Module 2- Semiconductor Physics

FaaDo

OEngi

neers.c

om

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 ( )cm3

28 1019. 47 1017. 104 1019.

Effective density ofstates in valence

band Nv ( )cm3

104 1019. 70 1018. 60 1018.

Intrinsic carrierconcertration

ni ( )cm3

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. cm3 (B) 18 4 1014. cm3

(C) 8 5 1014. cm3 (D) 3 6 1014. cm3

2. The intrinsic carrier concentration in silicon is to be

no greater than ni 1 1012 cm3. 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 n045 10 cm3. The hole

concentration is

(A) 4 5 1015. cm3 (B) 4 5 1015. m3

(C) 0 3 10 6. cm3 (D) 0 3 10 6. m3

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 cm3 (B) 1015 cm3

(C) 3 1015 cm3 (D) 4 1015 cm3

6. The thermal-equilibrium concentration of hole p0 in

silicon at T 300 K is 1015 cm3. The value of n0 is

(A) 3 8 108. cm3 (B) 4 4 104. cm3

(C) 2 6 104. cm3 (D) 4 3 108. cm3

7. In germanium semiconductor at T 300 K, the

acceptor concentrations is Na 1013 cm3 and donor

concentration is Nd 0. The thermal equilibrium

concentration p0 is

(A) 2 97 109. cm3 (B) 2 68 1012. cm3

(C) 2 95 1013. cm3 (D) 2 4. cm3

Statement for Q.8-9:

In germanium semiconductor at T 300 K, the

impurity concentration are

Nd 5 1015 cm3 and Na 0

8. The thermal equilibrium electron concentration n0

is

www.nodia.co.in

FaaDo

OEngi

neers.c

om

(A) 5 1015 cm3 (B) 115 1011. cm3

(C) 115 109. cm3 (D) 5 106 cm3

9. The thermal equilibrium hole concentration p0 is

(A) 396 1013. (B) 195 1013. cm3

(C) 4 36 1012. cm3 (D) 396 1013. cm3

10. A sample of silicon at T 300 K is doped with

boron at a concentration of 2 5 1013. cm3 and with

arsenic at a concentration of 1 1013 cm3. The

material is

(A) p type with p01315 10 . cm3

(B) p type with p0715 10 . cm3

(C) n type with n01315 10 . cm3

(D) n type with n0715 10 . cm3

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. cm3 (B) 7 cm3

(C) 4 86 103. cm3 (D) 3 cm3

12. Germanium at T 300 K is uniformly doped with

an acceptor concentration of Na 1015 cm3 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 cm3 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 cm3. 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 cm3. 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 cm3. 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. cm3 (B) 4 6 1016. cm3

(C) 39 1012. cm3 (D) 2 4 1012. cm3

17. A silicon semiconductor sample at T 300 K is

doped with phosphorus atoms at a concentrations of

1015 cm3. 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. cm3 (B) 4 6 1013. cm3

(C) 7 8 1014. cm3 (D) 8 4 1014. cm3

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. cm3 (B) 8 7 1021. cm3

(C) 4 6 1015. cm3 (D) 4 6 1021. cm3

21. A silicon sample doped n type at 1018 cm3 have a

resistance of 10 . The sample has an area of 10 6

www.nodia.co.in

108 Semiconductor Physics Chap 2.1

FaaDo

OEngi

neers.c

om

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 cm3

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. cm3 (B) 9 25 1014. cm3

(C) 11 46 1015. cm3 (D) 11 10 15. cm3

25. In a silicon sample the electron concentration

drops linearly from 1018 cm3 to 1016 cm3 over a length

of 2.0 m. The current density due to the electron

diffusion current is ( )Dn 352cm 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 cm3. 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 electrons 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 cm3. 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 cm3. Assume the following

parameters,

n 1000 cm V s2

,

NT

c

2 10300

19

3 2

cm3,

NT

v

1 10300

19

3 2

cm3,

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. cm3

30. When conductivity is minimum, the hole

concentration is

(A) 7 2 1011. cm3 (B) 1 8 1013. cm3

(C) 1 44 1011. cm3 (D) 9 1013 cm3

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

www.nodia.co.in

Chap 2.1 Semiconductor Physics 109

FaaDo

OEngi

neers.c

om

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 252cm s, The electron concentration

at is

(A) 4 86 108. cm3 (B) 2 5 1013. cm3

(C) 9 8 1026. cm3 (D) 5 4 1015. cm3

35. The hole concentration in p type GaAs is given by

px

L

10 116 cm3 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

cm3,x 0

Electron concentration n e

x

Ln0

145 10

cm3,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 cm3, n type

(B) 8 1015 cm3, p type

(C) 4 1015 cm3, n type

(D) 4 1015 cm3, 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 n01510 cm3 and ni 10

10

cm3. The excess-carrier life time is 10 6 s. The excess

hole concentration is p 4 1013 cm3. 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

www.nodia.co.in


5 1014

x(cm)

n(c

m)

-3

0.010

n(0)

0

Fig. P2.1.34

FaaDo

OEngi

neers.c

om

41. A semiconductor in thermal equilibrium, has a

hole concentration of p01610 cm3 and an intrinsic

concentration of ni 1010 cm3. 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 cm3. 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 cm3. 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 cm3 and Na 0. The

equilibrium recombination rate is Rp01110 cm3s1. A

uniform generation rate produces an excess- carrier

concentration of n p 1014 cm3. 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 0259400

3000 0345. .

For Ge at 300 K,

Nc 104 1019. , Nv 6 0 10

18. , Eg 0 66. eV

n ei2 19 18

3 0 66

0 0345104 10 6 0 10400

300

. .

.

.

ni 8 5 1014. cm3

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

Te

e

kT

T e T313 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

( . ). cm3

5. (A) p N ev

E E

kT

F v

0

( )

104 10190 22

0 0259..

.e 2 1015 cm3

6. (B) p N ev

E E

kT

F v

0

( )

E E kTN

pF v

v

ln0

At 300 K, Nv 10 1019. cm3

E EF v

0 0259104 10

100 239

19

15. ln

.. eV

n N ec

E E

kT

c F

0

( )

At 300 K, Nc 2 8 1019. cm3

E Ec F 112 0 239 0 881. . . eV

n044 4 10 . cm3

7. (C) pN N

NN

na d ad

i0

2

2

2 2

For Ge ni 2 4 103.

p0

13 132

13 210

2

10

22 4 10

( . ) 2 95 1013. cm3

www.nodia.co.in


FaaDo

OEngi

neers.c

om

8. (A) nN N

NN

nd a da

i0

2

2

2 2

5 10

2

5 10

22 4 10

15 152

13 2( . ) 5 1015 cm3

9. (B) pn

pi

0

2

0

13 2

13

2 4 10

2 95 10

( . )

. 195 1013. cm3

10. (A) Since N Na d , thus material is p-type ,

p N Na d03 3 132 5 10 1 10 15 10 . . cm3

11. (D) kT

0 0259200

3000 0173. . eV

For GaAs at 300 K,

Nc 4 7 1017. cm3, Nv 7 0 10

18. , Eg 1 42. eV

n ei2 17 18

3 1 42

0 01734 7 10 7 0 10200

300

. .

.

.

ni 1 48. cm3

n n p pn

i

2

0 0 0

2 0

2

55

n ni0 5 3 3 . cm3

12. (A) kT

0 0259400

3000 0345. . eV

n N N ei c v

E

kT

g

2

For Ge at 300 K,

Nc 104 1019. cm3 , Nv 6 10

18 cm3 , Eg 0 66. eV

n ei2 19 18

3 0 66

0 0345104 10 6 10400

300

.

.

.

7 274 1029.

ni 8 528 1014. cm3

pN N

na a i0

2

2

2 2

10

2

10

27 274 10

15 152

29.

p0151 489 10. cm3

E E kTp

nFi F

ln 0

0

0 03451 489 10

8 528 10

15

14. ln

.

.

0 019. eV

13. (A) nN N

nd d i0

2

2

2 2

For Ge at T 300 K, ni 2 4 1013. cm3

n0

14 142

13 2 1410

2

10

22 4 10 1055 10

( . ) . cm3

E E kTn

nF Fi

i

ln 0

0 02591055 10

2 4 10

14

13. ln

.

.

0 0383. eV

14. (A) nN N

nd d i0

2

2

2 2

n ni 0 05 0.

n n015 15 2

0

215 10 15 10 0 05. ( . ) ( . )

n01530075 10. cm3

ni 1504 1014. cm3

n N N ei c v

E

kT

g

2

For GaAs at T 300 K,

Nc 4 7 1017. , Nv 7 10

18, 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. cm3

N ed

5 10 2 8 1015 190 215

0 0259.

.

. 119 1016. cm3

17. (A) E E kTN

NF Fi

d

i

ln

0 025910

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

n0134 6 10 . cm3,

n ni0 n Nd0

19. (B) N nd i n Nd0 , e nn 0,

RL

A

L

e N An d

,

www.nodia.co.in


FaaDo

OEngi

neers.c

om

0 1

1 6 10 1100 5 10 100 1019 16 8.

( . )( )( )( ) 11 36. k

20. (A) RL

A

, e nn 0 , RL

e n An

0

nL

e ARn0

n Nd0 0 9 .

20 10

0 9 1 6 10 8000 10 2 108 7 10

4

19 6 3( . )( . )( )( )( ). 15 cm3

21. (B) e nn 0, RL

A

, nL

e ARn0

10 10

1 6 10 800 10 10

4

19 6( . )( )( )( ) 7 81 1017. cm3

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. cm3

n N N ei c v

E

kT

g

2

E kTN N

ng

c v

i

ln2

Eg 2 0 025910

391 10

19

9( . ) ln

. 1122. eV

At T 500 K , kT

0 0259500

3000 0432. . eV,

n ei2 19 2

1 122

0 043210

( )

.

. cm3,

ni 2 29 1013. cm3

( . )( . )( )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. cm3

25. (B) J eDdn

dxn n

( . )( )1 6 10 3510 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 191 1

0 0259e 7 18 1019.

ni 8 47 109. cm3

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 nin

p

0

1

2

3 6 107500

300

12

1

2

.

7 2 1011. cm3

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

www.nodia.co.in


FaaDo

OEngi

neers.c

om

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 cm3

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 1015 14

1 6 1010 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 cm3

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

( )cm3

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 Nd0610 cm3

p0

10 2

16

415 10

102 25 10

( . ). cm3

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 0 092 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

( . ). cm3

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

..

***********

www.nodia.co.in


Module 2- Semiconductor Physics

Documents

Transcript of Module 2- Semiconductor Physics