2.1 Semiconductor Physics
In the problems assume the parameter given in
following table. Use the temperature T � 300 K unless
otherwise stated.
Property Si GaAs Ge
Bandgap Energy 1.12 1.42 0.66
Dielectric Constant 11.7 13.1 16.0
Effective density ofstates in conduction
band Nc ( )cm�3
28 1019. � 47 1017. � 104 1019. �
Effective density ofstates in valence
band Nv ( )cm�3
104 1019. � 70 1018. � 60 1018. �
Intrinsic carrierconcertration
ni ( )cm�3
15 1010. � 18 106. � 24 1018. �
MobilityElectron
Hole1350480
8500400
39001900
1. In germanium semiconductor material at T � 400 K
the intrinsic concentration is
(A) 26 8 1014. � cm�3 (B) 18 4 1014. � cm�3
(C) 8 5 1014. � cm�3 (D) 3 6 1014. � cm�3
2. The intrinsic carrier concentration in silicon is to be
no greater than ni � �1 1012 cm�3. The maximum
temperature allowed for the silicon is (Assume
Eg � 112. eV)
(A) 300 K (B) 360 K
(C) 382 K (D) 364 K
3. Two semiconductor material have exactly the same
properties except that material A has a bandgap of 1.0
eV and material B has a bandgap energy of 1.2 eV.
The ratio of intrinsic concentration of material A to
that of material B is
(A) 2016 (B) 47.5
(C) 58.23 (D) 1048
4. In silicon at T � 300 K the thermal-equilibrium
concentration of electron is n0
45 10� � cm�3. The hole
concentration is
(A) 4 5 1015. � cm�3 (B) 4 5 1015. � m�3
(C) 0 3 10 6. � � cm�3 (D) 0 3 10 6. � � m�3
5. In silicon at T � 300 K if the Fermi energy is 0.22 eV
above the valence band energy, the value of p0 is
(A) 2 1015� cm�3 (B) 1015 cm�3
(C) 3 1015� cm�3 (D) 4 1015� cm�3
6. The thermal-equilibrium concentration of hole p0 in
silicon at T � 300 K is 1015 cm�3. The value of n0 is
(A) 3 8 108. � cm�3 (B) 4 4 104. � cm�3
(C) 2 6 104. � cm�3 (D) 4 3 108. � cm�3
7. In germanium semiconductor at T � 300 K, the
acceptor concentrations is Na � 1013 cm�3 and donor
concentration is Nd � 0. The thermal equilibrium
concentration p0 is
(A) 2 97 109. � cm�3 (B) 2 68 1012. � cm�3
(C) 2 95 1013. � cm�3 (D) 2 4. cm�3
Statement for Q.8-9:
In germanium semiconductor at T � 300 K, the
impurity concentration are
Nd � �5 1015 cm�3 and Na � 0
8. The thermal equilibrium electron concentration n0
is
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(A) 5 1015� cm�3 (B) 115 1011. � cm�3
(C) 115 109. � cm�3 (D) 5 106� cm�3
9. The thermal equilibrium hole concentration p0 is
(A) 396 1013. � (B) 195 1013. � cm�3
(C) 4 36 1012. � cm�3 (D) 396 1013. � cm�3
10. A sample of silicon at T � 300 K is doped with
boron at a concentration of 2 5 1013. � cm�3 and with
arsenic at a concentration of 1 1013� cm�3. The
material is
(A) p � type with p0
1315 10� �. cm�3
(B) p � type with p0
715 10� �. cm�3
(C) n � type with n0
1315 10� �. cm�3
(D) n � type with n0
715 10� �. cm�3
11. In a sample of gallium arsenide at T � 200 K,
n p0 05� and Na � 0. The value of n0 is
(A) 9 86 109. � cm�3 (B) 7 cm�3
(C) 4 86 103. � cm�3 (D) 3 cm�3
12. Germanium at T � 300 K is uniformly doped with
an acceptor concentration of Na � 1015 cm�3 and a donor
concentration of Nd � 0. The position of fermi energy
with respect to intrinsic Fermi level is
(A) 0.02 eV (B) 0.04 eV
(C) 0.06 eV (D)0.08 eV
13. In germanium at T � 300 K, the donor
concentration are Nd � 1014 cm�3 and Na � 0. The
Fermi energy level with respect to intrinsic Fermi
level is
(A) 0.04 eV (B) 0.08 eV
(C) 0.42 eV (D) 0.86 eV
14. A GaAs device is doped with a donor concentration
of 3 1015� cm�3. For the device to operate properly, the
intrinsic carrier concentration must remain less than
5% of the total concentration. The maximum
temperature on that the device may operate is
(A) 763 K (B) 942 K
(C) 486 K (D) 243 K
15. For a particular semiconductor at T � 300 K
Eg � 15. eV, m mp n
* *� 10 and ni � �1 1015 cm�3. The
position of Fermi level with respect to the center of the
bandgap is
(A) �0.045 eV (B) � 0.046 eV
(C) �0.039 eV (D) � 0.039 eV
16. A silicon sample contains acceptor atoms at a
concentration of Na � �5 1015 cm�3. Donor atoms are
added forming and n � type compensated
semiconductor such that the Fermi level is 0.215 eV
below the conduction band edge. The concentration of
donors atoms added are
(A) 12 1016. � cm�3 (B) 4 6 1016. � cm�3
(C) 39 1012. � cm�3 (D) 2 4 1012. � cm�3
17. A silicon semiconductor sample at T � 300 K is
doped with phosphorus atoms at a concentrations of
1015 cm�3. The position of the Fermi level with respect
to the intrinsic Fermi level is
(A) 0.3 eV (B) 0.2 eV
(C) 0.1 eV (D) 0.4 eV
18. A silicon crystal having a cross-sectional area of
0.001 cm2 and a length of 20 �m is connected to its
ends to a 20 V battery. At T � 300 K, we want a
current of 100 mA in crystal. The concentration of
donor atoms to be added is
(A) 2 4 1013. � cm�3 (B) 4 6 1013. � cm�3
(C) 7 8 1014. � cm�3 (D) 8 4 1014. � cm�3
19. The cross sectional area of silicon bar is 100 �m2.
The length of bar is 1 mm. The bar is doped with
arsenic atoms. The resistance of bar is
(A) 2.58 m� (B) 11.36 k�
(C) 1.36 m� (D) 24.8 k�
20. A thin film resistor is to be made from a GaAs film
doped n � type. The resistor is to have a value of 2 k�.
The resistor length is to be 200 �m and area is to be
10 6� cm2. The doping efficiency is known to be 90%.
The mobility of electrons is 8000 cm V s2 � . The
doping needed is
(A) 8 7 1015. � cm�3 (B) 8 7 1021. � cm�3
(C) 4 6 1015. � cm�3 (D) 4 6 1021. � cm�3
21. A silicon sample doped n � type at 1018 cm�3 have a
resistance of 10 � . The sample has an area of 10 6�
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108 Semiconductor Physics Chap 2.1
cm2 and a length of 10 �m . The doping efficiency of
the sample is (� n � 800 cm V s2 � )
(A) 43.2% (B) 78.1%
(C) 96.3% (D) 54.3%
22. Six volts is applied across a 2 cm long
semiconductor bar. The average drift velocity is 104
cm s. The electron mobility is
(A) 4396 cm V s2 � (B) 3 104� cm V s2 �
(C) 6 104� cm V s2 � (D) 3333 cm V s2 �
23. For a particular semiconductor material following
parameters are observed:
� n � 1000 cm V s2 � ,
� p � 600 cm V s2 � ,
N Nc v� � 1019 cm�3
These parameters are independent of
temperature. The measured conductivity of the
intrinsic material is � � �� �10 6 1( )� cm at T � 300 K.
The conductivity at T � 500 K is
(A) 2 10 4� � ( )� � �cm 1 (B) 4 10 5� � ( )� � �cm 1
(C) 2 10 5� � ( )� � �cm 1 (D) 6 10 3� � ( )� � �cm 1
24. An n � type silicon sample has a resistivity of 5
� � cm at T � 300 K. The mobility is � n � 1350
cm V s2 � . The donor impurity concentration is
(A) 2 86 10 14. � � cm�3 (B) 9 25 1014. � cm�3
(C) 11 46 1015. � cm�3 (D) 11 10 15. � � cm�3
25. In a silicon sample the electron concentration
drops linearly from 1018 cm�3 to 1016 cm�3 over a length
of 2.0 �m. The current density due to the electron
diffusion current is ( )Dn � 35 2cm s .
(A) 9 3 104. � A cm2 (B) 2 8 104. � A cm2
(C) 9 3 109. � A cm2 (D) 2 8 109. � A cm2
26. In a GaAs sample the electrons are moving under
an electric field of 5 kV cm and the carrier
concentration is uniform at 1016 cm�3. The electron
velocity is the saturated velocity of 107 cm s. The drift
current density is
(A) 1 6 104. � A cm2 (B) 2 4 104. � A cm2
(C) 1 6 108. � A cm2 (D) 2 4 108. � A cm2
27. For a sample of GaAs scattering time is �sc � �10 13 s
and electron’s effective mass is m me o
* .� 0 067 . If an
electric field of 1 kV cm is applied, the drift velocity
produced is
(A) 2 6 106. � cm s (B) 263 cm s
(C) 14 8 106. � cm s (D) 482
28. A gallium arsenide semiconductor at T � 300 K is
doped with impurity concentration Nd � 1016 cm�3. The
mobility � n is 7500 cm V s2 � . For an applied field of
10 V cm the drift current density is
(A) 120 A cm2 (B) 120 A cm2
(C) 12 104� A cm2 (D) 12 104� A cm2
29. In a particular semiconductor the donor impurity
concentration is Nd � 1014 cm�3. Assume the following
parameters,
� n � 1000 cm V s2 � ,
NT
c � �
�
�
�2 10
300
19
3 2
cm�3,
NT
v � �
�
�
�1 10
300
19
3 2
cm�3,
Eg � 11. eV.
An electric field of E � 10 V cm is applied. The
electric current density at 300 K is
(A) 2.3 A cm2 (B) 1.6 A cm2
(C) 9.6 A cm2 (D) 3.4 A cm2
Statement for Q.30-31:
A semiconductor has following parameter
� n � 7500 cm V s2 � ,
� p � 300 cm V s2 � ,
ni � �3 6 1012. cm�3
30. When conductivity is minimum, the hole
concentration is
(A) 7 2 1011. � cm�3 (B) 1 8 1013. � cm�3
(C) 1 44 1011. � cm�3 (D) 9 1013� cm�3
31. The minimum conductivity is
(A) 0 6 10 3 1. ( )� �� �� cm (B) 17 10 3 1. ( )� �� �� cm
(C) 2 4 10 3 1. ( )� �� �� cm (D) 6 8 10 3 1. ( )� �� �� cm
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Chap 2.1 Semiconductor Physics 109
32. A particular intrinsic semiconductor has a
resistivity of 50 ( )� � cm at T � 300 K and 5 ( )� � cm at
T � 330 K. If change in mobility with temperature is
neglected, the bandgap energy of the semiconductor is
(A) 1.9 eV (B) 1.3 eV
(C) 2.6 eV (D) 0.64 eV
33. Three scattering mechanism exist in a
semiconductor. If only the first mechanism were
present, the mobility would be 500 cm V s2 � . If only
the second mechanism were present, the mobility
would be 750 cm V s2 � . If only third mechanism were
present, the mobility would be 1500 cm V s2 � . The net
mobility is
(A) 2750 cm V s2 � (B) 1114 cm V s2 �
(C) 818 cm V s2 � (D) 250 cm V s2 �
34. In a sample of silicon at T � 300 K, the electron
concentration varies linearly with distance, as shown
in fig. P2.1.34. The diffusion current density is found
to be Jn � 0 19. A cm2. If the electron diffusion
coefficient is Dn � 25 2cm s, The electron concentration
at is
(A) 4 86 108. � cm�3 (B) 2 5 1013. � cm�3
(C) 9 8 1026. � cm�3 (D) 5 4 1015. � cm�3
35. The hole concentration in p � type GaAs is given by
px
L� �
�
�
�10 116 cm�3 for 0 � �x L
where L � 10 �m. The hole diffusion coefficient is
10 cm s2 . The hole diffusion current density at
x � 5 �m is
(A) 20 A cm2 (B) 16 A cm2
(C) 24 A cm2 (D) 30 A cm2
36. For a particular semiconductor sample consider
following parameters:
Hole concentration p e
x
Lp
0
1510�
�
��
�
��
cm�3,x � 0
Electron concentration n e
x
Ln
0
145 10� ��
�
�
�
cm�3,x � 0
Hole diffusion coefficient Dp � 10 cm s2
Electron diffusion coefficients Dn � 25 cm s2
Hole diffusion length Lp � � �5 10 4 cm,
Electron diffusion length Ln � �10 3 cm
The total current density at x � 0 is
(A) 1.2 A cm2 (B) 5.2 A cm2
(C) 3.8 A cm2 (D) 2 A cm2
37. A germanium Hall device is doped with 5 1015�
donor atoms per cm3 at T � 300 K. The device has the
geometry d � � �5 10 3 cm, W � � �2 10 2 cm and L � 0 1.
cm. The current is Ix � 250 �A, the applied voltage is
Vx � 100 mV, and the magnetic flux is Bz � � �5 10 2
tesla. The Hall voltage is
(A) �0.31mV (B) 0.31 mV
(C) 3.26 mV (D) �3.26 mV
Statement for Q.38-39:
A silicon Hall device at T � 300 K has the
geometry d � �10 3 cm , W � �10 2 cm, L � �10 1 cm. The
following parameters are measured: Ix � 0 75. mA,
Vx � 15 V, VH � �5 8. mV, tesla
38. The majority carrier concentration is
(A) 8 1015� cm�3, n � type
(B) 8 1015� cm�3, p � type
(C) 4 1015� cm�3, n � type
(D) 4 1015� cm�3, p � type
39. The majority carrier mobility is
(A) 430 cm V s2 � (B) 215 cm V s2 �
(C) 390 cm V s2 � (D) 195 cm V s2 �
40. In a semiconductor n0
1510� cm�3 and ni � 1010
cm�3. The excess-carrier life time is 10 6� s. The excess
hole concentration is �p � �4 1013 cm�3. The
electron-hole recombination rate is
(A) 4 1019� cm s� �3 1 (B) 4 1014� cm s� �3 1
(C) 4 1024� cm s� �3 1 (D) 4 1011� cm s� �3 1
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110 Semiconductor Physics Chap 2.1
5 10� 14
x(cm)
n(c
m)
-3
0.010
n(0)
0
Fig. P2.1.34
41. A semiconductor in thermal equilibrium, has a
hole concentration of p0
1610� cm�3 and an intrinsic
concentration of ni � 1010 cm�3. The minority carrier
life time is 4 10 7� � s. The thermal equilibrium
recombination rate of electrons is
(A) 2 5 1022. � cm s� �3 1 (B) 5 1010� cm s� �3 1
(C) 2 5 1010. � cm s� �3 1 (D) 5 1022� cm s� �3 1
Statement for Q.42-43:
A n-type silicon sample contains a donor
concentration of Nd � 106 cm�3. The minority carrier
hole lifetime is � �p0 10� s.
42. The thermal equilibrium generation rate of hole is
(A) 5 108� cm s� �3 1 (B) 104 cm s� �3 1
(C) 2 25 109. � cm s� �3 1 (D) 103 cm s� �3 1
43. The thermal equilibrium generation rate for
electron is
(A) 1125 109. � cm s� �3 1 (B) 2 25 109. � cm s� �3 1
(C) 8 9 10 10. � � cm s� �3 1 (D) 4 109� cm s� �3 1
44. A n �type silicon sample contains a donor
concentration of Nd � 1016 cm�3. The minority carrier
hole lifetime is � �p0 20� s. The lifetime of the majority
carrier is ( . )ni � � �15 1010 3cm
(A) 8 9 106. � s (B) 8 9 10 6. � � s
(C) 4 5 10 17. � � s (D) 113 10 7. � � s
45. In a silicon semiconductor material the doping
concentration are Na � 1016 cm�3 and Na � 0. The
equilibrium recombination rate is Rp0
1110� cm�3s�1. A
uniform generation rate produces an excess- carrier
concentration of � �n p� � 1014 cm�3. The factor, by
which the total recombination rate increase is
(A) 2 3 1013. � (B) 4 4 1013. �
(C) 2 3 109. � (D) 4 4 109. �
***********
Solutions
1. (D) n N N ei c v
E
kT
g
2 ��
�
��
�
��
Vt �
�
�
� �0 0259
400
3000 0345. .
For Ge at 300 K,
Nc � �104 1019. , Nv � �6 0 1018. , Eg � 0 66. eV
n ei
2 19 18
3 0 66
0 0345104 10 6 0 10400
300� � � � �
�
�
� �
�
. .
.
.�
�
�
� � �ni 8 5 1014. cm�3
2. (C) n N N ei c v
E
kT
g
2 ��
�
��
�
��
( ) . .
.
10 2 8 10 104 10300
12 2 19 19
3 1 12
� � � �
�
�
�
�
�
�T
e
e
kT �
T e T3
13 10
8
3
9 28 10� �
�� �. , By trial T � 382 K
3. (B)n
n
e
e
iA
iB
E
kT
E
kT
gA
gB
2
2�
�
�� �
��
��
�
��
e
E E
kT
gA gB
2257 5. � �n
niA
iB
47 5.
4. (A) pn
ni
0
2
0
10 2
4
1515 10
5 104 5 10� �
�
�� �
( . ). cm�3
5. (A) p N ev
E E
kT
F v
0 ��
�( )
� ��
104 1019
0 22
0 0259..
.e � �2 1015 cm�3
6. (B) p N ev
E E
kT
F v
0 ��
�( )
� E E kTN
pF v
v� �
�
�
�ln
0
At 300 K, Nv � �10 1019. cm�3
E EF v� ��
�
�
� �0 0259
104 10
100 239
19
15. ln
.. eV
n N ec
E E
kT
c F
0 ��( )
At 300 K, Nc � �2 8 1019. cm�3
E Ec F� � � �112 0 239 0 881. . . eV
n0
44 4 10� �. cm�3
7. (C) pN N
NN
na da
di0
2
2
2 2�
�� �
�
�
� �
For Ge ni � �2 4 103.
p0
13 132
13 210
2
10
22 4 10� �
�
�
� � �( . ) � �2 95 1013. cm�3
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Chap 2.1 Semiconductor Physics 111
8. (A) nN N
NN
nd ad
ai0
2
2
2 2�
�� �
�
�
� �
��
��
�
�
� � �
5 10
2
5 10
22 4 10
15 152
13 2( . ) � �5 1015 cm�3
9. (B) pn
pi
0
2
0
13 2
13
2 4 10
2 95 10� �
�
�
( . )
.� �195 1013. cm�3
10. (A) Since N Na d� , thus material is p-type ,
p N Na d0
3 3 132 5 10 1 10 15 10� � � � � � � �. . cm�3
11. (D) kT �
�
�
� �0 0259
200
3000 0173. . eV
For GaAs at 300 K,
Nc � �4 7 1017. cm�3, Nv � �7 0 1018. , Eg � 1 42. eV
n ei
2 17 18
3 1 42
0 01734 7 10 7 0 10200
300� � � �
�
�
�
�
�
�
. .
.
. �
� �ni 1 48. cm�3
n n p pn
i
2
0 0 0
2 0
2
55
� � �
n ni0 5 3 3� � . cm�3
12. (A) kT �
�
�
� �0 0259
400
3000 0345. . eV
n N N ei c v
E
kT
g
2 ��
�
��
�
��
For Ge at 300 K,
Nc � �104 1019. cm�3 , Nv � �6 1018 cm�3 , Eg � 0 66. eV
n ei
2 19 18
3 0 66
0 0345104 10 6 10400
300� � � �
�
�
�
�
�
�
.
.
.�
� �7 274 1029.
ni � �8 528 1014. cm�3
pN N
na ai0
2
2
2 2� �
�
�
� �
� �
�
�
� � �
10
2
10
27 274 10
15 152
29.
� � �p0
151 489 10. cm�3
E E kTp
nFi F� �
�
�
�ln 0
0
��
�
�
�
�0 0345
1 489 10
8 528 10
15
14. ln
.
.
� 0 019. eV
13. (A) nN N
nd di0
2
2
2 2� �
�
�
� �
For Ge at T � 300 K, ni � �2 4 1013. cm�3
n0
14 142
13 2 1410
2
10
22 4 10 1055 10� �
�
�
� � � � �( . ) . cm�3
E E kTn
nF Fi
i
� �
�
�
�ln 0 �
�
�
�
�
�0 0259
1055 10
2 4 10
14
13. ln
.
.
� 0 0383. eV
14. (A) nN N
nd di0
2
2
2 2� �
�
�
� �
n ni � 0 05 0.
� � � � � �n n0
15 15 2
0
215 10 15 10 0 05. ( . ) ( . )
� � �n0
1530075 10. cm�3
ni � �1504 1014. cm�3
n N N ei c v
E
kT
g
2 ��
�
��
�
��
For GaAs at T � 300 K,
Nc � �4 7 1017. , Nv � �7 1018, Eg � 1 42. eV
( . ) .
.
.1504 4 7 10 7 10300
2 17 18
3 1 42 300
0 025� � � �
�
�
�
��
Te 9T
�
�
�
By trial and error T � 763 K
15. (A) E E kTm
mFi midgap
p
p
� �
��
�
�� �
3
40 0446ln .
*
*eV
16. (A) n N N N ed a c
E E
kT
c F
0 � � ��
�
�
�
�
For Si, Nc � �2 8 1019. cm�3
N ed � � � ��
�
�
�
5 10 2 8 1015 19
0 215
0 0259.
.
. � �119 1016. cm�3
17. (A) E E kTN
NF Fi
d
i
� �
�
�
�ln
��
�
�
� �0 0259
10
15 100 287
15
10. ln
.. eV
18. (D) RV
I� � �
20
100200
m�
� � �� �L
RA
2 10
200 0 001
3
( ) ( . )� � �0 01 1. ( )� cm
� � e nn� 0, For Si, � n � 1350.
� � � �0 01 1 6 10 135019
0. ( . )( )n
n0
134 6 10� �. cm�3,
n ni0 �� � n Nd0 �
19. (B) N nd i�� � n Nd0 � , � � e nn� 0,
RL
A
L
e N An d
��
��
,
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112 Semiconductor Physics Chap 2.1
�� � �� �
0 1
1 6 10 1100 5 10 100 1019 16 8
.
( . )( )( )( )� 11 36. k�
20. (A) RL
A�
�, � � e nn� 0 , R
L
e n An
�� 0
� �nL
e ARn
0 �
n Nd0 0 9� .
��
� �� �
�
� �
20 10
0 9 1 6 10 8000 10 2 108 7 10
4
19 6 3( . )( . )( )( )( ). 15 cm�3
21. (B) � � e nn� 0, RL
A�
�, n
L
e ARn
0 ��
��
�
�
� �
10 10
1 6 10 800 10 10
4
19 6( . )( )( )( )� �7 81 1017. cm�3
Efficiency � � ��
� �n
Nd
0
17
18100
7 8 10
10100 78 1
.. %
22. (D) EV
L� � �
6
23 V/cm, v Ed n� � ,
� ndv
E� �
10
3
4
� 3333 cm V s2 �
23. (D) � � �1 eni n p( )� �
10 1 6 10 1000 6006 19� �� � �( . )( )ni
At T � 300 K, ni � �391 109. cm�3
n N N ei c v
E
kT
g
2 ��
��
�
��
� �
�
�
�E kT
N N
ng
c v
i
ln2
� ��
�
�
�Eg 2 0 0259
10
391 10
19
9( . ) ln
.� 1122. eV
At T � 500 K , kT �
�
�
� �0 0259
500
3000 0432. . eV,
n ei
2 19 2
1 122
0 043210��
�
�
�
( )
.
. cm�3,
� � �ni 2 29 1013. cm�3
� � � ��( . )( . )( )1 6 10 2 29 10 1000 60019 13
� � �� �5 86 10 3 1. ( )� cm
24. (B) ��
��
�1 1
e Nn d
Ne
d
n
�1
� ��
� �
1
5 1 6 10 135019( . )( )� �9 25 1014. cm�3
25. (B) J eDdn
dxn n�
� ��
�
�
�
��
�( . )( )1 6 10 35
10 10
2 10
1918 16
4� �2 8 104. A cm2
26. (A) J evn� � � �( . )( )( )1 6 10 10 1019 7 16 � 1 6. A cm2
27. (A) ve E
md
sc
e
��
*�
�
�
� �
�
( . )( )( )
( . )( . )
1 6 10 10 10
0 067 9 1 10
19 13 5
31
� �26 2 103. m s � �2 6 106. cm s
28. (A) N nd i�� � n Nd0 �
J e n En� � 0 � � ��( . )( )( )( )1 6 10 7500 10 10 12019 16 A cm2
29. (D) n N N ei c v
E
kT
g
2 ��
�
��
�
��
� � ��
�
�
�
( )( )
.
.2 10 1 1019 19
1 1
0 0259e � �7 18 1019.
� � �ni 8 47 109. cm�3
N n N nd i d�� � � 0
J E e n En� � � � 0
� � ��( . )( )( )( ) .1 6 10 1000 10 100 1 619 14 A cm2
30. (A) � � �� �e n e pn p0 0 and nn
pi
0
2
0
�
� � � �en
pe pn
ip� �
2
0
0 ,
d
dp
e n
pen i
p
�� �
��
0
2
0
20
1( ) ��
� �
��
�
��p ni
n
p
0
1
2�
�� �
�
�
�3 6 10
7500
300
12
1
2
.
� �7 2 1011. cm�3
31. (B) � ��
��min
22
i p n
p n
i p nen� �
� �� �
� � � ��2 1 6 10 3 6 10 7500 30019 12. ( . ) ( )( )
� � �� �17 10 3 1. ( )� cm
32. (B) � � �1
��e ni ,
1
11
2
1
2
2
2
1
2
�
�
� �
�
�
n
n
e
e
i
i
E
kT
E
kT
g
g
0 12
1 1
1 2. �� �
�
�
�
e
E
k T T
g
E
k
g
2
330 300
330 30010
�
�
�
�
� � ln
E kg � 22 300 10( ) ln � 1 31. eV
33. (D)1 1 1 1
1 2 3� � � �� � �
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Chap 2.1 Semiconductor Physics 113
1 1
500
1
750
1
1500�� � � � � � 250 cm V s2 �
34. (B) J eDdn
dxn n�
0 19 1 6 10 255 10 0
0 010
1914
. ( . )( )( )
.� �
� �
�
�
�� n,
n( ) .0 2 5 1013� � cm�3
35. (B) J eDdp
dxeD
d
dx
x
Lp p� � � � �
�
�
�
�
�
�10 116 �
e D
L
p1016
��
�
�
�
( . )( )( )1 6 10 10 10
10 10
19 16
4
J � 16 A cm2
36. (B) J eDdp
dx
eD
Lp p
x
p
p
� � ��
0
0
1510
J e Ddn
dxn n
x
��
0
0
��5 1014 eD
Ln
n
J J JeD
L
eD
Lp n
p
p
n
n
� � � ��10 5 10
15 14
� ��
��
�
�
� ��
� �1 6 10
10 10
15 10
5 10 25
105 219
15
4
14
3.
( ) ( ). A cm2
37. (A) VI B
nedH
x z��
�� �
� � �� �
� �
� �
( )( )
( )( . )( ).
250 10 5 10
5 10 1 6 10 5 100
6 2
21 19 5313 mV
38. (B) VH is positive p-type
VI B
epdp
I B
eV dH
x z x z
H
� � �
p ��
� �
� �
� � �
( . )( )
( . )( . )( )
0 75 10 10
1 6 10 5 8 10 10
3 1
19 3 5
� � � ��8 08 10 8 08 1021 3 15. .m cm�3
39. (C) uI L
epV Wdp
x
x
�
��
� �
� �
� �
( . )( )
( . )( . )( )( )
0 75 10 10
1 6 10 8 08 10 15 10
3 3
19 21 4 ( )10 5�
� p � � �39 10 2. m V s2 � � 390 cm V s2 �
40. (A) n-type semiconductor
Rp
p
� ��
� ��
�
� 0
13
6
194 10
104 10 cm s� �3 1
41. (C) nn
pi
0
2
0
10 2
16
410
1010� � �
( )cm�3
Rn
n
n
00
0
4
7
1010
4 102 5 10� �
�� �
��. cm s� �3 1
42. (C) Rp
n
p
00
0
��
, pn
ni
0
2
0
� , n Nd0
610� � cm�3
p0
10 2
16
415 10
102 25 10�
�� �
( . ). cm�3
Rn 0
4
6
92 25 10
10 102 25 10�
�
�� �
�
.. cm s� �3 1
43. (B) Recombination rate for minority and majority
carrier are equal . The generation rate is equal to
Recombination rate.
G R Rn p� � � �0 0
92 25 10. cm s� �3 1
44. (A) Recombination rates are equaln p
n p
0
0
0
0� �� ,
N nd i��
n Nd0 � , pn
ni
0
2
0
�
� � �n p
i
p
n
p
n
n0
0
0
00
2
2 0� �
��
�
�
� � � �10
15 1020 10
16
10
2
6
.� �8 9 106. s
45. (D) N n n Nd i d�� � �0
pn
ni
0
2
0
10 2
16
415 10
102 25 10� �
�� �
( . ). cm�3
Rp p
Rp
p
p
p
00
0
00
0
4
11
72 25 10
102 25 10� � � �
�� �
��
.. s
Rp
p
p
� ��
� ��
�
� 0
14
7
2010
2 25 104 44 10
.. cm s� �3 1
R
R
p
p0
20
11
94 44 10
104 44 10�
�� �
..
***********
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114 Semiconductor Physics Chap 2.1
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