) 2nd
d) 4th
Group B
(Short Answer Type
Questions)
2 Compare 'dnift"
and 'diffusion' transport
Se Topie: ENERGY in a semiconductor
BANDS & CURRENT Derive the Einstein
Type CARRIERS IN SEMICONDUCTORS, Relation.
Question No. 4
& 12.
Short Answer
What is a hetero-junction?
dagrams of How many types of
each types of hetero-junction, hetero-junctions are
considering straddling. possible? Draw
Se Topic:
ENERGY the band
Type
BANDS & CURRENT CARRIERS
Question No. IN SEMICONDUCTORS,
16. Short Answer
What is photovoltaic
effect? Write down the operating
e lopic: OPTO-ELECTRONICS, principle of solar cell.
Short Answer Type Question No. 1
& 2.
Sketch the cross
section
view of p-channel Depletion MOSFET
tpic: characteristics and transfer characteristics.
and explain with
neat sketch the
MOSFET, Long Answer Type
Question No. 1(a).
What
aIsBJT?power transistor? What are the special features of power transistor?
Signal
See
Topic
Compare with
pC:
small
BIPOLAR JUNCTION TRANSISTOR,
Short Answer Type Question No.
6.

ECDV-165
 POPULARPUBLICATIONS

Group-C
(Long Answer Type Questions)
7. a) What semiconductor physics? How can we
is Hall field? Why
Hall Effect is important in
calculate mobility of electron p-type semiconductor using nou Efact?
in
n a Hall experiment length of semiconductor specimen L = 10" cm, width W =l0 cm and
depth =10 cm
d and current through semiconductor substrate I, =1.0mA, applied voltage
12.5V, magnetic flux density B, = 500 gauss, Hall voltage Vy = -625 mV. What type of
m
carrier is there in semiconductor substrate? Calculate majority carrier concentration and
mobility.
c) What is quasi-Fermi level?
ee opic: ENERGY BANDS & CURRENT CARRIErS IN SEMIcONDUCTORS, Long Answer
Type Question No. 5(a), (b) & (¢).

8. a) Derive expressions for Built-in potential.

b) Define the diffusion capacitance of p-n junction diode and derive its expressIon.
)For a silicon one-sided abrupt junction with N, =2x10° cm and N, =8x10° cm
calculate the junction capacitance at zero bias and reversed bias of 4V (T= 300K).
See Topic: P-N JUNCTION, Long Answer Type Question No. 18(a), (6) & (c).

,
9. a) Explain working principle of Schottky Diode.
b) Describe punch-through effect in BJT.
c) For an ideal p-n-p transistor, the current components are given by =3mA, IE, =0.0 1mA

c2.99mA and Icn =0.001mA. Determine () the enitter efficiency 7. (i) the base transport
factor a. (ii) the common-base Current gain a, and (iv) cRO
d) Explain working principle of PNPN transistor.
a) See Topie: P-N JUNCTION, Long Answer Type Question No. 19.
b), c) & d) See Topic: BIPOLAR JUNCTION TRANSISTOR, Long Answer Type Question No. 5.

10. a) What is flat band voltage case of ideal MOSFET?

in

in case of real MOSFET depends on semiconductor doping.

b) How and why threshold voltage
oxide charge and oxide thickness?
following parameters
c) An ideal p-channel MOSFET has

W =15um, A, = 300cm* /V -s, L=1.3pm, a 350 A and -0.80. If transistor is operating

in non-saturation region at s 0.5, then calculate value of Transconductance g?
in channel length as drain voltage is increased in MOSFET
d)What is the effect of reduction
characteristics?
No. 14(a), (b), (¢) & (d).
Topic: MOSFET, Long Answer Type Question
See
ECDV-166
4Write short notes on any ELECTRONICDEVICES
three of the following
a) Tunnel diode
b) MOS capacitance
c) Effective mass
d) Ebres-Moll Model
e) Photo transistor.
s See Topic: P-N JUNCTION, Long
Answer Type Question
b) See Topic: MOSFET, No. 21(¢).
Long Answer Type
Question
See Topic: ENERGY BANDS & CURRENT No. 15(b).
Type Question No. 8(d). CARRIERS IN SEMICONDUCTORS,
Long Answer
d) See Topic: BIPOLAR JUNCTION
TRANSISTOR,
e) See Topic: OPTO-ELECTRONIcs, Long Answer Type Question No.
Long Answer Type 6(b).
Question No. 5(c).

QUESTION 2016

Group-A
(Multiple Choice Type Questions)

1.Choose the correct alternatives for any ten

of the following
) Energy bandgap of GaAs at 0 K is
a) 1.12 eV
b) 0.66 eV
c) 1.43 eV
d) 3.40 eV
i) According to the E-k diagram, Si is
a) direct bandgap
b) indirect bandgap
c) both (a) and (b) d) none of these

i) Boltzmann approximation is valid for

a) higher energy states b) lower
energy states
c) both (a) and (b) d) None of these

) Under forward bias, p- n junction current flows mainly due to

a) diffusion b) drift
c)both (a) & (b) d) none of these

9 Intrinsic Fermi level(Ewill be slightly above the midgap energy level (Emp, if

a) m, >m, b) m, <m,

c) mm, d) any one of these

ECDV-167
POPULARPUBLICATIONS

Vi)
Flat-Band voltage
of n-channel enhancement type MOSFET is
a) positive b) negative
c)positive or negative d) zero

viu) Which one of

the following is not a voltage controlled vice?
a) MOSFET
b) IGBT
c) BJT d) JFET

vii) Pinch-off voltage

of FET depends on
a)
channel width of channel
b) doping concentration
c) applied voltage
d) both of (a) and (b)

) For design of high

speed electronic system the preferred one snoud
a) Si n-MOs
b) Si p-MOSs
c) GaAs n-MOS d) GaAs p-MOS

x) Which of the following

is not a negative resistance device?
a) Zener diode
b) IMPATTT diode
c) Gunn diode d) LED

X1) It a voltmeter
is connected across the terminal of
an unbiased Germanium p-n junction diode.
The voltmeter reading will be
a) OV
b) 0.3V
c) 0.6V
d) 1.0V

Group-B
(Short Answer Type Questions)

2. What do you mean by effective mass? Derive the

expression for effective mass. How
effective mass differ from actual mass and in which can
condition effective mass will
negative and infinity? be positive,
See Topic: ENERGY BANDS & CURRENT CARRIERS
IN SEMIONDUCTORS,
Type Question No. 9. Short Answer

3. What is degenerate semiconductor (explain

with band diagram)? Draw
a Tunnel diode and explain the occurrence of the l-V characteristics of
negative differential resistance
characteristics. in the l-V
See Topic: P-N JUNCTION, Short Answer Type Question No.
3.

4. What is early effect? Explain how the eariy erect

modiies the input current in
CE configuration of an n-p-n transistor? case of CB and
See Topic: BIPOLAR JUNCTION TRANSISTOR, Short
Answer Type Question
No. 4,
ECDV-168
 ELECTRONICDEVICES
efine step graded a and linearly
graded
5ee
Der diffusion capacitance and transitionjunction.
Topie: P-N JUN
UNCTION, capacitance
See Short Answer Type
Question No. 8(a)
& (b).
a) What is
fill factor?
6
Derive the expressiorn tor
short circuit current
OPTO ELECTRONICS, and open circuit voitage
Se Topic: Short Answer Type for the solar cell
Question No. 4.

Group-Cc
(Long Answer
Type Questions)
7Explainthe working pnnciple of a
Zener diode and its
What is the difference between step use as a reference voltage device
graded and linearty graded
Define diffusion capaCitance and storage semiconductor PN junction?
Se Topic: P-N JUNCTION, capacitance in PN junction?
Long Answer Type Question No. 2(a), (b) &
(c).
& a) What is
photovoltaic effect?
b)What are quantum eficiency
and responsivity?
Write down the basic operating principle of
solar cell. Derive the expression for
&) See Topic: OPTO-ELECTRONICS, Long Vot
Answer Type Question No. 2(a) &
bSee Topic: P-N JUNCTION, (b).
Short Answer Type Question No. 4.

9a)What do you mean by MOS capacitor?

y Draw the C-V dependence curve
and specify the three different region in the
Define fiat band voltage with respect to MOS devices. graph.
See Topic: MOSFET, Long Answer Type Question No. 1(bi).
y See Topic:
MOSEET, Long Answer Type Question No. 1(b(i).
dSee Topic: MOSFET,
Long Answer Type Question No. 1(b)Mi).

0 a) Explain case
band bending and channel inversion in of n channel enhancement type
MOSFET.
9) What
is channel length modulation?

Deemine the probability of occupancy of a state that is located at 0.359eV above E, at

T300K
b See Topic: MOSFET, L.ong Answer Type Question No. 9.
Topic: MoSFET, Short Answer Type Question No. 2
1.
teSCRthe shot notes any three of the following
a)
b) Diode
Switching
Tunnel diode
) TRIAC
e) Diode
Capacitance
ECDV-169
POPULARPUBLICATIONS

Type Question No. 6{c).

a) See Topic:
BPOLAR JUNCTION
JUNCTION TRANSISTOR, Long Answer
TRANSISIO
LAR
b) See Topic: P-N Question1No.
21 (i).
JUNCTION, Long Answer Type
c)See Topic: P-N JUNCTION, Question hio. 21(c).
ong Answer Type 21g).
d) See Topic: P-N
JUNCTION, Long Answer Type Quest
See Topic: P-N JUNCTION, Long Answer Type Question

QUESTION 2017

Group-A
(Multiple Choice Type Questions)

1. Choose the correct alternatives for any ten of the folloing

i) Solar cell is a
a) photodetector b) photodiode
c) photovoltaic device d) optical emitter

i) Which of the following is not a negative resistance device?

a) Tunnel diode b) Zener diode
c) Impatt diode d) Gunn diode

i) If V is the voltage applied to the metal with respect to the p-type semiconductor in a MOs
capacitor then Ve 0 corresponds to
a) Depletion b) Accumulation
c)Inversion d) Strong inversion

iv) When a positive voltage is applied to a p -njunction, the barrier will be

a) decreased b) increased
c)unchanged d) none of these

v) Effective electron mass depends on

a) temperature b) doping concentration
c) bandgap d) curvature

vi) In case of BJT, the base idth should be narrow to minimize

a) drift current b) diffusion current
c) recombination current d) tunneling current

vil) To turn off SCR, it is necessary to reduce its current to less

a) Trigger current b) Holding current
c) Break-Over current d) none of these

ECDV-170
 ELECIRONIC DEYICES
vii) Photodiode operates in
a) reverse bias
c)without bias forward bias
b)

d) none of these
)A transistor configuration having
highest current
a) Common base gain
c) Common emitter b) Common collector
d) Emitter foliower

Metal n- type semiconductor form Ohmic

contact if
a) m
b) pm =p%
)Pm20s
d) Pm
x)Intrinsic carrier concentration
depends on
a) band gap
b) temperature
c) both (a) & (b)
d) none of these

xi) Above Pinch off voltage in a JEFT the current

a) decreases b)
becomes saturated
c) increases sharply
d) none of these

Group B
(Short Answer Type Questions)

2. a)What is density of states?

b) Explain the plot of Fermi Dirac distribution
-
function with energy for different temperatures
c)3 volt is applied across a 1 cm long Si bar. Determine mobility with the drift velocity is 104
cm/ s
)&b) See Topie: ENERGY BANDS & CURRENT CARRIERS IN SEMICoNDUCTORS, Short
Answer Type Question No. 14(a) & (b).
See Topic: ENERGY BANDS & CURRENT CARRIERS IN SEMIcONDUCTORs, Short Answer
Type Question No. 17.

3. a)
What are mobility and conductivity?
b) What are the effects of temperature and doping on mobility?
See Topic:
ENERGY BANDS & CURRENT CARRIERS IN SEMICONDUCTORS, Short Answer
Type Question No.
3(a) & (b).

What is meant by DC operating point or Q points the context of transistor characteristics?

in
a)
D)
What is load line? Why is biasing necessary?
e fopic: BIPOLAR JUNCTION TRANSISTOR, Short Answer Type Question No. 3.

ECDV-171
POPULARPUBLICATIONS

5.
What is early effect? current in case of CB and
Explain how, earty effect
effect modifies the input
mo
CE configuration
Owhe the
of an n-p-n transistor.
BPOLAR JUNCTIoN TRANSISTOR, Short Answer Type Question
or ol an
and gap and indirect band gap semiconductor? Draw the E-K diagram
GaAs
ee lopic: ENERGY BANDS
& cURRENT CARRIERS IN
SEMICONDUCTORS, Short Answer
Type Question No. 10.

Group-C
(Long Answer Type Questions)

7. a) Draw the VI characteristics of JFET &explain

it
b) Draw the small signal model
JFET has ,=4.5V, Is =10mmA and 1, =2.5 mA. Determine the transconductance
See Topic: MOSFETS, Long Answer Type Question No. 8(a). (b) & (©).

8. a) Describe briefñy the principle of operation of a tunnel diode. Draw the L-V characteristics and
mention the -1e resistance region.
b) What is Thermal runway?
c) What is photo transistor?
See Topie: P-N JUNCTION, Long Answer Type Question No. 15(a), (b) & (c).

9. a) Derive the equation for the different curent components in a BUT by Ebers- Moll model.
See Topic: BIPOLAR JUNCTION TRANSISTOR, Long Answer Type Question No. 4.

b) Descrbe the basic structure of schottky diode and explain why it is suitable for high frequency
operation.
See Topic: P-N JUNCTTON, Long Answer Type Question
No. 16.

contact and ohmic

10. a)What is heterojunction? What are the difference between schottky
contact?
See Topic: P-N JUNCTION,
Long Answer Type Question No. 17(a) & (c).

the energy of Femi level, E =(E + E, )/2, where Ec

b)Show that for instrinsic semiconductor,
conduction band and valance band.
and Ev are energy of
BANDS & CURRENT CARRIERS IN SEMICONDUCTORS, Long Answer
See Topic: ENERGY
Type Question No. 6.

ECDV-172
Write the short notes any three ELECTRONICDEYICEs
a) Varactor diode of thefollowing
b) Hall effect
c) Effective cell
d) Solar cll
e) PIN photodiode
Channel length modulation.
See Topic: P-N JUNCTION, Long
b) See Topic: ENERGY Answer Type
BANDS & Question No. 21(e).
Type Question No. 8(c). CURRENT
CARRIERS IN SEMIcoNDUCTORS,
c See Topic: ENERGY BANDS Long Answer
Type Question No. 8(e).
& CURRENT
CARRIErS IN SEMICONDUCTORS,
d) See Topic: OPTO-ELECTRONICs, Long Answer
e) See Topic: OPTO-ELECTRONICS, Long Answer Type Question
No. 5(b).
See Topic: MOSFET, Long Answer Long Answer Type Question No. 5(a).
Type Question No.
15(c).

QUESTION 2018

Group A
(Multiple Choice Type Questions)

1.Choose the correct alternatives

for any ten of the following
The unit of Density of State Function is
a) numberlunit energy/ unit volume
b) energy/ unit volume
c) energy/ unit area
d) None of these

) K-space diagram
in a crystal is a plot of
a) electron density versus momentum
b) electron energy versus momentum
c)quantum number versus momentum
0) electron energy versus
density of energy states

) Intrinsic carrier concentration

is given by
a) n,
=nPo b) n, = Poln,
c) n,= nPo d) , Po

Example of pentavalent impurity s

a) Boron b) Bismuth
c) Antimony d) Phosphorus

ECDV-173
POPULAR
PUBLICATIONS

v) Conductivity
is defined
as the ratio of
a) drift current
density to electric
b) drift current field
density to practical
c)particle flux density gradient
to particle density
d) drift velocty gradient
to electric field
vi) Mobility
is a parameter
which relates
a) drift current
density to electric
c) resistance field b) carrier dift velocity to electric field
to current
d) mobility to diffusion coefficient
vil) Junction capacitance
of a pn junction
a)the capacitance under is
forward bias
c) the capacitance under b) the capacitance under no bias
reverse bias d) None of these
vii) External Quantum
Efficiency is
a) the ratio of reflected to
incident photons.
b) the fraction of current
that produces luminescence
c) the relative number
of photons absorbed
d) the ratio of per unit distance
emitted photons to generated
photons
ix) Cut-off frequency
is the frequency at which the magnitude
a) Of the CE current
gain is unity b) Of the CB current gain
c) Of the CC current gain is unity is unity
d) None of these
x)Inverse active mode is the condition in
which
a) B-E is forward biased and B-C junction
is reverse biased
b) B-E is reverse biased and B-C junction is forward
biased
c)B-E is forward biased and B-C junction is
forward biased
d) B-E is reverse biased
and B-C junction is reverse biased

xi) Strong inversion occurred in N-Mosfet for condition

a) = pF
b) qnS=2oF
=
c)oS 0 d) pS< pF
xii) A D-MOSFET can operate in the
a) depletion mode only b) enhancement
c) depietion mode and enhancement mode mode only
d) low impedance
mode

ECDV-174
 ELECTRONIC DEVICES
Group-B
(Short Answer
Type Questions)
ot Depletion Capacitance?
Whatis
is
2 Establish a
e N JUNCTON,
Topic: P-N. mathematcal relation of the depletion capacitance
Short Answer Type
Question No. 11.
Explain the operation of a Solar Cell
Tanic:
OPTO-ELECTRONICS,
Short Answer Type
Question No.2.
Vhat
What are differences between step
graded and linearly
Topic: P-N JUNCTION, Long graded semiconductor PN junction?
Answer Type Question
No. 2(b).
Derive the drift equation of curent for electrons
Relationship? and holes. What do you mean
by Einstein
Se Topic: ENER Y BANDS & CURRENT
CARRIERS IN SEMICONDUCTORS,
Type Question No. 18. Short Answer

6 Drawand explain E-R diagram for

a direct and indirect and
sutable example. band gap semiconductor withn
Se Topic: ENERGY BANDS & CURRENT
CARRIERS IN SEMICONDUCTORS,
Type
Question No. 19. Short Answer

Group-C
Long Answer Type Questions)
. Whatis early effect? Explain how it influences the input
characteristics of a BJT
tiguration. Draw the output characteristics of BJT used in CB
in CB
configuration. Indicate different
pons in the characteristics
and explain them. What do mean by Pinch-off condition in JFET?
refty describe it.

3&4
.a) &
Part: See Topic: BIPOLAR JUNCTION TRANSISTOR, Long Answer Type Question
(b).
FRrt:See Topic: MOSFET, Short Answer Type Question Na. 3.

3) What is photovoltaic
effect?
in
Wrte
how an LED works as a source of a light.
the basic operating principle of solar cell. Derive the expression for Voc.
HS opic: OPTO-ELECTRONICS, Long Answer Type Question No. 2(a) & (b).
Opic: OPT0-ELECTRONICS, Short.Answer Type Question No. 4.

Derive way are they different from

instein relationship. What are quasi-Fermi levels? what
Fetm
In
energy
"9y level? Show that in case of intrinsic
semiconductor, Fermi level ies at the midway of
e energy
bandgap

ECDV-175
POPULARPUBLICATIONS
SEMICONDUCTORS, Long Answe
See Topic: ENERGY BANDS & CURRENT CARRIERS IN
Type Question No. 7.
diode. What de
10. With the help of energy characteristics of a tunnel
band diagram, explain the V phenomena? Mention an
conditions for tunneling
ae stance? What are the
two applicatione of tunnel can be used as oscillator.
Jusmy.
pucations diode. Tunnel diode
Sce Topic: P-N JUNCTIOx, Long Answer Type Question No. 20.

11. Write a short note on any three of the following

a) CMOS Inverter
b)SCR
c) Schottky barrier diode
d) MOS capacitance
e) Hall Effect
Photolithography
a) See Topic: MOSFET, Long Answer Type Question No. 15(d).
b) See Topic: BIPOLAR JUNCTION TRANSISTOR, Long Answer Type Question No. 6{e).
) See Topic: P-N JUNCTION, Long Answer Type Question No. 21(a).
d) See Topic: MOSFET, Long Answer Type Question No. 15(b).
e) See Topic: ENERGY BANDS & cURRENT CARRIERS IN SEMICONDUCTORS, Long Answer
Type Question No. 8(c).
) See Topic: MOSFET, Long Answer Type Question No. 15(a).

ECDV-176