半导体物理与器件第四版课后习题答案

1、4.12niNcNexpEgkTwhereNcoNcoNo3Texp300EgkTChapter4andNoarethevaluesat300K.T(K)kT(eV)/3、ni(cm)2000.017277.68104124000.034532.38106000.0518149.741014(a)Silicon,3、,3、T(K)ni(cm)ni(cm)200_102.1610101.38400148.601093.28106003.821016125.721012(b)GermaniumGaAs4.2Plot4.3(a)2niNcNEgexpkT1110192.8101.041910300e

2、xp0.02591.12T3002.510232.91238103001.12300exp0.0259TBytrialanderror,T367.5K(b)2ni2.912101238102.5300Bytrialanderror,T4.4AtT200K,0.017267eVAtT400K,0.034533eVn2400ni22007.701010kTkT221.4010400300Eg1025exp1.123000.0259T417.5K2000.02593004000.02593003.02517103200300exp0.034533Egexp0.017267Eg8exp0.017267

3、3.0251017orEg28.9561gorEgNowEg0.0345338expEg57.913917,3.02510ln1.318eV1027.7010NcoN28.957838.171434003001.318exp0.03453321175.92910NcoNo2.3702.65810376soNcoNo9.4110cm4.5niB1.10expkTThengcfF.xexp立Tofindthemaximumvalue:dgcfF11/2x-xexpdx2kT11/2xxexpkTkTwhichyields“1/21xc1/2IT2xkTkT2Themaximumvalueoccur

4、satEckT2niA0.90exp0.20kTForT200K,kT0.017267eVForT300K,kT0.0259eVForT400K,kT0.034533eV(a)ForT200K,niBexp0.209.325610niA0.017267(b)ForT300K,niBexp34.43100.02594niA(c)ForT400K,niBexp0.203.05103niA0.034533expkT(b)EfEg1fF，/EEexpkTEE.EEexpkTexpEfEkTLetEETheng1kTTofindthemaximumvalue4.6(a)gcfF.EEcexpEEfkT.

5、EEcexpEEckTexpEcEfkTdg1fFdx-xexpdxdxkTSameaspart(a).kT2MaximumoccursatorEkT4.7Let E Ec xnEinE2whereEiEcThennEinE2.EiEcexp.E2EcexpEiEckTE2EckTkT4kTandE2E。一2,4kTEiE22、 .2exp4ornEinE222exp0.08543.54.8Plot4.9Plot4.i0EFiEmidgap-kTln4*mp*mn*Silicon:mp0.56m。,mi.08m。EFiEmidgap0.0i28eV*Germanium:mp0.37m0,*mn

6、0.55moEFiEmidgap0.0077eV.*GalliumArsenide:mp0.48m0,*mn0.067moEFiEmidgap0.0382eV4.iiiNEcEkFimidgapkTln一2Nci一一i9i.04i0kTln79-0.4952kT22.8i0T(K)kT(eV)(ErEmidgap)(eV)2000.0i7270.00864000.034530.0i7i6000.05i80.02574.i2(a)EFi(b)Eh4.i3EmidgapMn*mp*mn3,0.0259ln40.70i.2ii0.63meVmidgap3,0.75一0.0259ln40.08043.

7、47meVLetgcEKconstantThennogcEfFEdEK-EciidEEEfexpkTKexpEcEEfdEkTLetEEcsothatdEkTdkTWecanwriteEEfEcEfEEcsothatexpEEfEcEfkTexpkTexpTheintegralcanthenbewrittenasexpd0SoexpnoKkTexpEcEfno2C1kTkTexpd0expEcEfkTwhichbecomesnoKkTexpEcEf4.15kT1Wehaveaomo*m4.14LetgcThenECiEcforEEcForgermanium,Then160.55a。nogcEE

8、cfFEdEorr1o15.4A*16,m0.55mo290.53C1EEcEcLetEcC1-Ec1EEcexpdEEEfkTTheionizationenergycanbewrittenas*2E-o13.6eVmosexpEfkTdE0.55、，213.6E0.029eV16EEc4.16kTWecanwritesothatdEkTdr1Wehaveaomor-*mEfEcEcEfThennoC1expEckTorkTForgalliumarsenide,r13.1,m0.067moThen113.10.530.067o104AEcexpn。CiexpWefindthatkTexpkTd

9、kT4.17Theionizationenergyis2orE*mo一13.6mos0.0053eV_Nc(a)EcEfkTIn-no0.06713.1213.619,2.8100.0259lnk7100.0259ln刍父1.5100.2148eV(b)EfEEgEcEf0.365eV1.120.21480.90518eV4.19(c) PoN191.0410(d) Holes(e) EfEhEfEexpkT(a)EcEfkTlnNcnoexp0.905180.02590.0259ln192.81010536.9010cmkTlnniEfeEgEcEf1.120.8436Efe0.2764eV

10、1.0419100.27637exp0.8436eV(b)Po0.02592.4141014cm3157100.0259ln61.5100.338eV(c)p-type4.18N(a)EfEkTlnPo4.20375(a)kT0.02590.032375eV3000.0259ln-(b) EcEf1.120.162(c) no2.8191.041016210EgEf0.958eV0.162eVE3/2173750.28no4.710exp3000.0323751.151014cm3(d)EnEf190.95810exp0.02592.41103cm3EfeEgEcEf1.420.281.14e

11、V3/2718375101.14poexp3000.03237534.99103cm一17,4.710(b)EcEf0.0259ln141.15100.2154eVEfEkTlnniEgpoEcEf1.420.21541.2046eV18710exp1.20460.0259_234.4210cm34.21(a)kT0.02593750.032375eVno2.81910375300EfEg3003/2exp0.280.0323756.86EcEf3/21.0419103753007.84(b)EcEfkTln0.0259lnEfPo192.8102.3010515310cm1.120.280.

12、840eV0.840exp0.0323757310cmNcn。_192.810156.862100.2153eV4.23(a)(b)n。n。niexpEfEhkT1.57.33E1.12191.04100.21530.9047eV0.904668exp0.025937.0410cm4.22(a)p-type(b)EfEg1.120.28eV4PoNexpEfE4.24kT(a)Ef1.0419100.28exp0.0259142.1010cmEcEfEgEf1.120.280.84eVnoNcexpEcEfkT0.84exp0.02593cm1010exp0.220.02591310cmPon

13、iexpEFiEFniexpkT101.510exp3.07106cmEfEFikT0.220.02591.8106exp98.8010cmPoniexp且一EFkT0.220.02590.0259ln(b)Ec1.12(c)n。Ef61.810exp23.6810cmNkTInPo191.041015510EgEfE0.220.02590.1979eV0.197880.92212eV190.922122.810exp0.0259339.66 10 cm(d)Holes(e)ErEfkTln-po-ni4.26(a)Po1810exp4.250.0259ln510151.510100.3294

14、eVEcEfnokT4000.02590.034533eV3001.0419103/2400(b)kT300Q2642eV0.250.02594.501.421410cm0.25一174.7101.130.034533eV_187101.17eV1.17exp0.0259210cm3/2400191.60110cm300Nc2.819103/24001.078300Nc_174.71019310cm3/2400300194.310910cm2ni7.23617310cmexp1.120.034533ni4.31092.381(a)Ef(b)Ec(c)no(d)(e)1919101.601105

15、.67021210cm24103Ef0.034533lnNEkTlnPo0.034533ln191.601101510NEkTln191.07810144.5010Po0.3482eVEcEf1.420.34821.072eV171.07177no7.23610exp0.0345330.2787eVEf1.120.278732.40104cm3Holes0.84127eV190.841274.310910exp0.034533931.134109cm34.27(a)Po191.0410exp6.680.250.025914310cmEhEfkTln-po-niEcEf1.120.250.870

16、eV0.034533ln15510122.3811019no2.8100.870exp0.025943no 7.23 10 cm4.28(b)kT0.034533eVNcEf0.0345331.04101.601Po2RNF1/2F3/219400192.8104.311lnEcEf1.12kTln30019310cm3/240030019310cmPo191.60110_146.68100.3482eV0.34820.7718eV19no4.31110exp0.771750.034533938.4910cm3(a)no2一lNcFi/2FForEfEckT2,EfEckTThenF1/2f1

17、.0kT20.5kT(b)no4.29no2_19_2.8101.0J3.1610193cm19510SoF1/2WefindEEf3.04.30(a)(b)Thennono2卜NcFi/2F2174.7107175.3010cm1.021.044.263.0E19L10Fi/2FEfkT0.02590.0777eVEfEckTFi/2F4kT4kT6.02NcFi/222.81.901024.71017183.1810cm19106.0203cm6.04.31FortheelectronconcentrationnEgcEfFETheBoltzmannapproximationapplies

18、,so3/242mnh3.EEcexp人kTor*3/22mn3exphEcEfkTEcexpkTDefineEEckTEEckTThen4.32(a)Silicon:Wehave.EcEfTofindmaximum,setnoNcexpkTdnxdx1/2expWecanwriteEcEfEcEdEdEf1/2x1expForEcEd0.045eVandEdorEf3kTeVwecanwriteKxexpwhichyields1x2EckTEc1kT2190.045cno2.810exp30.025919一一2.810exp4.737or173Fortheholeconcentrationp

19、EgE1fFEUsingtheBoltzmannapproximation*3/242mph3EEfEexpkTorEa*3/242mp3exph3EfEkTno2.4510WealsohavePoNexp-Again,wecanwriteEfEEfForEfEa3kTE0.045eVThen19Po1.04101.04orPo9.121016cmEfEkTEaEaEand0.045exp30.02591910exp4.7373cmexpEEkTsetDefinexEEkT(b)GaAs:ThennoassumeEc174.710expEd0.0058eV0.005830.0259Thenpx

20、K,xexp174.710exp3.224TofindmaximumvalueofpEpxdpx0Usingtheresultsfromdxabove,wefindthemaximumat1EEkT2orno1.871016cm3AssumeEaE0.0345eVThen180.0345po710exp30.025971018exp4.332or163Po9.20 10 cm3(a)NaNd1541015101015cm4.33Plotno2ni1.81064.34(b)Pono(a)1515341510310cmno(b)noNd1021.510j.1531016310cm7.54310cm

21、(c)no(c)no(d)2ni2.8expno(e)153101.08103cmNd31016cm1.8106216101.081043cmPoni1.8610cm1021.5101.12(d)2ni4.717107.01810375300161019103000.0259375PoNa1127.33410410157.5310cm1.51010cm1.0419101.42300exp0.0259375ni7.3341015cm1.348102ni_192.8101.041910exp1.123000.0259450ni1.722no1410142101.029Po1.72213210_14

22、1.029104.3533753001110cmcm45030013103cm_1321.7221014310cm1232.8810cmno(e)ni7.5801083cmPoNa827.580102ni15104.717101.42300exp0.0259450noNd103.85310Po14104.36(a)Ge:(i)noor101.447.015cm2101810ni3.85314310cmcm345030010310cm731.4810cm133ni2.410cm2Nd152102152101322.410no15Nd210cm13 2(b)Pono2nipo一2.410no151

23、0fF2.88(ii)PoGaAs:(i)no1.8NaNdno2nini1.8210Nd621015(ii)PoNa621.81015310101116103cm一15710or1510cmfF1exp1/0.0259_52.87101322.410二“153101.921011cm36310cm4.38(a)(b)101.62Nd1.08NaNdSilicon:p-type15cm3310cm153310cm3310cm(c)Theresultimpliesthatthereisonlyone33minoritycarrierinavolumeof10cm.4.37(a)Forthedon

24、orlevelndNd1lexp2EdEfkT0.200.0259ororndNd8.85104(b)WehavefF1exp=kTPoPoThen2ninoPo1.5NaNd2.51310131101.510133cmNowEEfEEcEcEforEEfkT0.245Then10210131.510Germanium:PoNaNd1.5107cm2NaNd2ni131.510131.5101322.410orPo3.261310cmThenno2niPo1322.410133.264101.7610133cmGalliumArsenide:4.39(a)(b)PoandnoNdno2nino

25、NaNd1.513310cm2niNaNd1.51.8610131.5100.216cmn-typeNa2101514810cm151.21081010210142.815310cm2Na1.89361024(c)PoNaNaNdno4.40no2niPo15_1515410Na1.210210Na4.81015cm3101.510-1/-15410435.62510cm1021.51021051531.12510cmnoPon-type4.41321918250ni1.04106.0103000.66exp0.0259250300241.89361012ni1.37610cm22nini21

26、2no一noniPo4no4n。niSo11no6.8810cm12Thenpo2.7510cmPo2.752212102Na2niNa_4_241.8936107.573510242.7521012Na2Na123sothatNa2.06410cm4.42Plot4.43Plot4.44Plot4.45noNdNa21.12NdNa2141014d14142101.210:2-2ni2ni141.2101413213221.110410410ni272724.9101.610ni133soni5.7410cmni3.310133Po一14310cmno1.1104.46(a)NaNdP-ty

27、PeMajoritycarriersareholes16PoNaNd3101.51631.510cmMinoritycarriersareelectrons1610no2niPo1.5101024O丁1.5103cm(b)BoronatomsmustbeaddedPoNaNaNd216.1616510Na3101.510SoNa3.51016cm31.5101022001.010150.1855400151.49100.018986003.8710160.000674no16510334.510cm4.49Nc(a)EcEFkTln-Nd192.810N4.47(a) ponin-type22

28、、nini(b) p。n。nopo14For10cm3,EcEf0.3249eV1510cm3,EcEf0.2652eV1610cm3,EcEf0.2056eV1017cm3,EcEf0.1459eV0.0259lnNdni1.510163no4-1.12510cm210electronsaremajoritycarriers4_3po210cmholesareminoritycarriers(c)noNdNa16151.12510Nd710一一163soNd1.82510cm(b)EFEnkTIn0.0259In101.510143For10cm,EfEFi0.2280eV15310cm,E

29、fEFi0.2877eV16310cm,EfEFi0.3473eV17310cm,EfEFi0.4070eVNd4.48EFiEFkTln也ni4.50ForGermaniumT(K)kT(eV)一，3、ni(cm)2004006000.017270.034530.05182.161010148.60103.821016poNaNa2222.niandNa1015cm3T(K)po(cm3)EFiEf(eV)Nd(a)no2222nino1.05Nd1.051015cm31.05j/15104.41520.5104一一1520.510n2i2soni5.252810Now21919Tni2.8

30、101.04103001.12exp0.0259T30032838T5.25102.912103002ni2.819101.0419102003001.12exp0.017267ni7.638104cm12972.973expTBytrialanderror,T536.5K(b)AtT300K,_NcEcEfkTln-no192.810EcEf0.0259ln100.2652eVAtT536.5K,AtT400K,2ni1.12exp0.034533ni2.810191.04191034003002.3811012cmAtT600K,2ni192.8101.04101936003001.12e

31、xp 0.0518，一536.5、，kT0.02590.046318eV300Nc192.8103/2536.53006.69619310cmAtni_149.74010cm200KandT400K,一一15p。Na310cmAt600K,Na2Na2niEcEfkTlnNcno153101523101429.74010196.69610EcEf0.046318ln1.05100.5124eVthenEcEf0.2472eV(c)Closertotheintrinsicenergylevel.4.51PoEhEfkTln一niAtT200K,kT0.017267eVT400K,kT0.0345

32、33eVT600K,kT0.0518eVAtT200K,1533.28810cmThen,T200K,EFiEf0.4212eVT400K,EFiEf0.2465eVT600K,EFiEf0.0630eV4.52(a)NaNaEFiEfkTln0.0259ln6ni1.810For14Na10cmEFiEf0.4619eVNa1015cm4.54EFiEf0.5215eV16Na10n。NdNaNcexpEcEFkTcmsoEFiEf05811eVNa1017cmNd515102.819100.215exp0.0259EFiEf(b)0.6408eV15510156.9510EfkTln0.0

33、259ln7.01018orNd1.21016cmForNaNaEfEfEfEf4.5314Na10cm0.2889eVNa10150.2293eV16Na100.1697eVcmcmNa1017cm0.1100eV(a)EFiEmidgap3一0.0259ln104orEFiEmidgap*3mpkTln-4mn0.0447eV(b)ImpurityatomstobeaddedsoEmidgapEf0.45eV(i)p-type,soaddacceptoratoms(ii)EFiEf0.04470.450.4947eVThenniexpEFiEFkT50.494710exp0.0259orP

34、o133Na1.9710cm4.55(a)Silicon(i)EcEfNckTln-Nd0.0259ln192.810156100.2188eV(ii)EcEf0.21880.02590.1929eVNdNcexpEcEfkT192.8100.1929exp0.0259Nd1.631AdditionalNddonoratoms(b)GaAs(i)EcEf1610cm1.0313Nd156101016cm4.70.0259ln-1017100.15936eV(ii)EcEf0.159360.02590.13346eVNd4.71017exp0.133460.0259152.71810cm3Nd1510一一153Nd1.71810cmAdditional29donoratoms(a)EnEfkTlnni4.56(a)EFiEfNkTlnNa0.0259In310151.510100.3161eV0.0259ln一一191.0410162100.1620eV(b)EfEFikTlnno0.02591631010ln1.5100.3758eV(b)EfEhNckTlncNd0.0259ln192.81