半導(dǎo)體物理與器件第四版課后習(xí)題答案4

1、Chapter4whereNcOandNOarethevaluesat300K.-1.12exp但0.0259T3002.51023=2.9121038300expq纏E0.0259TBytrialanderror,T=367.5KT(K)kT(eV)ni(cma)2000.0172747.68X104000.03453122.38M106000.0518149.74X10(a)Silicon(b)(b)n2=(5父10122=2.5X1025T(K)-/3、ni(cm)ni(cm)200102.16X101.38400_148.60M10_93.28M1096003.82乂1016_125.

2、72M10Germanium(c)GaAs=2.9121038品exp喘59裔Bytrialanderror,T三417.5K4.4AtT=200K,kT=：0.02592004.2Plot=0.017267eVAtT=400K,kT=0.02594.3(a)2ni=NcNnexpu-=0.034533eV(5X10112=(2.8叼0191.04乂1019工3300n；(400)(7.70父10102n“200)(1.40M102217=3.02510參考材料|,400;30020033qqexpexp0.017267=8exp10.0172670.0345333.0251017=8expE

3、g57.9139-28.95781orEg28.9561=lnf173.025M108.=38.1714orEg=1.318eVgNow上70父10102=NcoNel400-300-1.318exp-0.0345335.9291021=NcoN.o2.3702.65810爐soNcoNo=9.411037cm'coo4.5。BniAexpexp-1.10kT宣心.kTForT=200K,ForT=300K,ForT=400K,kT=0.01726eVkT=0.0259eVkT=0.034533eV(a)ForT=200K,退二expniA一"20=9.325100.0172

4、67(b)ForT=300K,niB-0.204=exp=4.4310一niA0.0259(c)ForT=400K,niB-0.20工=exp=3.0510niA0.0345334.6(a)gcfF工，E。Ecexp一；E-Ecexp_4I：Ec-EFILetEE"xkTE-EkTxThengcfF二.xexpTofindthemaximumvalue:dgcfFdx-1/2exp二.kT1/2-xxexp正二。whichyields(1/21x-c1/2=|T-2xkTkTx二2ThemaximumvalueoccursatwherelkT=Ec2E1=14kTandkTE2=Ec

5、2ThennEi.4kT=expnE2kT,2(b)=22exp-4-1=2.2一.2exp；-3.5g.1-fF,E.-Eexp-EE_klor-n-E=0.0854nE2e-eexp-ET-一klexp-EF-E：ILkT4.8PlotLetE.-E=xTheng；1-fF廣.xexpTofindthemaximumvalue氈fj",exp=0dxdxkT4.9PlotSameaspart(a).MaximumoccursatkTx=2orkT一T4.7nE1nE2匚匚-E1-Ec：l.E1-Ecexp一kT4.10*mp*mn*Silicon:mp=0.56m。，mn=1.0

6、8m。EFi-Emidgap-0.0128eV_*Germanium:mp=0.37m0,*mn=0.55m0EFi-Emidgap=-0.0077eV*GalliumArsenide:mp=0.48m0,EFiL3,丁，一Emidgap-kTlnE2-EcE2-EcexpkTmn=0.067m。EhEmidgap=：；0.0382eVThenn。od=gcEfFEdEoO二K-Ec，4.111dE1expEsElkTEFi-Emidgap1二一kTIn2NcLet1=2kTln,2.8X10194495緋T)_-191.0410E-Ec_csothatdE=kTdkTT(K)kT(eV)(E

7、Fi-Emidgap)(eV)2000.01727-0.00864000.03453-0.01716000.0518-0.0257WecanwriteE-Ef=Ec-EfE-Ecsothat-EEFexp-ILkT9P"expTheintegralcanthenbewrittenas4.12n。KkTexp(a)IrEc-EILkTexp-d-0(b)3._.EFi-Emidgap=-kTln4mn=30.0259In-0041.21whichbecomesn。=KkTexpjkT='-10.63meVEFi_Emidgap=一0.0259In-07540.080=43.47

8、meV4.14LetgcE)=GE-EcforE_EcThennoOOgcEfFEdEod二C1一eTexpE-EcdEE-Ef4.13LetgcE=K=constantoO三C1.E-EcEcIE-efexp.kTdELetasE-Ec二csothatdE=kTdkTTheionizationenergycanbewritten13.6 eVWecanwriteE-Ef=E-EcEc-Ef0.55、，=513.6=E=0.029eV162Then小二Gexp -Ec -EF一 kT4.16e E-Ec exp 二E聲We have ± = r i mo ao r mFor gall

9、ium arsenide, 三 r =13.1,orno =Ci exp -E-工一 kTThenr1 = 13.10.53)；=104 A*mu0.067m。oOkTexpijkTdWe find that0Theionizationenergyisjnexp(-" 9口 =exp(-“-1 )=書l0orE213.6 = 0.0672 13.613.1SoE=0.0053eV4.15no=CikT2exp-Ec-EkT4.17(a)Ec-EF=kTlnNcno，r1Wehave-a。Forgermanium,r也rm*r=16,m=0.55m0=0.0259ln2.8101971

10、015Thenr1=16-0.55三：290.53(b)=0.2148eVEf-E：=EgTEc-'Eforor1=15.4A=1.12-0.2148=0.90518eV(c)p°=N.exp二EF-E.kT(d)(e)=0.365eV19=1.0410exp-0.905180.0259=6.90103cm-4.19HolesEF-EFi(a)Ec-Ef=kTlnNc=0.0259ln4.18(a)(b)(c)(d)=kTlnni71015101.5M10)=0.338eVno=0.0259ln/192.8X10;5!2X10)=0.8436eVef-'E.=EgTE

11、c-'Ef=1.12-0.8436Ef-E.=kTlniN.Po=0.0259ln1.04M1019、12M1016J=0.162eVEc-Ef=Eg-Ef-E.=1.12-0.162=0.958eV19-0.958I；no=2.810exp0.0259=2.41103cm與niEFi-Ef=kTln=0.0259ln210165父1010)(b)(c)4.20(a)(b)noEFPoEFEf-E,.-0.2764eV,c,“19-0.27637po=1.0410exp0.0259143=2.41410cmp-typekT=0.0259竺=0.032375eV3003/217375=4

12、.7103000-0.28exp(0.032375=1.151014cm'-E：)=Eg-Ec-Ef)=1.42-0.28二710=1.14eV一1.14exp0.0323753_3=4.9910cmEc-EF=0.0259ln,4.7父1017；4.15父1014/=0.2154eV=1.420.21544.21(a)noEfPo(b)=1.2046eV18p。=710exp山0.0259=4.42102cmJ_375kT=0.0259=0.032375eV300c-c19i375甲2-0.28=2.810exp3000.032375153=6.8610cms-E.=Eg-Ec-Ef

13、>1.12-0.28=1.041019Ec-Ef=0.0259ln4.22(a)(b)=0.840eV375甲2-0.8401300exp0.032375_73=7.8410cm3=kTInNcno.192.8父10.156.862父10=0.2153eVEf-E/1.12-0.2153=0.9047eV190.904668|po=1.0410exp一_0.02593_3=7.0410cmp-typeEf-EEg1.12=0.28eV4po=N：exp-E；E-19-0.28三.1.0410exp0.0259143=2.1010cm一Ec-Ef=Eg-Ef-E.=1.12-0.28=0.

14、84eVEc-EF'：Ino=Ncexp一kT=2.81019exp-0.840.025953=2.3010cm一4.23(a)(b)nonoPo=niexpEEL-kT=1.51010exp-_0.0259=7.331013cm與EFi-EFexp一kT二：1.51010exp-0.22_0.025963=3.0710cmEF-EFi=1.8106exp0.22_0.025993=8.8010cmEFi-Efpoexp一kT4.24(a)(b)(c)(d)(e)=1.8106-0.22exp0.0259=3.68102cm-193=4.310910cm一21919ni=4.31091

15、01.60110exp-1.120.034533Ef-E.=kTln=0.0259lnPoJ一一191.041051015=0.1979eVEc-Ef=Eg-Ef-E.=1.12-0.19788=0.92212eV19-0.92212no=2810exp_0.025933=9.6610cmHolesEFi-Ef=kTln=0.0259ln15510101.510=0.3294eV4.25400kT=0.0259=0.034533eV300-3/2N.=1.041019400300(a)(b)(c)(d)(e)=1.6011019cmaNc2.810=5.67021024123=ni=2.381

16、10cm一EfEcno.Po-E,二kTln=0.034533ln=Q2787eV尸_191.601X105M1015-Ef=1.120.27873=0.84127eV=4.31091019exp-0.841270.03453393=1.13410cm'HolesEFi-EF=kTln:0.034533ln4.26(a)Poni1551015122.38110=Q2642eVpo=71018expjS=4.501014cm&Ec-Ef=1.42-0.25=1.17eVno=4.71017exp117-_0.0259=1.13104cm'(b)kT=0.034533eV(

17、a)(b)N.=710184003/2300二(0.034533ln/191.601X10;6.68M10=1.0781019cmJ=0.034533Inr_191.078X10144.50X10=0.3482eVEcEf=1.42-0.3482=1.072eVno=7.2361017exp370.03453343=2.4010cm4.27Ec=1.041019exp-z025_0.025914=6.6810cm-Ef=1.12-0.25=0.870eVno=2.81019expZ0Z£exp110.0259no=7.23104cmkT=0.034533eVN.=1.041019=1

18、.6011019cmNc二：2.8101919=4.31110cm0.3482eVEc-Ef=1.120.3482=0.7718eVno=4.3111019expZ50.03453393=8.4910cm4.282(a) no-NcFi/2fJ冗ForEF=EckT2,F=Ef-EckTL2=0kTkTThenF1/2f=1.0no=22.810191.0Vsi193=3.1610cm2.(b) no=NcFi/2fJ冗=24.710171.0后一一17_3=5.3010cm4.29Po=奈NJi/2("F)(a)Ef -EckT(b)no51019=_21.041019Fi/2fn

19、SoFi/2f=4.26WefindF.3.0=E-Ef一kTE.-Ef=3.00.0259=0.0777eV4.304kT,=4kTThenFi/2f二6.02no=NcFi/2f=22.810196.0而203=1.9010cma24.710176.0Jji183=3.1810cmnE=4mn-exp-Ec一日h3kTkTE-EcexpZIZETkTkTDefineE-Ecx二kTThennEnx=KJxexp?-xTofindmaximumnEJnx,setdnx=0=K-xa/2exp-xdx|_2x1/2-1exp-xor,./2/,10=Kxexp-x-xT2whichyields

20、1 E-Ec1x=E=Ec-kT2kT2FortheholeconcentrationpE=g.E1fFE1UsingtheBoltzmannapproximation4二2mp3/2pE:3,E.-Eh4.31FortheelectronconcentrationnE=gcEfFETheBoltzmannapproximationapplies,son(E片嗎工歷I；h34n(2m*p j/2 h3ITE-EFexp1orEfEa=3kTandEa-E.=0.045eVThenPo二：1.041019exp1-30.0450.0259=1.041019exp-4.737Thenpx=K；xe

21、xpJxorPo163=9.1210cm一TofindmaximumvalueofpEpx,set虹=0dxabove,Usingtheresultsfrom(b)GaAs:assumeEc-Ed=0.0058eVThen4.32(a)wefindthemaximumat1E=E.-kT2no二(4.710170.005830.0259=4.71017exp：3.224or163no=1.8710cmAssume巳-巳=0.0345eVSilicon:Wehaveno=NcexpEc-E-一kTThen二710-0.0345一3Wecanwrite0.0259三：71018exp：；4.332

22、ForEc-Ef=Ec-EdEd-EforPo163=9.2010cmEc-Ed-0.045eVandEd-Ef=3kTeVwecanwriteno=2.81019exp-0.045-3_0.02592.81019exp=-4.7374.33Plotor17no=2.4510cm4.34(a)=415-1015=31015cm'Wealsohaveef-E：Jpo=N.expkTAgain,wecanwriteEf-E：=Ef-EaEa-E-For(b)nonoNd(c)no(1.5黑1010231015=31016cm(1.5父10102163104號=7.510cm3.3=7.51

23、0cm_103ppo=Q=1.510cm(d)21919375ni=2.8101.0410300(d)n2=4.710177.01018375300(e)expT12300口0.025937511=ni=7.33410cm153po=Na=410cmexp江幽歸0.02593758_3=ni=7.58010cm153po=Na=410cmno名.334M10112,83=1.3410cm-410no7.580X108215410，一2=1.4410cm21919ni=28101.0410l'450"3300(e)2ni二4710177.01018450:300exp-1.12

24、300口0.025945013=q=1.72210cmexp二!幽心0.0259450=ni=3.85310,143n。=Nd=10cm10_3cmno一14"_14號1-+、；-J+1.722M101314=1.02910cmPo1.722M10132141.02910_12=2.8810cm_(3.853X10102po-1410=1.48107cm4.36(a)Ge:(i)no133q=2.410cmNdNd'2,24.351515(a)Po=Na-Nd=410-10153=310cm2M1015,2父1015¥132=+(2.4X10)2h2J(b)(c)1

25、.8X：1062310153=1.0810cmno=Nd=31016cm3Po-.8M106216310工=1.0810cm6no=po=1.810cmor15-3n°二Nd=210cmn：(2.4父10132po=15no21015=2.881011cm&(ii)po-Na-Nd=1016-71015=31015cm工ni2(2.4X10132no15Po310=1.921011cm-Then(b)GaAs:ni=1.8106cm-一一15no=Nd=210cm0.8M1062“工：po=1.6210cm21015(ii)po三Na-Nd=310cmorno15310=1.

26、0810Jcm3.(c)Theresultimpliesthatthereisonlyoneminoritycarrierinavolumeof3310cm.4.37(a)Forthedonorlevelnd31HUT.kT111exp衛(wèi)20.0259ornd1=8.8510“(b)WehavefFE二NowE-Ef=EEcEc-EforE-Ef=kT0.245fFE=-11exp1牒fFE)=2.8710-4.38(a) NaNd=p-type(b) Silicon:po=Na-Nd=2.51013-11013orpo=1.51013cmJThen2102ni1.5107no=13=1.51

27、0cmpo1.51013Germanium:+INaNd:2.JNa-Ndpo二2Fw131.5乂102or13_3po=3.2610cmThen2nino二po(2.4父1013j3.2641013n2-2.41013一13=1.76103cmGalliumArsenide:一一13po=NaNd=1.510cmand2ninopo(1.810621.510133=0.216cm4.39(a) NdNa='n-type1515(b) no=Nd-Na=210-1.210=81014cmJPo2nino1.510101481053=2.8110cm一22nini212n。=一n。=一q

28、po4no41=n0=-ni2113Sono=6.8810cm一，123Thenp0=2.7510cm一po中所2.7521012-2(c)Po三NaNa-Nd41015=Na1.21015-21015153=Na=4.810cmno1.5M1010241015_4=5.62510cm7.57351024r27521012Na2-21.893610242一一123sothatNa=2.06410cm4.40non2(1.5父10102二5Po21015=1.12510cm4.41expno-po=:n-typen"-1.0410196.01018250：3300I20.660.025

29、9250300_24=1.89361012=ni=1.37610cm4.42Plot4.43Plot4.44Plot4.45Nd-Nano二一2一+(Nd-Na：2+2J2ni141.110_14_142101.210一2/1414呼2X10-1.2X10;2J+q2J4.471413213221.110-410=410ni_27_2724.910=1.610-ni13_3soni=5.7410cm(a) Po；：；：n=n-type22nini(b) PononopoPo2ninono273.310141.11013二310cm3.(1.5X101°2421016=1.12510c

30、m_34.46(a)Na、Nd=p-type二electronsaremajoritycarriers43po=210cm=holesareminoritycarriersMajoritycarriersareholesPo=Na-Nd=31016-1.51016163二1.510cm(c)no=Nd-Na1.1251016=Nd-71015soNd=1.8251016cmMinoritycarriersareelectrons210 2ni 1.5 10no(b) Boron atoms must be added Po =Na Na -Nd5 1016 =Na 3 1016 -1.5 10

31、16So Na =3.5 1016 cm 'Po1.5 101643=1.5 10 cm4.48Eh -Ef =kTlnT(K)kT (eV)ni (cm )2000.01727102.16104000.03453148.60X106000.05183.82X1016For GermaniumPo吟no1.5 M1010 2165 103= 4.5 10 cmniand15Na=10cmT(K)Po(cm)(EFi-Ef)(eV)200151.0M100.1855400151.49x100.018986003.87 M10160.0006744.4921919Tni=2.8101.04

32、10300-1.12exp代0.0259T3002838Ti；5.2510=2.91210300(a)EcEf=kTInl-12972.973expT=0.0259ln192.810Bytrialanderror,T=536.5K(b)1510cma,Ec-Ef0.2652eV1016cm&,Ec-Ef=0.2056eV1017cm&,Ec一Ef=0.1459eVNd143_For10cm,Ec-Ef=0.3249eV%<niJ(b)AtT=300K,NEcEf=kTln<n0)Ec-EfK：0.0259ln192.8101510=0.2652eVEf-EFi二kT

33、lnAtT=536.5K,o0.0259lnNd1.51010kT=0.0259536.5300=0.046318eVFor1014cm±Ef-EFi=0.2280eV15310cm,Ef-EFi=0.2877eV1016cma,Ef-EFi=0.3473eV1017cm吃Ef-EFi=0.4070eVNc=2.810193/2536.5300_19=6.6961019cm=kT lnEc - Ef-；'：0.046318 ln4.50no啜+J佟)+ni2no=1.05Nd=1.051015cm1.05M1015-0.5X10152Ec-'Ef，一,196.696父

34、10工1.05父1015=0.5124eVthen匚Ec-Ef)=0.2472eV(c) Closer to the intrinsic energy level.=0.5父10152+n：soni2=5.251028Now4.51EFi -Ef =kTlnT =400K,EFi -Ef =0.2465eVT =600K,EFi -Ef =0.0630eV,niAtT=200K,kT=0.017267eVT=400K,kT=O034533eVT=600K,kT=0.0518eVThen,T=200K,EFi-Ef=Q4212eVAtT=200K,2ni19=2.8104.52(a)-1.12e

35、xp0.01726743=ni=7.63810cm一AtT=400K,ni2=2.810191.041019再300-1.12exp|0.034533123=ni=2.38110cmAtT=600K,EFi-EF=kTln-NU(0.0259In1Nini)p.8M10JForNa=1014cm”,EFi-Ef=0.4619eV153Na=10cm,EFi-Ef=0.5215eV163Na=10cmEFi-Ef=0.5811eV17JNa=10cm,EFi-Ef=0.6408eVni2=2.810191.041019600:300%1-1.12exp0.0518143=ni=9.74010cm

36、AtT=200KandT=400K,po=Na=31015cm&AtT=600K,po4十J*"i222、,15f、,1523黑10,3M10,7y142=十f+(9.740父10)2V2)15.3=3.28810cm(b)Nu)/.7.0父1018EF-E1%=kTln1=(0.0259)nNa廣NNNa-143ForNa=10cm,Ef-E.=0.2889eV,15一Na=10cmEf-E0.2293eV163Na=10cmEf-E0.1697eV.一17Na=10cmEf-E.=0.1100eV4.53(a)3,十，EFi-Emidgap=kTln(i)EcEf=kTI

37、nNcN73,o-o0.0259ln10=0.0259ln192.810=0.2188eV61015or(ii)Ec-Ef=0.21880.0259=0.1929eVEFiEmidgap=0.0447eVNd(b)Impurityatomstobeaddedso=Ncexp-Ec*kTEmidgap-Ef=0.45eV(i) p-type, so add acceptor atoms(ii)19-0.1929=2.810exp0.0259expi EFi - E F.kTEFi-Ef=0.04470.45=0.4947eVThenNd=1.6311016cm4=Nd.61015=Nd=1.03

38、11016cm-Additionaldonor atoms105exp/0.0259or(b)GaAsPo133=Na=1.9710cm(i)Ec-Ef=(.0.0259ln4.710171015=0.15936eV(ii)Ec-Ef=0.159360.0259=0.13346eVNd=4.71017e:1-0.133464.54153-15= 2.718 10 cm =Nd 10EcEfno=Nd-Na=Ncexpc-一kTso153=Nd=1.71810cmAdditional15Nd=510-2.81019-0.215exp0.0259donoratoms1515二5106.9510orNd163=1.2 10 cm4.56(a) EFi -Ef =kTln4.55(a)Silicon=0.0259ln/一一19、1.04M101c“cc、,16I=0.1620eV(2M10j(a)EFiEf=kTIn-i0.0259ln15310Z_101.510=0.3161eV(b)(b)EfYFi=kTlnNdEf-E