Semiconductor Objective Question

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


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


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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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


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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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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��

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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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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Semiconductor Objective Question

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