Semiconductor Objective Question

(1)

In the problems assume the parameter given in In the problems assume the parameter given in follo

following table. wing table. Use Use the the tempertemperatureature T T

=

300 K unless300 K unless other

otherwise wise stated.stated. P Prrooppeerrtty y SSii GaAsGaAs GeGe B Baannddggaap p EEnneerrggy y 1.1.112 2 11..442 2 00..6666 D Diieelleeccttrriic c CCoonnssttaannt t 1111..7 7 1133..1 1 1166..00 Effective density of

Effective density of states in conduction states in conduction band band N N _c_c( ( cmcm--33)) 2 8 2 8 _._.

_´

10101919 _{4 7}_{4 7}_._.

_´

₁₁₀₀1717 _{1 0}_{1 04}_._. ₄

_´

₁₁₀₀1919

Effective density of Effective density of

states in valence states in valence band band N N vv( ( cmcm )) --33 1 0 1 04 _._. 4

_´

11001919 _{7 0}_{7 0}_._.

_´

₁₁₀₀1818 _{6 0}_{6 0}_._.

_´

₁₁₀₀1818 Intrinsic carrier Intrinsic carrier concertration concertration n n_i_i ( ( cmcm--33)) 1 5 1 5 _._.

_´

10101010 _{1 8}_{1 8}_._.

_´

₁₁₀₀66 _{2 4}_{2 4}_._.

_´

₁₁₀₀1818 Mobility Mobility Electron Electron Hole Hole 1350 1350 480 480 8500 8500 400 400 3900 3900 1900 1900 1.

1. In In germangermanium ium semicosemiconductonductor r materimaterial al atat T T

=

400 K 400 K the intrinsic concentration is

the intrinsic concentration is (

(A) A) 226 6 8 _._.8

_´

10101414 _cm_cm--33 _(B_(B)_{) 18}₁₈_._.₄₄

_´

₁₀₁₀1414 _cm_cm--33 (

(CC) ) 8 5 8 5 ..

´

10101414 cmcm--33 ((DD) ) 3 6 3 6 ..

´

10101414 cmcm--33

2.

2. The intrinsic carrier concentration in silicon is to beThe intrinsic carrier concentration in silicon is to be no

no grgreaeateter r ththanan nn_i_i

=

1 1

´

10101212 _cm_cm--33_._. _Th_The_e _ma_maxi_xi_mu_mum_m te

tempmpererataturure e alallolowewed d fofor r ththe e sisililicocon n is is (A(Assssumumee

E

E g g

=

1112..12 eV)eV) (

(AA) ) 33000 0 K K ((BB) ) 33660 0 K K (

(CC) ) 33882 2 K K ((DD) ) 33664 4 K K

3.

3. Two semiconductor material have exactly the sameTwo semiconductor material have exactly the same properties except that material A has a bandgap of 1.0 properties except that material A has a bandgap of 1.0

eV and material B has a bandgap energy of 1.2 eV. eV and material B has a bandgap energy of 1.2 eV. The

The ratratio io of of intintrinrinsic sic conconcencentratratiotion n of of matmaterierial al A A toto that of material B is that of material B is ( (AA) ) 2200116 6 ((BB) ) 4477..55 ( (CC) ) 5588..223 3 ((DD) ) 11004488 4.

4. In In sisililicocon n atat T T

=

300 300 K K the the thethermarmal-el-equiquiliblibriuriumm concentration of electron is concentration of electron is nn00 4 4 5 5 1010

=

´

cmcm--33_{. The hole}_{. The hole} concen concentratitration on isis ( (AA) ) 4 5 4 5 _._.

_´

10101515_cm_cm--33 ₍_(B_B)₎_{4 5}_{4 5}_._.

_´

₁₀₁₀1515 _m_m--33 (C) (C) 0 0 _._.3 3

_´

1010--66 _cm_cm--33 _(D)_(D) ₀₀_._.₃₃

_´

₁₀₁₀--66 _m_m--33 5.

5.In silicon atIn silicon atT T

=

300300K if the Fermi energy is 0.22 eV K if the Fermi energy is 0.22 eV above the valence band energy, the value of

above the valence band energy, the value of pp00 isis (

(AA) ) 2 2

_´

11001515_cm_cm--33 _{(B) 10}_{(B) 10}1515_cm_cm--33 (

(CC) ) 3 3

_´

11001515_cm_cm--33 ₍_(D_D)₎₄₄

_´

₁₁₀₀1515 _cm_cm--33

6.

6. The thermal-equilibrium concentration of holeThe thermal-equilibrium concentration of hole pp00 inin silicon at

silicon at T T

=

300300 K K isis 10101515cmcm--33. The value of . The value of nn00 isis (

(AA) ) 3 8 3 8 _._.

_´

101088 _cm_cm--33 ₍_(B_{B) 4}_{) 4}_._.₄₄

_´

₁₁₀₀44 _cm_cm--33 (

(CC) ) 2 2 6 _._.6

_´

101044 _cm_cm--33 ₍_(D_{D) 4}_{) 4}_._.₃₃

_´

₁₁₀₀88 _cm_cm--33

7.

7. In In gergermanmanium ium semsemicoicondunductoctor r atat T T

=

300300 K, K, ththee accept

acceptor or concenconcentratiotrations ns isis N N aa

=

1010 13

13 _cm_cm--33 _and_and _dono_dono_r_r con

concencentratratiotion n isis N N dd

=

0. 0. ThThe e ththerermamal l eqequiuililibrbriuiumm concentration concentration pp00 isis (A) (A) 2 92 97 _._. 7

_´

101099 _cm_cm--33 _(B)_(B) ₂_{2 6}_._.₆₈₈

_´

₁₁₀₀1212 _cm_cm--33 (C) (C) 2 92 95 _._. 5

_´

11001313 _cm_cm--33 _(D)_(D) _{2 4}_{2 4}_._. _cm_cm--33 Statem

Statement for ent for Q.8-9:Q.8-9: In

In germangermanium semiconductium semiconductor or atat T T

=

300300 K, theK, the impurity concentration are

impurity concentration are

N N dd

=

5 5

´

1010 15 15 _cm_cm--33 _and_and N N aa

=

00 8.

8. The thermal equilibrium electron concentrationThe thermal equilibrium electron concentration nn00 is

(2)

(

(AA) ) 5 5

_´

10101515_cm_cm--33 ₍_(B_B)_{) 11}₁₁₅_._. ₅

_´

₁₀₁₀1111 _cm_cm--33 (

(CC) ) 11115 _._. 5

_´

110099_cm_cm--33 _(D₍_D)_{) 5}₅

_´

₁₁₀₀66 _cm_cm--33

9.

9. The thermal equilibrium hole concentrationThe thermal equilibrium hole concentration pp00 isis (

(AA) ) 39396 _._. 6

_´

11001313 ₍_(B_B)_{) 19}₁₉₅_._. ₅

_´

₁₀₁₀1313_cm_cm--33 (

(CC) 4 ) 4 3_._.36 6

_´

11001212 _cm_cm--33 _(D₍_D)₎₃₉₃₉₆_._. ₆

_´

₁₁₀₀1313_cm_cm--33

10.

10. A A sasampmple le of of sisililicocon n atat T T

=

30300 0 K K is is dodopeped d wiwithth bo

bororon n at a at a coconcncenentrtratatioion n of 25 of 25 _._.

_´

10101313 _cm_cm--33 _and_and _wit_wit_h_h a

arrsseenniic c aat t a a ccoonncceennttrraattiioon n oof f 1 1

´

11001313 cmcm--33. . TThhee material is

material is (A)

(A) pp

-

type withtype with pp00

13 13 1 15 5 1100

=

. .

´

cmcm--33 (B)

(B) pp

-

type withtype with pp00

7 7 1 15 5 1100

=

. .

´

cmcm--33 (C)

(C) nn

-

type withtype with nn00

13 13 1 15 5 1100

=

. .

´

cmcm--33 (D)

(D) nn

-

type withtype with nn00

7 7 1 15 5 1100

=

. .

´

cmcm--33 11

11.. In In a a samsamplple e of of gagalllliuium m ararseseninide de atat T T

=

20200 0 K,K,

n

n 0 0

=

55pp00 andand N N aa

=

0. The value of 0. The value of nn00 isis (A)

(A) 9 9 8_._.86 6

_´

110099 _cm_cm--33 _{(B) 7}_{(B) 7} _cm_cm--33 (C)

(C) 4 4 8_._.86 6

_´

110033 _cm_cm--33 _(D)_(D) _{3 cm}_{3 cm}--33

12.

12. Germanium atGermanium at T T

=

300 K is uniformly doped with300 K is uniformly doped with an acceptor concentration of

an acceptor concentration of N N aa

=

1010 15

15_cm_cm--33_{and a donor}_{and a donor} conce

concentratintration on of of N N dd

=

00. The position of fermi energy. The position of fermi energy with respect to intrinsic Fermi level is

with respect to intrinsic Fermi level is ( (AA) ) 00..002 2 eeV V ((BB) ) 00..004 4 eeV V ( (CC) ) 00..006 6 eeV V ((DD))00..008 8 eeV V 13. 13. IIn n ggeerrmmaanniiuum m aatt T T

=

33000 0 KK, , ththe e ddoonnoorr conce

concentratintration on areare N N dd

=

1010 14 14

cm

cm--33 andand N N aa

=

0. 0. ThThee Fer

Fermi mi eneenergy rgy levlevel el witwith h respecrespect t to to intintrinrinsic sic FerFermimi level is level is ( (AA) ) 00..004 4 eeV V ((BB) ) 00..008 8 eeV V ( (CC) ) 00..442 2 eeV V ((DD) ) 00..886 6 eeV V 14.

14.A GaAs device is doped with a donor concentrationA GaAs device is doped with a donor concentration o

of f 3 3

_´

10101515_cm_cm--33_{. For the device to operate properly, the}_{. For the device to operate properly, the} intrinsic carrier concentration must remain less than intrinsic carrier concentration must remain less than 5%

5% of of ththe e tototatal l coconcncenentrtratatioion. n. ThThe e mamaxiximumumm temperature on that the device may operate is

temperature on that the device may operate is (

(AA) ) 77663 3 K K ((BB) ) 99442 2 K K (

(CC) ) 44886 6 K K ((DD) ) 22443 3 K K

15.

15. FoFor r a a papartrticiculular ar sesemimicocondnducuctotor r atat T T

=

33000 0 K K

E E g g

=

115. . 5 eVeV,, m m p p mmnn * *

₌

₁₁₀₀ ** _a_an_nd_d n nii

=

1 1

´

1010 15 15 _cm_cm--33_._. _T_Th_he_e

position of Fermi level with respect to the center of the position of Fermi level with respect to the center of the bandgap is

bandgap is (A)

(A)

+

00..00445 5 eV eV ((BB))

-

0.046 eV 0.046 eV (C)

(C)

+

00..00339 9 eV eV ((DD))

-

0.039 eV 0.039 eV

16.

16. A A sisililicocon n samsamplple e cocontntaiains ns acacceceptptor or atoatoms ms at at aa concen

concentratitration on of of N N aa

=

5 5

´

1010 15

15 _cm_cm--33_._. _Do_Dono_nor_r_at_{atoms are}_{oms are} a

addddeed d ffoorrmmiinng g aanndd nn

-

tytype pe cocompmpenensasatetedd semiconductor such that the Fermi level is 0.215 eV semiconductor such that the Fermi level is 0.215 eV below the conduction band edge. The concentration of below the conduction band edge. The concentration of donors atoms added are

donors atoms added are (A)

(A) 112 _._.2

_´

10101616 _cm_cm--33 _(B)_(B) ₄₄_._.₆₆

_´

₁₁₀₀1616 _cm_cm--33 (

(CC) ) 39 39 _._.

_´

10101212 _cm_cm--33 ₍_(D_D)_{) 2}_{2 4}_._.₄

_´

₁₀₁₀1212 _cm_cm--33

17.

17. A A silsilicoicon n semsemicoiconducnductor tor sampsample le atat T T

=

300300 K K isis dope

doped d witwith h phophosphosphorus rus atoatoms ms at at a a conconcencentratratiotions ns of of 10

101515 cmcm--33. The position of the Fermi level with respect. The position of the Fermi level with respect to the intrinsic Fermi level is

to the intrinsic Fermi level is (

(AA) ) 00..3 3 eeV V ((BB) ) 00..2 2 eeV V (

(CC) ) 00..1 1 eeV V ((DD) ) 00..4 4 eeV V

18.

18. A A silsilicoicon n crycrystal having a stal having a crocross-ss-sectsectionional al arearea a of of 0.001

0.001 cmcm22 _{and a length of 20}_{and a length of 20}

_m

_{m is connected to its}_{m is connected to its} en

ends ds to to a a 20 20 V V babattttereryy. . AtAt T T

=

300300 KK, , we we wwaannt t aa cu

currrrenent t of of 10100 0 mA in mA in crcrysystatal. l. ThThe e coconcncenentrtratatioion n of of donor atoms to be added is

donor atoms to be added is (

(AA) ) 2 2 4 ..4

´

10101313cmcm--33 ((BB) 4 ) 4 ..6 6

´

11001313cmcm--33 (C)

(C) 7 7 _._.8 8

_´

11001414 _cm_cm--33 _(D)_(D) ₈₈_._.₄₄

_´

₁₁₀₀1414 _cm_cm--33

19.

19. The cross sectional area of silicon bar is 100The cross sectional area of silicon bar is 100

m

mm22_._. Th

The e lelengngth of th of babar r is 1 is 1 mmmm. . ThThe e babar r is dopis doped wited withh arsenic atoms. The resistance of bar is

arsenic atoms. The resistance of bar is (A) 2.58 m

(A) 2.58 m

W

(B) 11.36 k(B) 11.36 k

W

(C) 1.36 m

W

(D) 24.8 k(D) 24.8 k

W

20.

20.A thin film resistor is to be made from a GaAs filmA thin film resistor is to be made from a GaAs film doped

doped nn

-

type. The resistor is to have a value of 2 ktype. The resistor is to have a value of 2 k

W

.. The resistor length is to be 200

The resistor length is to be 200

m

m and area is to bem and area is to be 10

10--66 _cm_cm22_._._{The dopin}_{The doping}_g_eff_effici_icienc_ency_y_{is known to}_{is known to}_{be 90%.}_{be 90%.} T Thhe e mmoobbiilliitty y oof f eelleeccttrroonns s iis s 8800000 0 ccm m 22 V V

_-

ss_._. _T_Th_he_e doping needed is doping needed is (A) (A) 8 7 8 7 _._.

_´

10101515_cm_cm--33 _(B)_(B) _{8 7}_{8 7}_._.

_´

₁₀₁₀2121 _cm_cm--33 ( (CC) 4 ) 4 _._.6 6

_´

11001515 _cm_cm--33 ₍_(D_{D) 4}_{) 4}_._.₆₆

_´

₁₁₀₀2121 _cm_cm--33 21.

21.A silicon sample dopedA silicon sample doped nn

-

type attype at10101818 _cm_cm--33_{have a}_{have a} resistance of 10

resistance of 10

W

. The sample has an area of . The sample has an area of 1010--66 1

(3)

cm

cm22 _{and a length of 10}_{and a length of 10}

_m

_{m . The doping efficiency of}_{m . The doping efficiency of} the sample is ( the sample is (

m

_n_n

=

88000 0 ccm m 22 V V

-

ss)) ( (AA) ) 4433..22% % ((BB) ) 7788..11%% ( (CC) ) 9966..33% % ((DD) ) 5544..33%% 22. 22. SSiix x vvoolltts s iis s aapppplliieed d aaccrroosss s a a 2 2 ccm m lloonng g semic

semiconductoonductor r barbar. . The average The average drift velocity isdrift velocity is 101044 cm s. The electron mobility is

cm s. The electron mobility is (

(AA) ) 4433996 6 ccm m 22 V V

_-

ss ₍_(B_B)₎₃₃

_´

₁₀₁₀44 _c_{cm V}_{m V}22

_-

_s_s (C)

(C) 6 6

_´

101044 _c_cm_m22 _V_V

_-

_s_s _(D)_(D) ₃₃₃₃₃₃₃_{3 c}_cm_m22 _V_V

_-

_s_s

23.

23. For a For a particulparticular ar semiconsemiconductor material following ductor material following paramete

parameters rs are are observedobserved::

m

_n_n

=

1100000 0 ccm m 22 V V

_-

ss _,_,

m

_p_p

=

66000 0 ccm m 22 V V

_-

ss _,_, N N c c

=

N N vv

=

1010 19 19 cm cm--33 T Thheesse e ppaarraammeetteerrs s arare e iinnddeeppeennddeennt t oof f te

tempmpererataturure. e. ThThe e memeasasurured ed cocondnducuctitivivity ty of of ththee int

intrinrinsic sic matmaterierial al isis

s =

1010- - 6 6 ₍₍

_W

-

_c_cm_m₎₎--11 _a_at_t

T T

=

30300 0 K.K. The conductivity at The conductivity at T T

=

500500 K K isis (A) (A) 2 2

´

1010--44 ( (

W

W -

-

cmcm))--11 (B)(B) 4 4

´

1010--55( (

W

-

cmcm))--11 ( (CC) ) 2 2

_´

1100--55 ₍₍

_W

_-

_cm_cm₎₎--11 _(D₍_D)₎₆₆

_´

₁₁₀₀--33₍₍

_W

_-

_cm_cm₎₎--11 24.

24. AnAn nn

-

typtype e silsilicoicon n sampsample le has a has a resresististiviivity ty of of 55

W

-

ccm m aatt T T

=

30300 0 K. K. The The momobibilility ty isis

m

_n_n

=

13501350 c

cm m 22 V V

_-

ss_{. The donor impurity concentration is}_{. The donor impurity concentration is} (A)

(A) 2 2 8_._.86 6

_´

1100--1414 _cm_cm--33 _(B)_(B) _{9 2}_{9 25}_._. ₅

_´

₁₁₀₀1414 _cm_cm--33 (

(CC) ) 1111_._.446 6

_´

11001515_cm_cm--33 ₍_(D_D)_{) 11}₁₁_._.

_´

₁₀₁₀--1515 _cm_cm--33

25.

25. In In a a silsilicoicon n sampsample le the the eleelectrctron on conconcencentratratiotionn drops line

drops linearly fromarly from10101818 _cm_cm--33_to10_to101616 _cm_cm--33_{over a}_{over a}_lengt_length_h of

of 2.2.00

m

m. m. The The cucurrrrenent t densdensitity y due due to to ththe e elelecectrtronon d diiffffuussiioon n ccuurrrreennt t iis s ( ( D Dnn

=

3535 )) 2 2 c cm m s s .. ( (A) A) 9 9 3 _._.3

_´

101044 _A_A_cm_cm22 _(B₍_B)_{) 2}_{2 8}_._.₈

_´

₁₀₁₀44 _A_A_cm_cm22 (C) (C) 9 9 _._.3 3

_´

110099_A_A_cm_cm22 _(D)_(D) ₂₂_._.₈₈

_´

₁₁₀₀99 _A_A_cm_cm22 26.

26. In a GaAs sample the electrons are moving underIn a GaAs sample the electrons are moving under a

an n eelleeccttrriic c ffiieelld d of of 55 kV cmkV cm anand d ththe e cacarrrriierer con

concencentratratiotion n is is uniuniforform m at 10at 101616 _cm_cm--33_._. _Th_The_e _el_elec_ectr_tron_on velocity is the saturated velocity of

velocity is the saturated velocity of 101077 _cm_cm_s_{s. The drift}_{. The drift} current density is current density is ( (AA) ) 1 6 1 6 _._.

_´

101044 _A_A_cm_cm22 _(B₍_B)_{) 2}_{2 4}_._.₄

_´

₁₀₁₀44 _A_A_cm_cm22 (C) (C) 1 6 1 6 _._.

_´

101088_A_A_cm_cm22 _(D)_(D) ₂₂_._.₄₄

_´

₁₁₀₀88 _A_A_cm_cm22 27.

27.For a sample of GaAs scattering time isFor a sample of GaAs scattering time is

t

_sc_sc

=

1010--1313_s_s and

and eleelectrctron’on’s s effeffectective ive mass mass isis m m e e mmoo *

*

₌

₀₀₆₇₀₀₆₇_._. _{. I f an}_{. I f an} ele

electrctric field of ic field of 1 1 kV cm is appliekV cm is applied, the d, the dridrift veloft velocitcityy produced is produced is ( (AA) ) 2 2 6 _._.6

_´

110066 _c_cm_m_s_s ₍_(B_B)₎₂₂₆₆₃₃_c_cm_m_s_s (C) 1 (C) 14 4 _._.8 8

_´

101066 _cm_cm_s_s _(D)_(D) ₄₈₂₄₈₂ 28.

28. A gallium arsenide semiconductor atA gallium arsenide semiconductor at T T

=

300300 K K isis doped

doped with with impuriimpurity ty conceconcentratintrationon N N dd

=

1010 16 16

cm

cm--33. The. The mobility

mobility

m

_n_n iis s 7755000 0 ccm m 22 V V

_-

ss_{. For an applied field of}_{. For an applied field of} 10 V cm the drift current density is

10 V cm the drift current density is (A) 120 A cm

(A) 120 A cm22 _{(B) 120 A cm}_{(B) 120 A cm}22

(C)

(C) 12 12

´

110044 A A cmcm22 (D)(D) 12 12

´

110044A A cmcm22

29.

29. In a particular semiconductor the donor impurityIn a particular semiconductor the donor impurity concentration is

concentration is N N dd

=

1010 14

14 _cm_cm--33_{. Assume the following}_{. Assume the following} parameters, parameters,

m

_n_n

=

1100000 0 ccm m 22 V V

_-

ss_,_, N N _c_c

=

´

æ

T T

è

ç

ö

ø

÷

2 2 1010 300 300 19 19 3 2 3 2 cm cm--33_,_, N N _v_v

=

´

æ

T T

è

ç

ö

ø

÷

1 1 1010 300 300 19 19 3 2 3 2 cm cm--33_,_, E E g g

=

1111.. eVeV.. An

An eleelectrctric ic fiefield ld of of EE

=

10 V cm is applied. The10 V cm is applied. The electric current density at 300 K is

electric current density at 300 K is (A) 2.3 A cm

(A) 2.3 A cm22 _{(B) 1.6 A cm}_{(B) 1.6 A cm}22 (C) 9.6

(C) 9.6 A A cmcm22 _{(D) 3.4}_{(D) 3.4} _A_A_cm_cm22 Statem

Statement ent for for Q.30-31Q.30-31::

A semiconductor has following parameter A semiconductor has following parameter

m

nn

=

7755000 0 ccm m V V ss 2 2

_-

_,_,

m

_p_p

=

33000 0 ccm m 22 V V

_-

ss_,_, n nii

=

3 6 3 6

´

1100 12 12 . . cmcm--33 30.

30. WhWhen en cocondnducuctitivvitity y is is mimininimumum, m, ththe e hoholele concen concentratitration on isis (A) (A) 7 2 7 2 _._.

_´

10101111 _cm_cm--33 _(B₍_B)_{) 1 8}_{1 8}_._.

_´

₁₀₁₀1313_cm_cm--33 ( (CC) ) 144 144 _._.

_´

11001111 _cm_cm--33 _(D₍_D)_{) 9}₉

_´

₁₁₀₀1313_cm_cm--33 31.

31. The minimum conductivity isThe minimum conductivity is (

(AA) ) 0 0 6 _._.6

_´

1100- - 3 3 ₍₍

_W

_-

_c_cm_m₎₎--11 _(B₍_B)₎₁₁_._.₇₇

_´

₁₀₁₀- - 3 3 ₍₍

_W

_-

_cm_cm₎₎--11 (C)

(4)

32.

32. A A papartrticiculular ar inintrtrininsisic c sesemimicocondnducuctotor r hahas s aa resistivity of 50

resistivity of 50( (

W

W -

-

cmcm))atatT T

=

300300K and 5K and 5( (

W

W -

-

cmcm))atat

T

=

330 K. If change in mobility with temperature is330 K. If change in mobility with temperature is neglected, the bandgap energy of the semiconductor is neglected, the bandgap energy of the semiconductor is ( (AA) ) 11..9 9 eeV V ((BB) ) 11..3 3 eeV V ( (CC) ) 22..6 6 eeV V (D(D) ) 00..664 4 eeV V 33. 33. TThhrreee e ssccaatttteerriinng g memecchhaanniissm m exexiisst t iin n aa se

semimicocondunductctoror. . If If ononly ly the the fifirsrst t memechchananisism m wewerere present, the mobility would be 500

present, the mobility would be 500 ccm m 22 V V

-

ss. If only. If only th

the e sesecocond nd memechchananisism m wewere re prpreseesentnt, , ththe e momobibililityty w

wouould ld be be 75750 0 cm cm 22 V V

_-

ss_{. If only third mechanism were}_{. If only third mechanism were} present, the mobility would be 1500

present, the mobility would be 1500ccm m 22 V V

_-

ss_{. The net}_{. The net} mobility is mobility is (A) 2750 (A) 2750 ccm m 22 V V

_-

ss _{(B) 1114}_{(B) 1114} _c_cm_m22 _V_V

_-

_s_s (C) 818 (C) 818 ccm m 22 V V

_-

ss _{(D) 250}_{(D) 250} _c_cm_m22 _V_V

_-

_s_s 34.

34. In a sample of silicon atIn a sample of silicon at T T

=

300 K, the electron300 K, the electron concentration varies linearly with distance, as shown concentration varies linearly with distance, as shown in fig. P2.1.34. The diffusion current density is found in fig. P2.1.34. The diffusion current density is found t

to o bbee J J _n_n

=

00. . 1919 A A ccmm22_._. _If_If _th_th_e_e _el_el_ec_ectr_tron_on _di_dif_ffu_fu_si_sion_on coefficient is

coefficient is DDnn

=

2525 2 2 cm

cm ss, , The The electelectron ron concenconcentratitrationon at is at is (A) (A) 4 84 _._.86 6

_´

110088 _cm_cm--33 _(B)_(B) _{2 5}_{2 5}_._.

_´

₁₀₁₀1313_cm_cm--33 (C) (C) 9 9 _._.8 8

_´

11002626 _cm_cm--33 _(D)_(D) ₅₅_._.₄₄

_´

₁₁₀₀1515 _cm_cm--33 35.

35.The hole concentration inThe hole concentration in pp

-

type GaAs is given bytype GaAs is given by

p p xx L L

=

æ

-

-è

è

ç

ö

ø

÷

10 10 1616 11 cmcm--33 forfor 00

£

x x

£

LL where

where LL

=

1010

m

m. The hole diffusion coefficient ism. The hole diffusion coefficient is 1

10 0 ccm m 22 ss. . ThThe e hohole le didiffffususioion n cucurrrrenent t dedensnsitity y atat

x x

=

55

m

mm isis (A) 20 A cm (A) 20 A cm22 _{(B) 16 A cm}_{(B) 16 A cm}22 (C) 24 (C) 24 A A cmcm22 _{(D) 30}_{(D) 30} _A_A_cm_cm22 36.

36. For For a a parparticticulaular r semiconsemiconductductor or samsample ple conconsidsiderer following parameters: following parameters: Hole concentration Hole concentration p p ee x x L L p p 0 0 15 15 10 10

=

-æ æ è è ç ç ç ç ö ö ø ø ÷ ÷ ÷ ÷ cm cm--33_,_, x x

³

00 Electron concentration Electron concentrationn n ee x x L Lnn 0 0 14 14 5 5 1010

=

´

-æ æ è è ç ç öö ø ø÷÷ _cm_cm--33 , , x x

£

00 Hole diffusion coefficient

Hole diffusion coefficient DD p p

=

110 0 ccm m ss 2 2

Elect

Electron ron diffusdiffusion ion coefficoefficientscients DDnn

=

225 5 ccm m ss 2 2

Hole diffusion length

Hole diffusion length LL p p

=

´

-5

5 1010 44 _cm,_cm, Electron diffusion length

Electron diffusion length LLnn

=

-10 10 33 _cm_cm The total current density at

The total current density at xx

=

0 0 isis (A) 1.2

(A) 1.2 A A cmcm22 _{(B) 5.2}_{(B) 5.2} _A_A_cm_cm22 (C) 3.8 A cm

(C) 3.8 A cm22 _{(D) 2 A cm}_{(D) 2 A cm}22

37.

37. A gerA germamaninium Hall devum Hall devicice e is dopeis doped d wiwith 5 th 5

_´

10101515 donor atoms per

donor atoms percmcm33 _at_at

T

=

300300 K. The device has theK. The device has the geometry

geometry dd

=

5 5

´

1010--33 cm,cm, W W

=

2 2

´

1010--22 cm andcm and LL

=

00..11 cm. The current is

cm. The current is I I x x

=

250250

m

A, the applied voltage is A, the applied voltage is

V

V x x

=

10100 0 mVmV, and the magne, and the magnetitic flux isc flux is BB z z

=

´

-5 5 1010 22 tesla. The Hall voltage is

tesla. The Hall voltage is (A)

(A)

-

00..3311mmV V (B(B) ) 00..331 1 mmV V (

(CC) ) 33..226 6 mV mV ((DD))

-

3.26 mV 3.26 mV Statem

Statement ent for for Q.38-39Q.38-39:: A

A sisililicocon n HaHall ll dedevivice ce atat T T

=

33000 0 K K hhaas s tthhee geometry geometry dd

=

1010--33 _cm_cm_,_, W W

=

1010--22 _cm,_cm, L L

=

1010--11 _{cm. The}_{cm. The} fol

followlowing ing parparameameterters s are are meameasursured:ed: I I x x

=

00..7575 mA,mA,

V

V x x

=

1515 VV,, V V H H

= +

5 85 8.. mV, teslamV, tesla

38.

38. The The majorimajority carrier concty carrier concentratentration ision is ( (AA) ) 8 8

´

11001515 cmcm--33,, nn

-

typetype (B) (B) 8 8

_´

10101515 _cm_cm--33_,_, p p

-

typetype ( (CC) ) 4 4

´

11001515 cmcm--33,, nn

-

typetype ( (DD) ) 4 4

_´

10101515 _cm_cm--33_,_, p p

-

typetype 39.

39. The majority carrier mobility isThe majority carrier mobility is (

(AA) ) 44330 0 ccm m 22 V V

_-

ss ₍_(B_B)₎₂₂₁₁₅_{5 c}_cm_m22 _V_V

_-

_s_s (

(CC) ) 33990 0 ccm m 22 V V

_-

ss ₍_(D_D)₎₁₁₉₉₅_{5 c}_cm_m22 _V_V

_-

_s_s

40.

40. In In a a semisemiconconducductortor nn00

15 15 10 10

=

cmcm--33 _and_and n nii

=

1010 10 10 cm

cm--33_{. The excess-carrier life time is 10}_{. The excess-carrier life time is 10}--66 _{s. The excess}_{s. The excess} ho

holle e coconcncenentrtratatioion n isis

d

p p

=

4 4

´

10101313 _cm_cm--33_._. _T_Th_he_e electron-hole recombination rate is

electron-hole recombination rate is ( (AA) ) 4 4

_´

11001919 _cm_cm- - 3 3 _s_s--11 ₍_(B_B)₎₄₄

_´

₁₁₀₀1414 _cm_cm- - 3 3 _s_s--11 (C) (C) 4 4

_´

10102424 _cm_cm- - 3 3 _s_s--11 _(D)_(D) ₄₄

_´

₁₀₁₀1111 _cm_cm- - 3 3 _s_s--11 1 1110 0 SSeemmiiccoonndduuccttoor r PPhhyyssiiccs s CChhaap p 22..11 5 5 ´´10101414 x x(cm)(cm) n n ( ( c c m m ) ) - 3 3 0.010 0.010 n n(0)(0) 0 0 Fig. P2.1.34 Fig. P2.1.34

(5)

41.

41. A A semsemicoicondunductoctor r in in thermathermal l equiequiliblibriurium, m, has has aa hole concentrati

hole concentration on of of pp00

16 16 10 10

=

cmcm--33 _and_and_an_an_int_int_rin_rinsic_sic conce

concentratintration on of of nnii

=

1010 10

10 _cm_cm--33_._._The_The_min_min_ori_ority_ty_car_carrie_rie_r_r l

liiffe e ttiimme e iis s 4 4

_´

1010--77_s._s. _Th_The_e _th_ther_erma_mal_l _eq_equi_uili_libr_briu_iu_m_m recombination rate of electrons is

recombination rate of electrons is (A) (A) 2 5 2 5 _._.

_´

10102222 _cm_cm- - 3 3 _s_s--11 _(B)_(B) ₅₅

_´

₁₀₁₀1010 _cm_cm- - 3 3 _s_s--11 ( (CC) ) 2 5 2 5 _._.

_´

10101010 _cm_cm- - 3 3 _s_s--11 _(D₍_D)_{) 5}₅

_´

₁₀₁₀2222 _cm_cm- - 3 3 _s_s--11 Statement for Q.42-43: Statement for Q.42-43: A

A n-n-tytype pe sisililiccon on sasampmple le cocontntaiains ns a a dodononorr conce

concentratintration on of of N N dd

=

1010 6

6 _cm_cm--33_._._The_The_min_min_ori_ority_ty_car_carrie_rie_r_r hole lifetime is

hole lifetime is

t

_p_p0₀

=

1010

m

s.s.

42.

42.The thermal equilibrium generation rate of hole isThe thermal equilibrium generation rate of hole is (A)

(A) 5 5

´

101088 cm cm - - 3 3 ss--11 (B)(B) 101044 cm cm - - 3 3 ss--11 (

(C) C) 2 2 25 ..25

´

101099 cm cm - - 3 3 ss--11 (D) 10(D) 1033 cm cm - - 3 3 ss--11

43.

43. ThThe e ththerermamal l eqequiuililibrbriuium m gegeneneraratition on rarate te foforr electron is electron is ( (A) A) 1121125 .. 5

´

101099cm cm - - 3 3 ss--11 (B(B) ) 225 225 ..

´

101099 cm cm - - 3 3 ss--11 (C) (C) 8 9 8 9 _._.

_´

1100--1010 _cm_cm- - 3 3 _s_s--11 _(D)_(D) ₄₄

_´

₁₀₁₀99 _cm_cm- - 3 3 _s_s--11 44.

44. A A nn

-

tytype pe sisililicocon n sasampmple le cocontntaiains ns a a dodononorr conce

concentratintration on of of N N _d_d

=

10101616 _cm_cm--33_._._The_The_min_min_ori_ority_ty_car_carrie_rie_r_r hole lifetime is

hole lifetime is

t

_p_p0₀

=

2020

m

s. The lifetime of the majoritys. The lifetime of the majority carrier is carrier is ( ( nnii

=

. .

´

)) -1 15 5 110010 10 _cm_cm 33 ( (AA) ) 8 9 8 9 ..

´

110066 s s ((BB) ) 88..9 9

´

1100--66 ss (C) (C) 4 5 4 5 _._.

_´

1010--1717_s_s ₍_(D_D)₎ _{1 13}_{1 1}_._. ₃

_´

₁₁₀₀--77_s_s 45.

45. In In a a silsilicoicon n semisemiconconducductor tor matmaterierial al the the dopidoping ng conce

concentratintration on areare N N aa

=

1010 16

16 _cm_cm--33 _and_and

N

N aa

=

00. . TThhee equil

equilibriuibrium m recombrecombinatioination n rate rate isis RR p p00

11 11 10 10

=

cmcm--33ss--11. . A A uni

uniforform m gengeneraeratiotion n ratrate e producproduces es an an excexcess- ess- carcarrierierr conce

concentratintration on of of

d

n n

=

d

pp

=

10101414 _cm_cm--33_._. _The_Th_e _fa_fact_ctor_or_,_, _by_by which the total recombination rate increase is

which the total recombination rate increase is ( (A) A) 2 2 3 ..3

´

11001313 (B(B) 4 ) 4 ..4 4

´

11001313 (C) (C) 2 2 _._.3 3

_´

110099 _(D)_(D) ₄₄_._.₄₄

_´

₁₁₀₀99 *********** ***********

Solutions

1. 1. (D)(D) n n i i N N c c N N vv ee E E kT kT g g 2 2

₌

- -æ æ è è ç ç ç ç ö ö ø ø÷÷÷÷ V V tt

=

æ

è

ç

ö

ø

÷

=

00259 00259 400400 300 300 0034500345 . . .. For Ge at 300 K, For Ge at 300 K, N N cc

=

1 01 04 4

´

1100 19 19 . . ,, N N vv

=

6 0 6 0

´

1100 18 18 . . ,, EE g g

=

0 660 66. . eV eV n n _i_i22 1199 1188 ee 3 3 0 660 66 0 0345 0 0345 1 1004 14 10 0 6 0 16 0 100 400400 300 300

= ´

´

æ

è

ç

ö

ø

÷

´

--æ æ . . .. . . . . è è ç ç öö ø ø÷÷

Þ

nnii

=

8 5 8 5

´

1100 14 14 . . cmcm--33 2. 2. (C)(C) n n i i N N c c N N vv ee E E kT kT g g 2 2

₌

- -æ æ è è ç ç ç ç ö ö ø ø÷÷÷÷ ( ( )) .. .. . . 1 10 0 2 2 8 18 10 0 11004 14 100 300 300 1 122 22 1199 1199 3 3 1 121 12

=

´

æ

è

ç

ö

ø

÷

--æ æ è è ç ç öö T T e e e e kT kT øø÷÷ T T 33ee T T 13 10 13 10 8 8 3 3 9 2 9 28 8 1100 - - ´´

-=

=

. .

´

, , BBy y ttrriiaall T T

=

382 K 382 K 3. 3. (B)(B) nn n n e e e e iA iA iB iB E E kT kT E E kT kT gA gA gB gB 2 2 2 2

=

--

=

--æ æ - -è è ç ç ç ç ö ö ø ø÷÷÷÷ e e E E EE kT kT g gA A ggBB 22 22575575..

Þ

nn

=

n n iA iA iB iB 47 47..55 4. 4. (A)(A) pp nn n n i i 0 0 2 2 0 0 10 10 22 4 4 15 15 1 15 5 1100 5 5 1010 4 5 4 5 1100

=

´

=

´

( ( . . )) . . cmcm--33 5. 5.(A)(A) p p N N _v_v ee E E EE kT kT F F vv 0 0

=

--( ( -- ))

=

´

-1 0 1 04 4 11001919 0 0 2222 0 0259 0 0259 . . . . . . e e

=

2 2

´

10101515 _cm_cm--33 6. 6. (B)(B) p p N N vv ee E E EE kT kT F F vv 0 0

=

--( ( -- ))

Þ

E E E E kkT T N N p p F F vv v v

-

=

æ

è

ç

ö

ø

÷

ln ln 0 0 At 300 K, At 300 K, N N vv

=

110 0

´

1100 19 19 . . cmcm--33 E E F F

-

EEvv

=

´

æ

è

ç

ö

ø

÷

=

00259 00259 1 01 04 4 1100 10 10 0 2390 239 19 19 15 15 . . lnln .. .. eV eV n n N N _c_c ee E E EE kT kT c c F F 0 0

=

-( ( )) At 300 K, At 300 K, N N cc

=

2 2 8 8

´

1100 19 19 . . cmcm--33 E E _c_c

-

EE_F_F

=

11112 . . 2

-

0 0 2. . 2339 9

=

0 80 . . 88811eeV V n n00 4 4 4 4 4 4 1100

=

. .

´

cmcm--33 7. 7. (C)(C) pp N N a a N N dd N N N N nn a a d d i i 0 0 2 2 2 2 2 2 22

=

-

+

æ

-

-è

è

ç

ö

ø

÷

+

For Ge For Ge nn_i_i

=

2 2 _._.4 4

´

110033 p p00 1 13 3 1133 22 13 13 22 10 10 2 2 10 10 2 2 2 2 4 4 1100

=

+

æ

è

ç

ö

ø

÷

+

( ( . .

´

))

=

2 92 95 5

´

1100 13 13 . . cmcm--33

(6)

8. 8. (A)(A) nn N N d d N N aa N N N N nn d d a a i i 0 0 2 2 2 2 2 2 22

=

-

+

æ

-

-è

è

ç

ö

ø

÷

+

=

´

+

æ

´

è

ç

ö

ø

÷

+

´

5 5 1010 2 2 5 5 1010 2 2 2 2 4 4 1100 1 155 1155 22 13 13 22 ( ( . . ))

=

5 5

´

10101515 _cm_cm--33 9. 9. (B)(B) pp nn p p i i 0 0 2 2 0 0 13 13 22 13 13 2 2 4 4 1100 2 9 2 95 5 1100

=

´

( ( . . )) . .

=

1 91 95 5

´

1100 13 13 . . cmcm--33 10.

10. (A) Since(A) Since N N a a

>

N N dd, thus material is p-type ,, thus material is p-type ,

p p ₀₀

₌

N N _a_a

_-

N N _d_d

_{= ´}

₂₂_._.₅₅ ₁₁₀₀33

_-

_{- ´}

_{1 10}_{1 1}

_´

₀33

₌

₁₅₁_._.₅

_´

₁₀₁₀1133 _c_cm_m--33 11 11.. (D)(D) kT kT

=

æ

è

ç

ö

ø

÷

=

00259 00259 200200 300 300 0001017373 . . .. eeVV For GaAs at 300 K, For GaAs at 300 K, N N _c_c

=

4 7 4 7 _._.

´

11001717_cm_cm--33_,_, N N _v_v

=

7 0 7 0 _._.

´

11001818_,_, E E_g_g

=

11. . 4242 eV eV n n ii ee 2 2 1177 1188 3 3 1 1 4242 0 0173 0 0173 4 47 17 10 0 770 10 100 200200 300 300

=

´

æ

è

ç

ö

ø

÷

--æ æ è è ç ç öö . . .. . . . . _ø_ø÷÷

Þ

nnii

=

11. . 4848 cmcm --33 n n ii n n p p pp nn 2 2 0 0 0 0 00 2 2 00 2 2 5 5 5 5

=

n n 00

=

5 5 nnii

=

33. . 33cmcm --33 12. 12. (A)(A) kT kT

=

æ

è

ç

ö

ø

÷

=

00259 00259 400400 300 300 0034500345 . . .. eeVV n n _i_i N N _c_cN N _v_v ee E E kT kT g g 2 2

₌

- -æ æ è è ç ç ç ç ö ö ø ø÷÷÷÷ For Ge at 300 K, For Ge at 300 K, N N cc

=

1 01 04 4

´

1100 19 19 . . cmcm--33 _,_, N N vv

=

6 6

´

1010 18 18 _cm_cm--33 _,_, E E g g

=

0 660 66. . eV eV n n ii ee 2 2 1199 1188 3 3 0 660 66 0 0345 0 0345 1 1004 14 10 0 6 16 100 400400 300 300

=

´

æ

è

ç

ö

ø

÷

--æ æ è è ç ç öö ø ø . . . . . . ÷÷

₌

_{7 2}₇_._.₂₇₇₄₄

_´

₁₁₀₀2929 n nii

=

8 5 28 5 28 8

´

1100 14 14 . . cmcm--33 p p N N a a N N aa nn i i 0 0 2 2 2 2 2 2 22

=

+

æ

è

ç

ö

ø

÷

+

=

+

æ

è

ç

ö

ø

÷

+

´

10 10 2 2 10 10 2 2 7 7 22774 4 1100 1 15 5 1155 22 29 29 . .

Þ

p p00

=

´

15 15 1 4 1 48. . 89 9 1100 cmcm--33 E E E E kkT T pp n n F Fi

-

i F F

=

æ

è

ç

ö

ø

÷

ln ln 00 0 0

=

´

æ

è

ç

ö

ø

÷

00345 00345 1 4 81 4 89 9 1100 8 5 2 8 5 28 8 1100 15 15 14 14 . . lnln .. . .

=

00190019.. eV eV 13. 13. (A)(A) nn N N d d N N dd nn i i 0 0 2 2 2 2 2 2 22

=

+

æ

è

ç

ö

ø

÷

+

For Ge at For Ge at T T

=

300300 K,K, nnii

=

2 2 4 4

´

1100 13 13 . . cmcm--33 n n00 1 144 1144 22 1 133 22 1144 10 10 2 2 10 10 2 2 2 2 4 4 110 0 1100555 5 1100

=

+

æ

è

ç

ö

ø

÷

+

(( ..

´

))

=

..

´

ccmm --33 E E E E kkT T nn n n F F FFii i i

-

=

æ

è

ç

ö

ø

÷

ln ln 00

₌

´

æ

è

ç

ö

ø

÷

00259 00259 1010555 5 1100 2 2 4 4 1100 14 14 13 13 . . lnln .. . .

=

0038300383.. eV eV 14. 14. (A)(A) nn N N d d N N dd nn i i 0 0 2 2 2 2 2 2 22

=

+

æ

è

ç

ö

ø

÷

+

n n ii

=

00..0505nn00

Þ =

n n 00

´

+

´

+

nn 1 155 1155 22 0 0 2 2 1 15 ..5 10 10 ((115 ..5 10 10 )) ((00..0505 ))

Þ

nn00

=

´

15 15 30 300. . 0775 5 1100 cmcm--33 n nii

=

1515004 4

´

1100 14 14 . . cmcm--33 n n i i N N c c N N vv ee E E kT kT g g 2 2

₌

- -æ æ è è ç ç ç ç ö ö ø ø÷÷÷÷ For GaAs at For GaAs at T T

=

300 K,300 K, N N _c_c

=

4 7 4 7 _._.

´

11001717_,_, N N _v_v

=

7 7

´

10101818_,_, E E_g_g

=

11. . 4242 eV eV ( ( . . ) ) .. . . . . 1 155004 4 447 17 10 0 7 17 100 300 300 2 2 1177 1188 3 3 1 42 1 42 303000 0 025 0 025

=

´

æ

è

ç

ö

ø

÷

-- ´´ T T e e 99T T æ æ è è ç ç öö ø ø÷÷

By trial and error

By trial and error T T

=

763763K K

15. 15. (A)(A) E E E E kkT T mm m m F Fi i mmiiddggaapp p p p p

-

=

æ

è

ç

ö

ø

÷

=

3 3 4 4 ln ln 0044600446.. * * * * eV eV 16. 16. (A)(A) n n N N d d N N a a N N cc ee E E EE kT kT c c F F 0 0

=

-

=

--æ æ - -è è ç ç öö ø ø÷÷ For Si, For Si, N N _c_c

=

2 2 _._.8 8

´

11001919_cm_cm--33 N N dd

=

= ´

´

+

´

ee --æ æ è è ç ç öö ø ø÷÷ 5 5 10 10 1155 2 2 8 8 11001199 0 215 0 215 0 0259 0 0259 . . . . . .

₌

_{1 1}_{1 19}_._.₉

_´

₁₁₀₀1616 _cm_cm--33 17. 17. (A)(A) E E E E kkT T N N N N F F FFii d d i i

-

=

æ

è

ç

ö

ø

÷

ln ln

=

´

æ

è

ç

ö

ø

÷

=

00259 00259 1010 1 15 5 1100 02870287 15 15 10 10 . . lnln . . .. eV eV 18. 18. (D)(D) RR V V I I

=

2020

=

100 100mm 200200

W

s =

L L

=

´

- - RA RA 2 2 1010 2 2000 0 00000011 3 3 ( ( ))( ( . . ))

=

-

-0 0_._.0101₍₍

_W

_cm_cm₎₎ 11

s »

e e

m

nnnn00, For, For SiSi,,

m

nn

=

13501350..

Þ

_{0 0}_{0 01}₁

=

_{1 6 10}_{1 6 1}

´

₀--1919 ₁₁₃₃₅₅₀₀ 0 0 . ( . ( . . ))( ( ))nn n n00 13 13 4 4 6 6 1100