[ Roll No.

: · ]

National Institute o!fJ'echno{ogy, (])e{hi

Name of the Examination: PhD: Autumn 2023, End Semester Examination
Branch : ECE (VLSI) Semester :I

Title of the Course : Semiconductor Devices Course Code : ECVM 501

Time: 3 Hours Maximum Marks: 50

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Note:Allparts of a single question must be answered together. ELSEQUESTIONSHALLNOTBEEVALUATED.

Use following data if not given in a problem: Eo = 8.8Sxl0-14Fjcm, Er (SiOz) = 3.9, e- (Si) = 11.8, At room
temperature for Si [I!n= 13s0cmZjV·S, I!p=480 cmZjV·S,n. = 1.sxl010jcm3, Eg= 1.12 eV], k = 8.62 xl0-SeVjK,
't"n= 't"p=11!s,Eg(Ge)= 0.7 eV, n, (Ge)= 2.sxl013 jcm3•

Course Outcomes (CO) Cognitive Levels

COl Describe the fundamental physical processes related to electronic transitions in Remember
semiconductors and the basic lawsj definitions (Level I)
CO2 To understand the advanced physics behind electronic devices based on the Understand
above processes. (Level II)
C03 Application of above concepts to understand the physical processes and Apply
principle of operation of various electronic and opto-electronic solid devices. (Level III)
C04 To develop the circuit level concepts of above electronic solid-state devices. Evaluate
(Level V)

Q.No. Question Marks CO BL PO

1. Estimate the expressions for developed electric field of a p-n junction [5] CO2 Level 1
where the space charge profile at depletion region is given as II
p(x)=q.h(2x+3), where x is a distance of the device from physical
contact at x = 0 and h is constant.

3K.T [2+1] C04 Level 2

2. The current equation for a pn junction diode for V > -- is given as, V
q
I = I o.exp ( --q.v ) ,where, I ° = A.exp [ -1.l2eV] .
KI KI
Calculate the suitable forward bias voltage required at 320K
temperature for this diode to maintain the same current as available in
~V
this diode at 300 Kfor 0.5 V forward bias. Hence, compute --.
~T
3. Sketch and label the energy band diagram of p-np transistor under [2] COl Levell 3
unbiased, active and saturation mode of operation. Also sketch and
label the minority carrier distribution for all the above operations.

4. For a pn junction diode the maximum electric field is given as, [1+1] CO2 Level 4
II
 Emax = 2.q.(~ - V).NA_ND
~ cs·(NA. + ND)
Derive the expression for breakdown voltage (VBR) for a p-n diode of
above type in terms of Emax given above. Comment on the breakdown
voltage as ND is increased.
~----~~-=~~--~~~~~------~~~~--------~------~------4-----~----~_------_-
5. (a) Sketch and label the energy band diagrams of a metal- [1+1+1 C03 Level 2
semiconductor junction +1.5+1. III
for n- type semiconductor for every case with V= 0 volt; V = 0.2 5
volt (Forward + 4]
bias) and V= 1 volt (Reverse bias).
[Given: q.X = 4.0e V, Eg = I. le V; KT = 0.026e V;
nj = I.5xIOIO / cm3at 300 K
temperature, q'¢m = 4.5e V, q.¢s = 4.2e V].

(b) Calculate depletion widths for all the above-mentioned biasing

cases.

(c) Estimate the maximum electric fields for all the above-
mentioned biasing cases.

6. On a Si sample light is incident at t = 0 uniformly, which generates the [3] C02 Level 2
excess electron-hole pairs (EHP). The generation rate for excess II
carriers is 6xl022jcm3. Sample is doped with 2xl017 jcm3 As atoms.
Determine the conductivity of the sample at t = 5 msec in absence of
any field. Assume, carrier lifetime, T p = 10- sec.
7

~----+---------------------------------------------------~------4-----~----+--------
7. A p-n diode is switched from zero current state to a forward current [2+1] COl Level I 3
state at t = 0 and the amount of stored minority charge changes from
Qpto 2Qp.

(a) What will be the change in the diffusion length for holes?

(b) What will be the change in the hole current?

8. In a four-layer combination of p-n-p-n diode, let the collector currents [2] C03 Level 2
are 2 J,lA and 1.8 J,lA. If the CE transistor gains are 167 and 160, then III
what will be the total reverse saturation current of this two-transistor
combination?

9. A pnp transistor has IEp = 2 rnA, lEN= 0.02 rnA, Icr = 1.96 rnA and ICN= [2] COl Level I 1
0.01 rnA.Find:
(a) Base transport Factor (B).
(b) Emitter Injection efficiency (y)
(c) CEand CBgains (a and (J)
(d) Base current (IB) and emitter current (IE)

10. In a Si semiconductor, the doping profile is given below. Sketch and [ 1 +1] C02 Level 2
label the energy band diagram from x= 0 to x= 2 urn of the sample. Also II
indicate the direction of electric filed if any from x= 0 to x= 2 urn.
2
J

t-!IJ_tJAt
{;" Ie I'
-_
/C:JJ\ ..)

y --7 z.(/.AJ'f-)
\ '2
, 0'
I

11. Write the correct option only, in you answer booklet against each of the [6] COl Levell 1
following questions:
(a) What does a high resistance reading in both forward- and reverse-bias
directions of a diode indicate?
(i) A Good diode (ii) An open diode (iii) A shorted diode (iv) A
defective ohmmeter

(b) Usually during MOS scaling, the oxide layer thickness increases/
decreases and gate capacitance of the device increases/ decreases.

(c) One eV is equal to: (i) 6.02 x 1023J (ii) 1.6 x 10-19J (iii) 6.25 x 1018 J (iv)
1.66 x 10-24J.

(d) Sub threshold condition in MOS device is due to weak/ strong

inversion of the channel which leads to drift/ diffusion of carriers
from source to drain.

(e) The concentration of holes in valence band is estimated by the product

ofNe/ Nvand f(Ev)/ [1- f(Ev)].
(1) How many valence electrons does a silicon atom have? (i) 1 (ii) 2 (iii)
3 (iv) 4.

12. Write the expression for threshold voltage for a real MOSfield effect [2] COl Levell 1
transistor (MOSFET)explaining all the terms.

13. Justify the necessity of using poly - Si as a gate material instead of any [2] CO2 Level 1
ordinary metal in MOSstructure. II

14. (a) An n- type Si semiconductor sample having with equilibrium [3] C03 Level 2
carrier concentration, no= 1014/cm3. After steady shining of light, let III
optically generated EHP's are 1013EHP/cm3/lls when 'rn = 'rp= Lus.
Calculate total e and hole concentrations after shining of light. [n.=1.5
x 1010/cm3]

(b) Find the positions of Quasi-Fermi levels with respect to intrinsic [3]
energy level. Draw the energy band diagram.

3
 f

Useful Equations

Fenni-Dirac e: distribution: Jr.£) II!

fl,E- B/JllT
1
+1
!ll ,,1:,- EllkT for E » EF
.

110 .: n.etE,- EJllT

Po ... IIjl{E.-e/VI:T

Po == N.,[l ~ J(E..)] - N~-(E,-E:JI.T

'II:' r\/"
n~0;; Nc4!-.....- ....If.. '. PI'" N,.-.,..,--"v......,
'11:'
•• ... 111 - Vii:ii:.
('(". e-E,fli.T ;;;;2(2'11'h~t\:V2{m*. mp.\l~t!.-F.,fD.l'
J.
II> -) •• 'It

n = !(e-{E,-P.,JIkT :; n~(F.-Btilk7
p ;;; N.I!-{F,-EJ/ItT = ¥(~-1i}/"T

Djffusion length: L v'i>r D kT

lIB Eim.tein relation: - - -
J.I. q

For steady state diffusion: -

cP6n .. - all • -&n
tJx.l .D"T" L!

Equilibrium: Vo"" kT In P, = itT In l'!..t_ = kT In N.N" ~ = ~ = ,fIv,Ju

q Pit q tiflN.t q n~ p. n"

N N ]!t)
q EA
Junction Depletion: CJ "" tA [ ( ~.--.... ~
2E VO - V) Nd + N" W

. WN.
One-sided abrupt P +-n: X"II" N . N "'" W
.+ d

Ap" ... P(XIIII) - p" ... p,,(~VliT - 1)

Q, t;
l,(x" ,...0) ....-:;- "" qA :;- Ap.. = qA
o,p,,(e IIVlll -
L 1)
P" p