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XII Phys Ch-14 (Semi-Conductors)

Chapter-14
(Semi - Conductors)
 Classification of Metals, Conductors, and Semi-conductors:
On the basis of the relative values of electrical conductivity (σ ) or resistivity (ρ = 1/σ ), the solids are
broadly classified as:
(i) Metals: Possess very low resistivity (or high conductivity).Ex. copper, iron, silver etc.
ρ ~ 10–2 – 10–8 Ω m
σ ~ 102 – 108 S m–1
(ii) Semi-conductors: Possess resistivity or conductivity intermediate to metals and insulators. Ex.
Si, Ge etc.
ρ ~ 10–5 – 106 Ω m
σ ~ 105 – 10–6 S m–1
(iii) Insulators: Possess high resistivity (or low conductivity). Ex. Glass. Rubber .
 Semi-conductors are of two types:
(i) Elemental semi-conductor − Example: Si and Ge
(ii) Compound semi-conductor − Example: CdS, GaAs, CdSe, InP, etc.

 Energy Band: The range of energies possessed by an electron in a solid is called energy band.
 Valence band: The electrons in the outermost orbit of an atom are called valence electrons. A band
which is occupied by the valence electrons or a band having highest energy is defined as valence band.
The valence band may be partially or completely filled. This band can never be empty.
 Conduction band: In certain materials the valence electrons are loosely attached to the nucleus. At
ordinary temperature some valence electrons get detached to become free electrons. These electrons
are responsible for the conduction of current. So they are called conductions electrons and the band
(range of energies) possessed by conduction electrons are known as conduction band. This band may
be an empty band or partially filled band.
 Forbidden energy gap: The separation between valence band and conduction band is known as
forbidden energy gap. If an electron is to be transfered from valence band to conduction band,
external energy is required, which is equal to the forbidden energy gap.
 Band Theory of Solids:

Let Si or Ge crystal contains N atoms. The electron energy will be same if all the atoms are separated from
each other by a large distance. In a crystal, the atoms are close to each other (2 to 3 Å) and therefore the
electrons interact with each other. The overlap (or interaction) will be more felt by the electrons in the
outermost orbit while the inner orbit or core electron energies may remain unaffected. For Si, the outermost
orbit is the third orbit (n = 3), while for Ge it is the fourth orbit (n = 4). The number of electrons in the
outermost orbit is 4 (2s and 2p electrons). Hence, the total number of outer electrons in the crystal is 4N. So,
out of the 4N electrons, 2N electrons are in the s-states and 2N electrons are in the p-states.
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XII Phys Ch-14 (Semi-Conductors)
Suppose these atoms start coming nearer to each other to form a solid. The energies of these
electrons in the outermost orbit may change due to the interaction between the electrons of different atoms.
The 6N states for l = 1, spread out and form an energy band [region B in Figure]. Similarly, the 2N states
for l = 0, split into a second band separated from the first one by an energy gap.
In the region C, no energy gap exists where the upper and lower energy states get mixed. Finally, if the
distance between the atoms further decreases, the energy bands again split apart and are separated by an
energy gap Eg (region D). The total number of available energy states 8N has been re-apportioned between
the two bands (4N states each in the lower and upper energy bands). Therefore, lower band ( called the
valence band) is completely filled while the upper band is completely empty. The upper band is called the
conduction band.

 Energy band diagram:

 Metal or conductors:
 Conduction band is partially filled and the valence band is partially empty or the conduction and
valence band overlap.
 Due to overlap, electrons can easily move into the conduction band. This situation makes a large
number of electrons available for electrical conduction.
 When the valence band is partially empty, electrons from their lower levels can move to higher
levels making conduction possible.

 Insulators:
 In an insulator, the forbidden energy gap is very large. In general, the forbidden energy gap is
more than 3eV and almost no electrons are available for conduction. The electron cannot be
excited from the valence band to the conduction band by thermal excitation.

 Semiconductors:
 A finite but small band gap (Eg < 3 eV) exists. Because of the small band gap, at room temperature
some electrons from valence band can acquire enough energy to cross the energy gap and enter the
conduction band. These electrons (though small in numbers) can move in the conduction band.
Hence, the resistance of semiconductors is not as high as that of the insulators.
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XII Phys Ch-14 (Semi-Conductors)

(1) Intrinsic Semi-conductor:

A semiconductor which is pure and contains no impurity is known as an intrinsic semiconductor. In an
intrinsic semiconductor, the number of free electrons and holes are equal. Common examples of intrinsic
semiconductors are pure Ge and Si.

(The crystal structure of Ge/ Si in 2-D)

The following points about intrinsic semiconductor:
 In intrinsic semi-conductors, the number of free electrons ne is equal to the number of holes nh.
That is, ne = nh = ni
Where,
ni → Number density of Intrinsic carrier
nh → Number density of holes in valence band.
ne → Number density of free electrons in conduction band.
 The number of free electrons or holes in an intrinsic semiconductors is given by
ne  nh  AT 3 / 2 e  Eg / 2 kT
 The total current, I is thus the sum of the electron current Ie and the hole current Ih:
I = Ie + Ih
 An intrinsic semi-conductor will behave similar to an insulator at T = 0 K

 Doping:
The process in which desirable impurity atoms are added deliberately to a pure semiconductor so as to
modify its properties in a controlled manner is called doping. The impurity atoms are called dopants.
The semiconductor containing impurity atoms is known as impure or doped or extrinsic semiconductor.
There are three different methods of doping a semiconductor.
(i) The impurity atoms are added to the semiconductor in its molten state.
(ii) The pure semiconductor is bombarded by ions of impurity atoms.
(iii) When the semiconductor crystal containing the impurity atoms is heated, the impurity atoms diffuse into
the hot crystal.
The doping material is either pentavalent atoms (bismuth, antimony, phosphorous, arsenic which has five
valence electrons) or trivalent atoms (aluminium, gallium, indium, boron which have three valence
electrons).
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XII Phys Ch-14 (Semi-Conductors)
 Hole concept:
At absolute zero temperature each of the valance electrons of semiconductor is bound by covalent bond. The
atoms of the crystal perform thermal oscillations at the room temperature. This result in the breaking of
several covalent bonds and electrons became free which responsible for electrical conduction. Deficiency of
electron is created at the place from where the electron became free. Hence the deficiency of electron is
known as hole. Thus we get two types of currents in a semiconductor,
(i) Due to motion of free electron (Ie)
(ii) Due to motion of bound electron or hole (Ih)
(2) Extrinsic Semi-conductor:
An extrinsic semiconductor in which an impurity with a valence higher or lower than the valence of the pure
semiconductor is added, so as to increase the electrical conductivity of the semiconductor.
There are two types of extrinsic semi-conductors are:
(i) n-type semi-conductor
(ii) p-type semi-conductor
(i) n-type semi-conductor:
When a small amount of pentavalent impurity is added to a pure semiconductor is known as n-type
semiconductor. The addition of pentavalent impurity provides a large number of free electrons in the
semiconductor crystal. Pentavalent atoms such as arsenic or phosphorous or antimony or bismuth has five
valence electrons which will replace Si or Ge atoms. Pentavalent dopant donates one extra electron for
conduction and hence, is known as donor impurity.
The ionisation energy required to set this electron free is very small ( ~ 0.01 eV for germanium, and 0.05 eV
for silicon, to separate this electron from its atom. This is in contrast to the energy required to jump the
forbidden band (about 0.72 eV for germanium and about 1.1 eV for silicon) at room temperature in the
intrinsic semiconductor.
The electrons are the majority carriers and holes are the minority carriers. Therefore, they are called n-type
semi-conductors. For n-type semi-conductors, ne >> nh

(ii) p-type semi-conductor:

When a small amount of trivalent impurity is added to a pure semiconductor is known as p-type
semiconductor. The addition of trivalent impurity provides a large number of holes in the semiconductor.
Dopant has one valence electron less than Si or Ge. Therefore, the atom can form covalent bonds with three
neighbouring Si atoms, but does not have any electron to offer to the fourth Si atom. Therefore, the bond
between the fourth neighbour and the trivalent atom has a vacancy or hole.

Hole is available for conduction. One acceptor atom gives one hole. Holes are the majority carriers and
electrons are the minority carriers. So they are called p-type semiconductor. For p-type semi-
conductor, nh >> ne
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XII Phys Ch-14 (Semi-Conductors)
The electron and hole concentration in a semiconductor in thermal equilibrium is given by ne .nh  ni2
 Energy band diagram of the semi-conductors at T > 0 K:

n-type semi-conductor p-type semi-conductor

 Difference between Intrinsic Semiconductor and Extrinsic Semiconductor:

Intrinsic Semiconductor Extrinsic Semiconductor
It is a pure semiconductor material with no It is prepared by doping a small quantity of impurity
impurity atoms in it. atoms to the pure semiconductor.
The number of free electrons in the conduction The number of free electrons and holes is never equal.
band and the number of holes in valence band is There is an excess of electrons in n-type semiconductors
exactly equal. and an excess of holes in p-type semiconductors.

 p-n Junction:
If one side of a single crystal of pure semiconductor (Ge or Si) is doped with acceptor impurity atoms and
the other side is doped with donor impurity atoms, a p-n junction is formed. p- region has a high
concentration of holes and n- region contains a large number of electrons. Therefore, the holes diffuse
from p-side to n-side and electrons diffuse from n-side to p-side.
Two important processes occur during the formation of a p-n junction: diffusion and drift. When an electron
diffuses from n to p, it leaves behind it an ionised donor on n-side. The ionised donor (+ve charge) is
immobile as it is bounded by the surrounding atoms. Therefore, a layer of positive charge is developed
on n-side of the junction. Similarly, a layer of negative charge is developed on the p-side.

 Properties of p-n junction:

 This space-charge region on either side of the junction together is called depletion region.
 The positive space-charge region on n-side of the junction and negative space-charge region on p-
side of the junction, appearing as electric field, is developed and directed from + ve charge to − ve
charge.
 Due to the field, an electron from p-side moves to n-side and a hole from n-side of the junction moves
to p-side.
 The motion of charge carriers due to electric field is called drift current and is opposite in direction
to the diffusion current.
 Initially, diffusion current is large and drift current is small. As diffusion continues, the space charge
regions on either side of the junction extends, thereby increasing the electric field strength and hence
drift current. The process continues until the diffusion current is equal to drift current.
 Thus, a p-n junction is formed. Under equilibrium, there is no net current.
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XII Phys Ch-14 (Semi-Conductors)
 Loss of electrons from the n-region and gain of electron by the p-region causes a difference of
potential across the junction of two regions. This potential tends to prevent the movement of electron
from n to p region. Therefore, it is called a barrier potential.

 Semi-conductor Diode:
 A semi-conductor diode is basically a p-n junction with metallic contacts provided at the ends for the
application of an external voltage.
 A p-n junction diode is symbolically represented as shown in the figure below.
 The direction of arrow indicates the conventional direction of current (when the diode is under
forward bias).

 Applying Voltage across p-n junction:

The potential difference across a p-n junction can be applied in two ways: (i) Forward biasing (ii) Reverse
biasing
(i) Forward biasing:
When the positive terminal of the battery is connected to p-side and negative terminal to the n-side, so that
the potential difference (V) acts in opposite direction to the barrier potential, then the p-n junction diode is
said to be forward biased.
When the p-n junction is forward biased, the applied positive potential repels the holes in the p-region, and
the applied negative potential repels the electrons in the n-region, so the charges move towards the junction.
If the applied potential difference is more than the potential barrier (V0), some holes and free electrons enter
the depletion region. Hence, the potential barrier as well as the width of the depletion region is reduced.

{ Barrier potential (1) without battery,

(2) Low battery voltage, and
(3) Highvoltage battery. }
 Direction of applied voltage (V) is opposite to the build in potential (V0).
 As the depletion layer width decreases, the barrier height is reduced.
 Effective barrier height under forward bias is (V0 − V).

 Electron in n-region moves towards the p-n junction and holes in p-region move towards the
junction. The width of the depletion layer decreases and hence, it offers less resistance.
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XII Phys Ch-14 (Semi-Conductors)
 Diffusion of majority carriers takes place across the junction. This leads to forward current.
 The total diode forward current is sum of hole diffusion current and conventional current due to
electron diffusion.
(ii) Reverse biasing:
When the positive terminal of the battery is connected to the n-side and negative terminal to the p-side, so
that the applied potential difference is in the same direction as that of barrier potential, the junction is said
to be reverse biased.
When the p-n junction is reverse biased electrons in the n- region and holes in the p-region are attracted
away from the junction.

 Reverse bias supports the potential barrier. Therefore, the barrier height increases and the width of
depletion region also increase.
 Effective barrier height under reverse bias is (V0 + V).

 No conduction across the junction due to majority carriers; few minority carriers cross the junction
after being accelerated by high reverse bias voltage
 This constitutes a current that flows in opposite direction − celled reverse current.
 The current under reverse bias is essentially voltage independent upto a critical reverse bias voltage,
known as breakdown voltage (Vbr ). When V = Vbr, the diode reverse current increases sharply.

 Forward bised characteristic:

The circuit for the study of forward bias characteristics of p-njunction diode is as-
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XII Phys Ch-14 (Semi-Conductors)

The voltage between p–end and n–end is increased from zero in suitable equal steps and the corresponding
currents are noted down. Since voltage is the independent variable. Therefore, it is plotted along X–axis.
Since, current is the dependent variable, it is plotted against Y–axis. From the characteristic curve, the
following conclusions can be made.
(i) The forward characteristic is not a straight line. Hence the ratio V/I is not a constant (i.e) the
diode does not obey Ohm’s law. This implies that the semiconductor diode is a non-linear
conductor of electricity.
(ii) Initially, the current is very small. This is because, the diode will start conducting, only when the
external voltage overcomes the barrier potential (0.7V for silicon diode). Above 0.7V, the current
increases rapidly. The voltage at which the current starts to increase rapidly is known as cut-in
voltage or knee voltage of the diode.
 Reverse bias characteristics:
The circuit for the study of reverse bias characteristics of p-njunction diode is as –

The voltage is increased from zero in suitable steps. For each voltage, the corresponding current readings
are noted down and shown by graph. From the characteristic curve, it can be concluded that, as voltage is
increased from zero, reverse current (in the order of microamperes) increases and reaches the maximum
value at a small value of the reverse voltage. When the voltage is further increased, the current is almost
independent of the reverse voltage upto a certain critical value. This reverse current is known as the reverse
saturation current or leakage current. This current is due to the minority charge carriers, which depends on
junction temperature.
 Application of Junction Diode as a Rectifier:
A rectifier is an electrical device used for converting alternating current/voltage into direct current/voltage.
A rectifier composed of one or more diodes. A diode is like a one-way valve that allows an electrical current
to flow in only one direction. This process is called rectification.
 Half Wave Rectifier:
Half wave rectifier is based on the principle that the resistance of p-n junction becomes low when it is
forward biased and becomes high when reverse biased.
The circuit diagram for a p-n junction diode as a half wave rectifier is:

 Working:
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XII Phys Ch-14 (Semi-Conductors)
 During the positive half cycle of the input a.c., the p-n junction is forward biased i.e the forward
current flows from p to n, the diode offers a low resistance path to the current. Thus we get output
across-load i.e. a.c input will be obtained as d.c output.
 During the negative half cycle of the input a.c., the p-n junction is reversed biased i.e. the reverse
current flows from n to p and the diode offers a high resistance path to the current. Thus we get no
output across-load. This principle is shown in the diagram given below.

Since the rectified output of this circuit is only for half of input ac wave, it is called half wave rectifier.
 Full wave Rectifier:
Two diodes are used to give output rectified voltage corresponding to both positive as well as negative half
of the ac cycle. Hence, it is known as full-wave rectifier.

For a full-wave rectifier the secondary of the transformer is provided with a centre tapping and so it is
called centre-tap transformer.

 Working:
 Now consider p-side of the diodes D1 and D2 are connected to the secondary terminals of the
transformer. The n-side of the diodes are connected together and the output (load) is taken between
this common point and the midpoint of the transformer.
 When voltage at A with respect to the centre tap is positive and the voltage at B is negative. Then,
D1 is forward biased and D2 is reversed biased. Hence, D1 conducts and D2 does not. Hence, during
this positive half cycle we get an output current (and a output voltage across the load resistor RL)
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XII Phys Ch-14 (Semi-Conductors)
 When voltage of A becomes negative, then B becomes +ve. Therefore, D1 does not conduct and
D2 conducts giving an output current and output voltage (across RL) during the negative half cycle of
the input ac. Hence, we obtain output voltage during both the positive as well as negative half of
cycle.

 The rectified voltage is in the form of pulses of the shape of half sinusoids. Though it is
unidirectional it does not have a steady value. To get steady dc output a capacitor is connected
across the output terminals (parallel to the load RL). One can also use an inductor in series with RL
for the same purpose. Since these additional circuits filter out the ac ripple and give a pure dc
voltage, so they are called filters.

 Zener Diode:
It can operate in the reverse breakdown voltage region continuously without being damaged. The symbol of
zener diode is as -

 It is a heavily doped p-n junction. Due to this, depletion region formed is very thin and the electric
field of the junction is extremely high, even for a small reverse bias voltage.
 The I−V characteristics of a zener diode are shown in the figure below.

 It is widely used to regulate the voltage across the circuit.

 Zener Diode as Voltage Regulator:

 After the break down voltage, small change in voltage across the zener diode produces a large
change in current through the circuit.
 If voltage is increased beyond zener voltage, then the resistance of the zener diode drops
considerably.
 Zener diode and a resistor are connected to a fluctuating dc supply such that the zener diode is
reverse biased.
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XII Phys Ch-14 (Semi-Conductors)
 When the voltage across the diode tends to increase, the current through the diode rises out of
proportion and causes a sufficient increase in voltage drop across the resistor. Therefore, the O/P
voltage lowers back to normal.

 Photodiode:
A junction diode made from light sensitive semi-conductor is called a photodiode.
It is fabricated with a transparent window to allow light to fall on the diode. It always works on reverse
bias condition below the breakdown voltage.
Working of a photo diode:


 Current AB that flows when no light is incident is called dark current.
 When photons of light having energy hν ( > Eg , forbidden energy gap) fall on the photodiode, then
electron-hole pairs are generated in or near the depletion region and more electrons from valence
band move to the conduction band due to absorption of photons.
 The current in the circuit increases. As the intensity of light is increased, the current goes on
increasing as in part BC.
 When the current does not increase with the increase in intensity of light, the photodiode is said to be
saturated. Portion CD of the graph represents saturated current.
 Light Emitting Diodes (LEDs):

 All junction diodes emit some light when forward biased.

 Junction diode is made of gallium arsenide (GaAs). The energy is released in infrared region while
those made of gallium arsenide phosphide (GaAsP) emit radiation in visible region. They are called
LEDs.
 The most important part of a LED is the p-n junction. The junction acts as a barrier to the flow of
electrons between the p and n regions. Only when sufficient voltage is applied to the LED, the
electrons cross the junction into the p-region and current flows through it.
 Diode is encapsulated with a transparent cover so that emitted light can come out.
 LEDs are biased such that the light emitting efficiency is maximum.
 Semi-conductor used to fabricate visible LEDs must have at least 1.8 eV band gap. (i.e. from 3 eV to
1.8 eV)
 LEDs have low operational voltage and less power. They requires less warm-up time.
 Solar Cell:
It is a semi-conductor device used to convert photons of solar light into electricity.
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XII Phys Ch-14 (Semi-Conductors)

 It generates emf when solar radiations fall on the p-n junction.

 A p- Si wafer of about 300 μm is taken, over which a thin layer n− Si is grown on one side by
diffusion process.
 The generation of emf by a solar cell when light falls on it is due to following three processes:
 Generation of e-h pairs due to light close to the junction
 Separation of electrons and holes due to electric field of the depletion region
 The electrons reaching the n-side are collected by the front contact and holes reaching p-side are
collected by the back contact. Thus, p-side becomes positive and n-side becomes negative giving rise
to photovoltage.
 Semi-conductors with band gap close to 1.5 eV are ideal materials for solar cell fabrication.

 Junction Transistor:
A semiconductor device with three connections, capable of amplification in addition to rectification is called
transistor. A portable radio constitutes circuits containing transistors rather than valves. There are two types
of transistors:
(i) n-p-n transistor (ii) p-n-p transistor
An n-p-n transistor is composed of two n-type semiconductors separated by a segment of p-type semi-
conductor. Howeverm, a p-n-p transistor is formed by two p-sections separated by a thin segment of n-type
semi-coductor.

Schematic representation n-p-n transistor: Symbol:

Schematic representation p-n-p transistor: Symbol:

 Three segments of transistor:

 Emitter − Segment is on one side of the transistor. It is of a moderate size and heavily doped. The
emitter is always forward biased with respect to base. So that it supplies a huge number of majority
carriers (electrons or holes) for the current flow through the transistor.
 Base − It is the central segment. It is very thin and lightly doped.
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XII Phys Ch-14 (Semi-Conductors)
 Collector − It collects major portion of the majority carrier supplied by the emitter. It is moderately
doped and large in size compared to emitter. The collector is always reverse biased.

 VCC and VEE create the biasing. The biased transistor is said to be in active state.
 VCB − Collector base voltage and VEB − Base emitter voltage
 Base is the common terminal for the two power supplies whose other terminals are connected to
emitter and collector respectively.
 Heavily doped emitter has a high concentration of majority carriers, which will be holes in p-n-
p transistor and electron in an n-p-n transistor.
 These majority carriers enter the base region in large numbers. The base is lightly doped. Therefore,
it has few majority carriers.
 In p-n-p, the base has the majority carriers as electrons. The large number of holes entering the base
from the emitter swamps the small number of electrons there.
 Since the base collector junction is reverse biased, the holes which appear as minority carriers at the
junction can easily cross the junction and enter the collector.
 Base is made thin so that the holes cross the junction instead of moving to the base terminal.

 Direction of motion of electron is opposite to current. However, the direction of motion of holes is
identical with the direction of conventional current.
 In active state of the transistor, the emitter-base junction acts as a low resistance while the base
collector acts as a high resistance.

 Transistor Action:
(i) Working of n-p-n transistor: The emitter-base junction of a transistor is forward biased whereas
collector-base junction is reversed biased. The forward biasing causes the electrons flow from
emitter towards base. This constitutes emitter current IE. As the base is lightly doped and very
thin. Therefore, only a few electrons (< 5%) combine with holes to constitute base current IB. The
remaining (> 95%) electrons cross over into the collector region to constitute collector current IC.
It is clear that the emitter current is the sum of collector current and base current: I E  I B  I C
(ii) Working of p-n-p transistor: The forward bias causes the holes in p-type emitter to flow towards
the base. This constitute the emitter current IE. As the base is lightly doped and very thin, therefore,
only a few holes (< 5%) combine with electrons to constitute base current IB. The remaining (> 95%)
holes cross over into the collector region to constitute collector current IC. It is clear that
I E  I B  IC
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XII Phys Ch-14 (Semi-Conductors)

 Basic transistor circuit configurations and transistor characteristics:

There are three types of circuit connections (called configurations or modes) for operating a transistor.
They are :-
(a) Common base (CB)
(b) Common emitter (CE)
(c) Common collector (CC)
The different modes are shown in fig for n-p-n transistor. The transistor is most widely used in the CE
configuration and more commonly used transistors are n-p-n Si transistors.

 Common Emitter Transistor Characteristics:

When a transistor is used in CE configuration, the input is between the base and the emitter and the
output is between the collector and the emitter. The variation of the base current IB with the base-emitter
voltage VBE is called the input characteristic. Similarly, the variation of the collector current IC with the
collector-emitter voltage VCE is called the output characteristic.

(Circuit arrangement)

 Input characteristics:
Input characteristic curve is drawn between the base current (IB) and voltage between base and emitter (VBE),
when the voltage between collector and emitter (VCE) is kept constant at a particular value. VBE is increased in
suitable equal steps and corresponding base current is noted. IB values are plotted against VBE for constant
VCE. The input characteristic thus obtained is shown in fig. The input impedance of the transistor is defined
as the ratio of small change in base – emitter voltage to the corresponding change in base current at a given
VCE.
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XII Phys Ch-14 (Semi-Conductors)

(Input characteristics) (Output characteristics)

 Output characteristics:
Output characteristic curves are drawn between IC and VCE, when IB is kept constant. If VBE is increased by a
small amount, both IB and IC will increase proportionately. This shows that when IB increases IC also
increases. The plot of IC versus VCE for different fixed values of IB gives one output characteristic.

 Parameters of Transistors:
(i) Input resistance (ri):
This is defined as the ratio of change in base emitter voltage (ΔVBE) to the resulting change in base current
 V 
(ΔIB) at constant collector-emitter voltage (VCE). Input resistance, ri   BE 
 I B VCE

(ii) Output resistance (r0):

This is defined as the ratio of change in collector-emitter voltage (ΔVCE) to the change in collector current
 V 
(ΔIC) at constant base current (IB). The output resistance, ro   CE 
 I 
 C I
B

(iii) Current amplification factor (β):

This is defined as the ratio of the change in collector current to the change in base current at a constant
collector-emitter voltage (VCE) when the transistor is in active state.
 I 
Current amplification factor,  ac   C 
 I B VCE
This is also known as small signal current gain.
If we simply find the ratio of IC and IB, we get what is called dc amplification factor β of the transistor.
I
Hence,  dc  C
IB
Since IC increases with IB almost linearly and IC = 0 when IB = 0, the values of both βdc and βac are nearly
equal. So, for most calculations βdc can be used. Both βac and βdc vary with VCE and IB (or IC) slightly.

 Transistor as a device:
The transistor can be used as a device application depending on the configuration used (namely CB, CC and CE),
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XII Phys Ch-14 (Semi-Conductors)

(a) Base-biased transistor in CE configuration, (b) Transfer characteristic.

(i) Transistor as a Switch:

When the transistor is used in the cut-off or saturation region, it acts as a switch. Applying Kirchhoff’s
voltage rule to above figure (a),
VBB = IBRB + VBE
VCE = VCC − ICRC
Where,
VBB − dc input voltage (Vi)
VCE − dc output voltage (Vo)
∴ Vi = IBRB + VBE and
Vo = VCC − ICRC
When Vi < 0.6, the transistor is in cut-off. Therefore, IC = O
∴ Vo = VCC
When Vo > 0.6 V, then IC increases. Therefore, VO decreases as the term ICRC increases. With increase
in Vi, IC increases almost linearly and as a result, Vo decreases linearly till its value becomes less than about
1.0 V. Change becomes non-linear and the transistor goes to saturation. If Vi is increased further,
then Vo becomes almost zero. When Vi is low, Vo is high and if Vi is high, then Vo is low. When the transistor
is not conducting, it is said to be switched off and when it is driven into saturation, it is said to be switched
on.
(ii) Transistor as an Amplifier(Common Emitter CE Configuration):
The transistor acts as an amplifier when the input circuit (emitter–base) is forward biased with low voltage
VBB and the output circuit (collector–base) is reverse biased with high voltage VCC .
An amplifier is a circuit capable of magnifying the amplitude of weak signals. The important parameters of
an amplifier are input impedance, output impedance, current gain and voltage gain.
If ΔVo and ΔVi are small changes in output and input voltage, then ΔVo/ΔVi is called small signal voltage
gain, AV of the amplifier.
Vo = VCC − ICRC
ΔVo = 0 − RCΔIC
Similarly, Vi = IBRB + VBE
∴ ΔVi = RBΔIB + ΔVBE
∴ AV = − RCΔIC/RBΔIB
= − βac (RC/RB)
Where, βac is equal to Δ IC / Δ IB
 Diagram

An ac input signal vi is superimposed on bias VBB (dc). The output is taken between collector and
ground.
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XII Phys Ch-14 (Semi-Conductors)
Applying Kirchhoff’ law to the output loop,
VCC = VCE + ICRC
VBB = VBE + IBRB
vi ≠ 0
Then, VBB + vi = VBE + IBRB + ΔIB (RB + ri)

It is current gain denoted by AV.

Change IC due to change in IB causes a change in VCE and the voltage drop across resistor RC,
because VCC is fixed.
∴ΔVCC = ΔVCE + RCΔIC = 0
⇒ ΔVCE = − RCΔIC
Change in VCE is the output voltage Vo.
∴ Vo = ΔVCE = − βac RCΔIB
Voltage gain of amplifier

Negative sign represents that the o/p voltage is in opposite phase to i/p voltage.
Power gain (AP) is the product of current gain and voltage gain.
AP = βac × Av
Feed back amplifier and transistor oscillator
In oscillator, the ac o/p is produced without any external i/p signal.
An oscillator is a device in which the o/p power is returned back to the i/p, in phase with the starting
power (i.e., as a positive feedback).

Feedback can be achieved by inductive coupling or LC or RC network.

Feedback is accomplished by inductive coupling from one coil winding ( T1) to another coil winding
( T2).
Current flows through T2.
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XII Phys Ch-14 (Semi-Conductors)

The current increases from X to Y.

Coupling between T2 and T1 causes a current to flow in the emitter current. It is a feedback from i/p to
o/p.

As a result, this feedback current also increases from to .

Current in T2 connected in the collector circuit acquires value Y as the transistor becomes saturated.
There is no further increase in collector current to the magnetic field amount. T2 stops growing. Due to
static field, there is no feedback from T2 to T1. Collector current decreases from Y to Z.
Decrease in IC causes the magnetic field to decay around the coil T2.
T1 also decays. Emitter current reaches when transistor is cut-off. Both IE and IC stop flowing.
Therefore, the transistor comes back to its original state.
Resonant frequency of this tuned circuit determines the frequency at which the oscillator will oscillate.

Digital Electronics and Logic Gates

 Analog Signal: A continuously varying signal (Voltage or current) is called analog signal. For example
an alternating voltage varying sinusoidally is an analog signal.

 Digital Signal: A signal (Voltage or current) that can have only two discrete values is called a digital
signal. In digital electronics, we use only two levels of voltage ‘0’ and ‘1’.
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XII Phys Ch-14 (Semi-Conductors)
 Logic Gates:
A digit circuit with one or more input signals but only one output signal is called a logic gate. It
controls the flow of information. Logic gate follows a certain logical relationship between the input and
output voltage. The five common logic gates used are NOT, AND, OR, NAND, NOR. Each logic gate is
indicated by a symbol and its function is defined by a truth table that shows all the possible input logic
level combinations with their respective output logic levels. Truth tables help understand the behaviour
of logic gates.
(i) NOT gate
Not gate produces an inverted version of the input at its output. This is why it is also known as an
inverter. The symbol and truth table of NOT gate is-

Symbol Truth table

Input Output

A Y

0 1

1 0

(ii) OR gate:
An OR gate has two or more inputs with one output. The logic symbol and truth table are shown in Fig.
The output Y is 1 when either input A or input B or both are 1s, that is, if any of the input is high, the
output is high.
Symbol Truth table

Input Output

A B Y

0 0 0

0 1 1

1 0 1

1 1 1

(iii) AND gate:

An AND gate has two or more inputs and one output. The output Y of AND gate is 1 only when input A
and input B are both 1. The logic symbol and truth table for this gate are given in Fig.

Symbol Truth table

Input Output

A B Y

0 0 0
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XII Phys Ch-14 (Semi-Conductors)

The Boolean expression 0 1 0

for AND function
�.� = � 1 0 0

1 1 1

(iv) NAND:
This is an AND gate followed by a NOT gate. If inputs A and B are both ‘1’, the output Y is not ‘1’. The
gate gets its name from this NOT AND behaviour. The symbol and truth table of NAND gate is shown
in fig. NAND gates are also called Universal Gates.
Symbol Truth table

Input Output

A B Y

0 0 1

The Boolean expression 0 1 1

for NAND function
� = �. � 1 0 1

1 1 0
(v) NOR gate:
It has two or more inputs and one output. A NOT- operation applied after OR gate gives a NOT-OR gate
(or simply NOR gate). Its output Y is ‘1’ only when both inputs A and B are ‘0’, i.e., neither one input
nor the other is ‘1’. The symbol and truth table for NOR gate is given in Fig.

Symbol Truth table

Input Output

A B Y

The Boolean expression 0 0 1

for NOR function
0 1 0
�= �+�
1 0 0

1 1 0

 Integrated Circuits (IC):

It is the concept of fabricating an entire circuit on a small single chip of a semi-conductor. Monolithic
integrated circuit is a widely used technique in which a single chip is used. Its dimension is 1 mm × 1 mm or
even smaller. Depending on the nature of input signals, ICs can be of two types.
(i) Linear or analogue ICs: The linear ICs process analogue signals, which change smoothly and
continuously over a range of values between a maximum and a minimum. The output is directly proportional
to the input. Example: operational amplifier.
(ii) Digital ICs : These process signals that have only two values. These contain logic gates.
(Logic gate ≤ 10) → Small scale integration
(Logic gate ≤ 100) → Medium scale integration
(Logic gate ≤ 1000) → Large scale integration
(Logic gate > 1000) → Very large scale integration