1、Semiconductor Physics and Devices: Basic Principles, 4th edition Chapter 4By D. A. Neamen Problem Solutions_1Chapter 44.1kTENngciexp2gOc30where and are the values at 300 K.c(a) Silicon(K)T(eV)kT(cm )in320460172.3458. 41068.27.9(b) Germanium (c) GaAs(K)T(cm )in3(cm )in32046106.248. 8.91027.5_4.2Plot_
2、4.3(a) kTENngciexp2319191 04.08.05T25.exp33823019.105. T259.expBy trial and error, K367T(b)252120.05inTT9.301exp39.8By trial and error, K.47_4.4At K, 20T30259.keV176.At K, 44.eV035.1721024.70in01726.exp345.3023ggE3458gg985exp1025.37gEor 174.3802.3ln96.817gEor eV1Now3210047. ocN5.18exp7216237.09.5ocs
3、o cm4.ocN_Semiconductor Physics and Devices: Basic Principles, 4th edition Chapter 4By D. A. Neamen Problem Solutions_24.5kTkTAnBi 20.exp90.exp1.For K, eV2T176.For K, eV325For K, eV40034(a) For K,61025.9176.expAnBi(b) For K,30T43.25.i(c) For K,4310.0.expAnBi_4.6(a) kTEEfgFcFcexpcckTFcexpLet xEcThen
4、kfgFTo find the maximum value:Txxdfcep21/0/1kkwhich yields2212/xTxThe maximum value occurs atkEc(b)kTEEfgFFexp1kTFexpLet xEThen fgF1To find the maximum value0expkTdxfdSame as part (a). Maximum occurs at2kTorE_4.7kTEEncccc221121expwhereand kTc4122cThenkEkEn121exp5.3exp24or085.21En_4.8Plot_Semiconduct
5、or Physics and Devices: Basic Principles, 4th edition Chapter 4By D. A. Neamen Problem Solutions_34.9Plot_4.10*ln43pmidgapFi kTESilicon: , o56.0* om08.1eV2idgapFiGermanium: , o37.*on5.*eVmidgapiEGallium Arsenide: , op48.0*onm67.*eV32.midgapFi_4.11cmidgapFi NkTEln21kT4952.08.04l19(K)T(eV)k( )(eV)midg
6、apFiE204672.345018. 086.1725._4.12(a) *ln43pmidgapFi kTE21.70l59.0meV631(b) 08.5ln.4midgapFiEmeV7._4.13Let constantKEgcThendfnFEcoEkTKcFexp1dcELet so that kTkTWe can writecFcFEEso thatexpexpexpkTkTFThe integral can then be written asdEKnFco 0which becomeskTkFcoexp_4.14Let for ccECg1cThendfnFEcoEkTCc
7、Fcexp1dECc 1Let so that kTkTdWe can writeFcFEESemiconductor Physics and Devices: Basic Principles, 4th edition Chapter 4By D. A. Neamen Problem Solutions_4ThenkTECnFcoexp1dEkcEcc eorkTCnFoexp1dk0We find that1expexp00 dSokTEkCnFco21_4.15We have *1marooFor germanium, , 6r o5.0Then3.295.0161ororA4.1The
8、 ionization energy can be written aseV6.132*somEeV0965.02E_4.16We have *1marooFor gallium arsenide, , 1.3rom067*ThenoAr45.067.131The ionization energy is6.13.076.1322*somEoreV05._4.17(a) ocFcnNkTEl159078.2l059.eV14(b) FcgFEEeV8.2.(c) kTNpoex0259.1p104.9cm36(d) Holes(e) ioFinkTEl105.7l0259.eV38_4.18(
9、a) oFpNkTEln169024.l059.eV16(b) EEFgFceV8(c) 0259.exp8.219oncm34Semiconductor Physics and Devices: Basic Principles, 4th edition Chapter 4By D. A. Neamen Problem Solutions_5(d) ioFi npkTEl1065.2l09.eV36_4.19(a) ocFcnNkTEl519028.l059.eV8436FcgFEE.1eV270(b) 0259.637exp4.9opcm1(c) p-type_4.20(a) eV0327
10、5.0259.kT.8exp17.4/oncm40532.041FcgFEEeV1.375.exp3072/8opcm9.4(b) 140.ln25FcEeV1.025.FcgeV46.09.exp718opcm2.3_4.21(a) eV03275.0259.kT.8exp18./oncm50632.01FcgFEEeV84.375.84exp30712/9opcm.7(b) ocFcnNkTEl1590862.l059.eV213eV47EF0259.exp04.9opcm317_4.22(a) p-type(b) eV28.041.gFEkTNpFoex0259.p10.9cm423EE
11、FgFceV81kTNnccoexp0259.48.219cm5303_Semiconductor Physics and Devices: Basic Principles, 4th edition Chapter 4By D. A. Neamen Problem Solutions_64.23(a) kTEnFiioexp0259.15.0cm37kTEnpFiioex0259.p15.0cm6733(b) kTEnFiioex0259.p18.6cm93kTEnpFiioex0259.p18.6cm233_4.24(a) oFpNkTEln15904.l0259.eV17(b) EEFg
12、FceV2.8.(c) 059.1exp8.219oncm36(d) Holes(e) ioFi nkTEl105.l0259.eV34_4.25eV0345.0259.kT2/14.Ncm1906.32/198.2ccm193.43192 060.in45.2exp2467.5cm1038in3(a) oFpNkTEln15906.l0345.eV278(b) eV8427.273.FcE(c) 05.exp139.4oncm3(d) Holes(e) ioFi nkTEl125038.l045.eV26_4.26(a) 0259.exp178opcm45.3eV17.FcE0259.exp
13、17.oncm233Semiconductor Physics and Devices: Basic Principles, 4th edition Chapter 4By D. A. Neamen Problem Solutions_7(b) eV0345.kT2/3187Ncm9.32/1704ccm26.3oFpNkTEln14905.78l034.eV82eV21FcE0345.7exp36.77oncm402_4.27(a) 0259.exp104.9opcm683eV87FcE0259.exp1.29oncm4373(b) eV05.kT2/190Ncm6.32/19482ccm0
14、3.3oFpNkTEln149068.l0345.eV82eV71FcE0345.71exp13.49oncm08_4.28(a) FcoNn2/1For , kTEF5.0cThen .12/1F89oncm106.33(b) FcoN2/.17.4cm0353_4.29FoNp2/1F2/191904.05So 62/FWe find kTE.3eV07.2590FE_4.30(a) 4kTcFThen 0.62/1FcoNn2/1.8.9cm203Semiconductor Physics and Devices: Basic Principles, 4th edition Chapte
15、r 4By D. A. Neamen Problem Solutions_8(b) 0.617.42oncm833_4.31For the electron concentrationEfgnFcThe Boltzmann approximation applies, socnhm32/*4kTEFexporhEnFcn243/*kTEkTccexpDefineExcThenxKnepTo find maximum , setndx210/xxep12/orKxep02/1which yieldskTEkTcc212For the hole concentrationfgEpF1Using t
16、he Boltzmann approximationEhmp32/*4kTFexorkTEhmEpFpex243/*kTpDefinekExThenxKpepTo find maximum value of , setxpEUsing the results from above, 0xdwe find the maximum atkTE21_4.32(a) Silicon: We havekTENnFccoexpWe can writeFdcFcEFor eV and eV045.d kTE3we can write29.exp18.29on7340orcm1745.2onWe also h
17、avekTENpFoexAgain, we can writeEaFFForand eVka3045.EThen29.exp104.9op734orcm1602.9opSemiconductor Physics and Devices: Basic Principles, 4th edition Chapter 4By D. A. Neamen Problem Solutions_9(b) GaAs: assume eV058.dcEThen329.exp107.4on4orcm16087.on3Assume eV5.EaThen3029.4exp18op7orcm1620.9op3_4.33
18、Plot_4.34(a) cm1515034op3cm41520.7.n(b) cm6doN3cm1620.3.p3(c) cm105ion(d) 39192 754.8. i02.expcm134.7in3cm5aoNpcm81520.0.3(e) 1992 45.8. in02.3expcm17.in21321414 07.02oncm149.3cm1228.0.7op3_4.35(a) 154daoNpcm15033cm3262 08.8. oin(b) cm1d3cm4162.03.op3(c) cm68in(d) 31172 0754i29.4expcm815.7in3cm04aoN
19、pcm2152804 3(e) 1872.0.4in45029.3expcm10853.incm4doNcm71420p3_4.36(a) Ge: cm1304.2in(i) 2iddonN2131515 04.02Semiconductor Physics and Devices: Basic Principles, 4th edition Chapter 4By D. A. Neamen Problem Solutions_10orcm1502doNn31524.oipcm8.3(ii) 15607daocm1503315224.oipncm9.3(b) GaAs: cm608i(i) c
20、m152doNncm3156 p(ii) cm150daocm315268.38. n(c) The result implies that there is only one minority carrier in a volume of cm .30_4.37(a) For the donor levelkTENnFddexp21059.or 418.dNn(b) We havekTEEfFFexp1Now FcFor245.0kEThen0259.41expEfFor87.2fF_4.38(a) p-typedaN(b) Silicon:131305.2oporcm130.Thencm7
21、1320255oipn3Germanium:22idadao nNN2131313 04.05.05. orcm1326.opThencm13132076.4.0oinGallium Arsenide:cm5.daNp3andcm216.0.18362oin3_4.39(a) n-typeadN(b) 151502.oncm14083cm514028oip3Semiconductor Physics and Devices: Basic Principles, 4th edition Chapter 4By D. A. Neamen Problem Solutions_11(c) daoNp1
22、51515 02.04cm8a3cm415206on3_4.40cm1552102 0oipn3n-type_4.41318192 025.604. in.6.exp24108936.cm7in322ioionpin1So cm , 08.6o3Then cm1275piaaonN212075.a242108936.a22475.10573. aN24108936.aso that cm12064.aN_4.42Plot_4.43Plot_4.44Plot_4.4522iadado nNNn10.10. 41442442.in13131400. i27276.9inso cm13.5incm1
23、3142720.oip_4.46(a) p-typedaNMajority carriers are holes161605.3opcm1605.Minority carriers are electronscm416202oipn3(b) Boron atoms must be addeddaN161616 05.305So cm.acm31620.4on_Semiconductor Physics and Devices: Basic Principles, 4th edition Chapter 4By D. A. Neamen Problem Solutions_124.47(a) n
24、-typeionp(b) oip22cmon1641005.5.3electrons are majority carrierscm2op3holes are minority carriers(c) adNn15160705.dso cm82d3_4.48ioFi npkTElFor Germanium(K) T(eV) (cm )in320460172.3458. 106.42.and 22iaaonNpcm150a3(K) T(cm )o3 (eV)FiE046150.49687.8.190674._4.49(a) dcFcNkTElnd1908.2l059.For cm , eV143
25、34.Fccm , eV56Ecm , eV1603205.ccm , eV719F(b) idFinNkTEl105.l029.dFor cm , eV14038Ficm , eV5 7.Ecm , eV163340icm , eV7.F_4.50(a) 22iddonNncm150.05.1d32215.inso 282105.inNow319192 04 Ti25.exp33828019.105. T97.expBy trial and error, K5.36T(b) At K,30ocFcnNkEl15908.2l9.0ceV6At K,5.3TeV4638.0.29k2/18.cN
26、cm963Semiconductor Physics and Devices: Basic Principles, 4th edition Chapter 4By D. A. Neamen Problem Solutions_13ocFcnNkTEl1590.6l04318.ceV52then eV7.FcE(c) Closer to the intrinsic energy level._4.51ioFi npkTElAt K, eV2001726.K, eV4345K, eV68kAt K,T319192 024.08. in76.expcm41638.7in3At K,40T319192
27、 0 i45.2expcm12038.in3At K,6T319192 064 i58.2expcm1407.9in3At K and K, 2TTcm5aoNpAt K,622iaaon2141515 07.903cm1528.Then, K, eV20T21.0FiEK, eV4465K, eV63.i_4.52(a) 6108.ln0259.lnaiaFi NNkTEFor cm , eV140a34FiEcm , eV5.cm , eV16a35icm , eV7N608.F(b) aaF NkTE1.7ln029.lnFor cm , eV140a38.EFcm , eV5N3cm
28、, eV16a31697.0cm , eV7F_4.53(a) *ln43pmidgapFi kTE10l259.oreV047.midgapFi(b) Impurity atoms to be added soeV5.iE(i) p-type, so add acceptor atoms(ii) eV497.0.047.FiThenkTnpFiioex0259.4715orcm13.aoNp_Semiconductor Physics and Devices: Basic Principles, 4th edition Chapter 4By D. A. Neamen Problem Solutions_
