半导体器件物理与工艺+施敏++答案

1SOLUTIONSMANUALTOACCOMPANYSEMICONDUCTORDEVICESPHYSICSANDTECHNOLOGY2NDEDITIONSMSZEUMCCHAIRPROFESSORNATIONALCHIAOTUNGUNIVERSITYNATIONALNANODEVICELABORATORIESHSINCHU,TAIWANJOHNWILEYANDSONS,INCNEWYORKCHICESTER/WEINHEIM/BRISBAND/SINGAPORE/TORONTO0CONTENTSCH1INTRODUCTION0CH2ENERGYBANDSANDCARRIERCONCENTRATION1CH3CARRIERTRANSPORTPHENOMENA7CH4PNJUNCTION16CH5BIPOLARTRANSISTORANDRELATEDDEVICES32CH6MOSFETANDRELATEDDEVICES48CH7MESFETANDRELATEDDEVICES60CH8MICROWAVEDIODE,QUANTUMEFFECTANDHOTELECTRONDEVICES68CH9PHOTONICDEVICES73CH10CRYSTALGROWTHANDEPITAXY83CH11FILMFORMATION92CH12LITHOGRAPHYANDETCHING99CH13IMPURITYDOPING105CH14INTEGRATEDDEVICES1131CHAPTER21AFROMFIG11A,THEATOMATTHECENTEROFTHECUBEISSURROUNDBYFOUREQUIDISTANTNEARESTNEIGHBORSTHATLIEATTHECORNERSOFATETRAHEDRONTHEREFORETHEDISTANCEBETWEENNEARESTNEIGHBORSINSILICONA543IS1/2A/22A2/221/2A3/4235BFORTHE100PLANE,THEREARETWOATOMSONECENTRALATOMAND4CORNERATOMSEACHCONTRIBUTING1/4OFANATOMFORATOTALOFTWOATOMSASSHOWNINFIG4AFORANAREAOFA2,THEREFOREWEHAVE2/A22/54310826781014ATOMS/CM2SIMILARLYWEHAVEFOR110PLANEFIG4AANDFIG6221/241/4/A22961015ATOMS/CM2,ANDFOR111PLANEFIG4AANDFIG631/231/6/1/2A2A232232A7831014ATOMS/CM22THEHEIGHTSATX,Y,ANDZPOINTARE,43,41AND433AFORTHESIMPLECUBIC,AUNITCELLCONTAINS1/8OFASPHEREATEACHOFTHEEIGHTCORNERSFORATOTALOFONESPHERE4MAXIMUMFRACTIONOFCELLFILLEDNOOFSPHEREVOLUMEOFEACHSPHERE/UNITCELLVOLUME14A/23/A352BFORAFACECENTEREDCUBIC,AUNITCELLCONTAINS1/8OFASPHEREATEACHOFTHEEIGHTCORNERSFORATOTALOFONESPHERETHEFCCALSOCONTAINSHALFASPHEREATEACHOFTHESIXFACESFORATOTALOFTHREESPHERESTHENEARESTNEIGHBORDISTANCEIS1/2A2THEREFORETHERADIUSOFEACHSPHEREIS1/4A24MAXIMUMFRACTIONOFCELLFILLED134A/2/43/3/A374CFORADIAMONDLATTICE,AUNITCELLCONTAINS1/8OFASPHEREATEACHOFTHEEIGHTCORNERSFORATOTALOFONESPHERE,1/2OFASPHEREATEACHOFTHESIXFACESFORATOTALOFTHREESPHERES,AND4SPHERESINSIDETHECELLTHEDIAGONALDISTANCE2BETWEEN1/2,0,0AND1/4,1/4,1/4SHOWNINFIG9AISD21222222AAA34ATHERADIUSOFTHESPHEREISD/238A4MAXIMUMFRACTIONOFCELLFILLED13433834AP/A33/1634THISISARELATIVELYLOWPERCENTAGECOMPAREDTOOTHERLATTICESTRUCTURES41D2D3D4DD1D2D3D4D01D1D2D3D4D1D0021D1D2D1D3D1D4D04D2D2COS12D2COS13D2COS14D23D2COS04COS31COS1311094705TAKINGTHERECIPROCALSOFTHESEINTERCEPTSWEGET1/2,1/3AND1/4THESMALLESTTHREEINTEGERSHAVINGTHESAMERATIOARE6,4,AND3THEPLANEISREFERREDTOAS643PLANE6ATHELATTICECONSTANTFORGAASIS565,ANDTHEATOMICWEIGHTSOFGAANDASARE6972AND7492G/MOLE,RESPECTIVELYTHEREAREFOURGALLIUMATOMSANDFOURARSENICATOMSPERUNITCELL,THEREFORE4/A34/56510832221022GAORASATOMS/CM2,DENSITYNOOFATOMS/CM3ATOMICWEIGHT/AVOGADROCONSTANT222102269727492/6021023533G/CM3BIFGAASISDOPEDWITHSNANDSNATOMSDISPLACEGAATOMS,DONORSAREFORMED,BECAUSESNHASFOURVALENCEELECTRONSWHILEGAHASONLYTHREETHERESULTINGSEMICONDUCTORISNTYPE7ATHEMELTINGTEMPERATUREFORSIIS1412C,ANDFORSIO2IS1600CTHEREFORE,SIO2HASHIGHERMELTINGTEMPERATUREITISMOREDIFFICULTTOBREAKTHESIOBONDTHANTHESISIBONDBTHESEEDCRYSTALISUSEDTOINITIATEDTHEGROWTHOFTHEINGOTWITHTHECORRECTCRYSTALORIENTATIONCTHECRYSTALORIENTATIONDETERMINESTHESEMICONDUCTORSCHEMICALANDELECTRICAL3PROPERTIES,SUCHASTHEETCHRATE,TRAPDENSITY,BREAKAGEPLANEETCDTHETEMPERATINGOFTHECRUSIBLEANDTHEPULLRATE8EGT117636473X1024TTFORSIEG100K1163EV,ANDEG600K1032EVEG1024TTFORGAASEG100K1501EV,ANDEG600K1277EV9THEDENSITYOFHOLESINTHEVALENCEBANDISGIVENBYINTEGRATINGTHEPRODUCTNE1FEDEFROMTOPOFTHEVALENCEBANDVETAKENTOBEE0TOTHEBOTTOMOFTHEVALENCEBANDEBOTTOMPBOTTOME0NE1FEDE1WHERE1FE/KT1E/11FEE1/E1KTEEFIFEFEKTTHEN1FEEXPKTEEF2THENFROMAPPENDIXHAND,EQS1AND2WEOBTAINP42MP/H23/2BOTTOME0E1/2EXPEFE/KTDE3LETXAE/KT,ANDLETEBOTTOM,EQ3BECOMESP42MP/H23/2KT3/2EXPEF/KT0X1/2EXDXWHERETHEINTEGRALONTHERIGHTISOFTHESTANDARDFORMANDEQUALSP/24P22MPKT/H23/2EXPEF/KTBYREFERRINGTOTHETOPOFTHEVALENCEBANDASEVINSTEADOFE0WEHAVE,P22MPKT/H23/2EXPEFEV/KTORPNVEXPEFEV/KTWHERENV22MPKT/H2310FROMEQ18NV22MPKT/H23/2THEEFFECTIVEMASSOFHOLESINSIISMPNV/22/3H2/2KT3236192M101066230010381210625623234P941031KG103M0SIMILARLY,WEHAVEFORGAASMP391031KG043M011USINGEQ194CVVCNNKTEEEILN22ECEV/23KT/4LN326NPMM1AT77KEI116/231381023T/4161019LN10/062058329105T0582541030583EVAT300KEI112/232910530005600090569EVAT373KEI109/2329105373054500120557EVBECAUSETHESECONDTERMONTHERIGHTHANDSIDEOFTHEEQ1ISMUCHSMALLERCOMPAREDTOTHEFIRSTTERM,OVERTHEABOVETEMPERATURERANGE,ITISREASONABLETOASSUMETHATEIISINTHECENTEROFTHEFORBIDDENGAP12KE/DDECFTOPCFTOPCEEXKTEECEEKTEECEECEEEEEEEEEKT021023DEDEXXXXXXKT2325KTPP505051KT2313APMV9109103110591091026KGM/SLPH2634101099106266727109M727BNLLPMM006301727115414FROMFIG22WHENNI1015CM3,THECORRESPONDINGTEMPERATUREIS1000/T18SOTHATT1000/18555KOR28215FROMECEFKTLNNC/NDNAWHICHCANBEREWRITTENASNDNANCEXPECEF/KTTHENNDNA2861019EXP020/002591261016CM3ORND1261016NA2261016CM3ACOMPENSATEDSEMICONDUCTORCANBEFABRICATEDTOPROVIDEASPECIFICFERMIENERGYLEVEL16FROMFIG28AWECANDRAWTHEFOLLOWINGENERGYBANDDIAGRAMS517ATHEIONIZATIONENERGYFORBORONINSIIS0045EVAT300K,ALLBORONIMPURITIESAREIONIZEDTHUSPPNA1015CM3NPNI2/NA9651092/101593104CM3THEFERMILEVELMEASUREDFROMTHETOPOFTHEVALENCEBANDISGIVENBYEFEVKTLNNV/ND00259LN2661019/1015026EVBTHEBORONATOMSCOMPENSATETHEARSENICATOMSWEHAVEPPNAND310162910161015CM3SINCEPPISTHESAMEASGIVENINA,THEVALUESFORNPANDEFARETHESAMEASINAHOWEVER,THEMOBILITIESANDRESISTIVITIESFORTHESETWOSAMPLESAREDIFFERENT18SINCENDNI,WECANAPPROXIMATEN0NDANDP0NI2/N0931019/101793102CM3FROMN0NIEXPKTEEIF,WEHAVEEFEIKTLNN0/NI00259LN1017/965109042EVTHERESULTINGFLATBANDDIAGRAMIS619ASSUMINGCOMPLETEIONIZATION,THEFERMILEVELMEASUREDFROMTHEINTRINSICFERMILEVELIS035EVFOR1015CM3,045EVFOR1017CM3,AND054EVFOR1019CM3THENUMBEROFELECTRONSTHATAREIONIZEDISGIVENBYNND1FEDND/1ETKEEFD/USINGTHEFERMILEVELSGIVENABOVE,WEOBTAINTHENUMBEROFIONIZEDDONORSASN1015CM3FORND1015CM3N0931017CM3FORND1017CM3N0271019CM3FORND1019CM3THEREFORE,THEASSUMPTIONOFCOMPLETEIONIZATIONISVALIDONLYFORTHECASEOF1015CM320NDKTEEFDE/16110135016E11014511110165331015CM3THENEUTRALDONOR10165331015CM34671015CM34THERATIOOFDDNNO33576408767CHAPTER31AFORINTRINSICSI,MN1450,MP505,ANDNPNI965109WEHAVE51031311PNIPNQNQPQNMMMMRCMBSIMILARLYFORGAAS,MN9200,MP320,ANDNPNI225106WEHAVE81092211PNIPNQNQPQNMMMMRCM2FORLATTICESCATTERING,MNT3/2T200K,MN13002/32/33002002388CM2/VST400K,MN13002/32/3300400844CM2/VS3SINCE21111MMM500125011M167CM2/VS4AP51015CM3,NNI2/P9651092/51015186104CM3MP410CM2/VS,MN1300CM2/VSRPQPQNQPPNMMM113CMBPNAND2101615101651015CM3,N186104CM3MPMPNANDMP351016290CM2/VS,MNMNNAND1000CM2/VSRPQPQNQPPNMMM1143CM8CPNABORONNDNAGALLIUM51015CM3,N186104CM3MPMPNANDNAMP2051017150CM2/VS,MNMNNANDNA520CM2/VSR83CM5ASSUMENDNANI,THECONDUCTIVITYISGIVENBYSQNMNQMNNDNAWEHAVETHAT16161019MNND1017SINCEMOBILITYISAFUNCTIONOFTHEIONIZEDIMPURITYCONCENTRATION,WECANUSEFIG3ALONGWITHTRIALANDERRORTODETERMINEMNANDNDFOREXAMPLE,IFWECHOOSEND21017,THENNINDNA31017,SOTHATMN510CM2/VSWHICHGIVESS816FURTHERTRIALANDERRORYIELDSND351017CM3ANDMN400CM2/VSWHICHGIVESS16CM16/2NNBNQPNQIPPNMMMSFROMTHECONDITIONDS/DN0,WEOBTAINBNNI/THEREFORE9BBBNQNBBBNQIPIIPIM2111/1MRR7ATTHELIMITWHENDS,CF2LNP453THENFROMEQ16226053410501011010433CFWIVRCMFROMFIG6,CF42D/S10USINGTHEA/D1CURVEWEOBTAIN7810241050102260/43CFWIVRMV8HALLCOEFFICIENT,742605010103010521061101049333WIBAVRZHHCM3/CSINCETHESIGNOFRHISPOSITIVE,THECARRIERSAREHOLESFROMEQ221619104617426106111HQRPCM3ASSUMINGNAP,FROMFIG7WEOBTAINR11CMTHEMOBILITYMPISGIVENBYEQ15B38011104611061111619RMQPPCM2/VS9SINCERRANDPNQPQNMMR1,HENCEPNPNRMM1FROMEINSTEINRELATIONMD50/PNPNDDMM10PANDNDNNNRRMMM115011WEHAVENA50ND10THEELECTRICPOTENTIALFISRELATEDTOELECTRONPOTENTIALENERGYBYTHECHARGEQFQ1EFEITHEELECTRICFIELDFORTHEONEDIMENSIONALSITUATIONISDEFINEDASEXDXDFDXDEQI1NNIEXPKTEEIFNDXHENCEEFEIKTLNIDNXNDXXDNXNQKTXDD1E11AFROMEQ31,JN0ANDAQKTENEANQKTNDXDNDXAXAXNN00MEBEX00259104259V/CM12ATTHERMALANDELECTRICEQUILIBRIA,0DXXDNQDXNQJNNNEMXNNLNNNDLNNLXNNNDDXXDNXNDXLLNNLLNNNN11000000MMME1100000NLNDNNDXNNLNNNVLNNLLLMM131116610101010LPGPNTCM3151115101010NNNNNDNOCM3CM101010106593111115292PNNPDI14A815715101021010511TTHPPNNSTS48103109PPPDLTCM20101021010167STSSTHLRNSSNCM/SBTHEHOLECONCENTRATIONATTHESURFACEISGIVENBYEQ67CM1020101032010110101021096510398481781629LRPPLRPLPNONSLSGPPTTT15PNQPQNMMSBEFOREILLUMINATIONNONNONPPNN,AFTERILLUMINATION,GNNNNPNONONTGPPPPPNONONTGQPQNQPPQNNQPPNNOPNONNOPNONTMMMMMMS1216ADIFF,DXDPQDJPP161019124101211015EXPX/1216EXPX/12A/CM2BDIFF,DRIFT,PTOTALNJJJ4816EXPX/12A/CM2CENNQNJMDRIFT,Q4816EXPX/1216101910161000EE3EXPX/12V/CM17FORE0WEHAVE022XPDPPTPNPPNONTATSTEADYSTATE,THEBOUNDARYCONDITIONSAREPNX0PN0ANDPNXWPNOTHEREFOREPPNONNONLWLXWPPPXPSINHSINH0PPPNONXNPPLWLDPPQXPQDXJCOTH000PPPNONWXNPPLWLDPPQXPQDWXJSINH1018THEPORTIONOFINJECTIONCURRENTTHATREACHESTHEOPPOSITESURFACEBYDIFFUSIONIS13GIVENBY/COSH100PPPLWJWJA26105105050PPPDLTCM980105/10COSH1220ATHEREFORE,98OFTHEINJECTEDCURRENTCANREACHTHEOPPOSITESURFACE19INSTEADYSTATE,THERECOMBINATIONRATEATTHESURFACEANDINTHEBULKISEQUALSURFACE,SURFACE,BULK,BULK,PNPNPPTTSOTHATTHEEXCESSMINORITYCARRIERCONCENTRATIONATTHESURFACEDPN,SURFACE10146710101013CM3THEGENERATIONRATECANBEDETERMINEDFROMTHESTEADYSTATECONDITIONSINTHEBULKG61410101020CM3S1FROMEQ62,WECANWRITE022PPPGXPDTTHEBOUNDARYCONDITIONSAREDPX1014CM3ANDDPX01013CM3HENCEDPX1014PLXE/901WHERELP61010316M20THEPOTENTIALBARRIERHEIGHTCFFMB424002VOLTS21THENUMBEROFELECTRONSOCCUPYINGTHEENERGYLEVELBETWEENEANDEDEISDNNEFEDEWHERENEISTHEDENSITYOFSTATEFUNCTION,ANDFEISFERMIDIRACDISTRIBUTIONFUNCTIONSINCEONLYELECTRONSWITHANENERGYGREATERTHANMFQEFANDHAVINGAVELOCITYCOMPONENTNORMALTOTHESURFACECANESCAPETHESOLID,THETHERMIONICCURRENTDENSITYISDEEEVHMQVJKTEEXQEXFMF2132324FPWHEREXVISTHECOMPONENTOFVELOCITYNORMALTOTHESURFACEOFTHEMETALSINCETHEENERGYMOMENTUMRELATIONSHIP2122222ZYXPPPMMPE14DIFFERENTIATIONLEADSTOMPDPDEBYCHANGINGTHEMOMENTUMCOMPONENTTORECTANGULARCOORDINATES,ZYXDPDPDPDPP24PHENCEZMKTPYMKTPXXMKTMEPPZYXPMKTMEPPPXDPEDPEDPPEMHQDPDPDPEPMHQJZYFXXXFZYX22223PP2/2322200Y22222WHERE220MFXQEMPFSINCE212ADXEAXP,THELASTTWOINTEGRALSYIELD2MKT21THEFIRSTINTEGRALISEVALUATEDBYSETTINGUMKTMEPFX222THEREFOREWEHAVEMKTDPPDUXXTHELOWERLIMITOFTHEFIRSTINTEGRALCANBEWRITTENASKTQMKTMEQEMMFMFFF222SOTHATTHEFIRSTINTEGRALBECOMESKTQUKTQMMEMKTDUEMKTFF/HENCEKTQTAETHQMKJMKTQMFPFEXP4223222EQUATION79ISTHETUNNELINGPROBABILITY110234193120M1017210054110612201011922HEQVMNB612100101932202410310172SINH201T23EQUATION79ISTHETUNNELINGPROB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RTHEOFHLAYERWIDTDEPLETIONTOTAL261718171819121VVNNNNQNNNWBIDADASDAAESIMILARLYWEOBTAINFORTHEBASECOLLECTORFUNCTIONV07951065910102LN02590291617BIVANDM102544CM10425457950102101102101061100512261716171619122WTHEREFORETHENEUTRALBASEWIDTHISM904010254410364512221BWWWWBUSINGEQ13ACM105432102106590311025905017292EENNEPPKTQVDIKTQVNONEBEB4INTHEEMITTERREGION1862510510659CM1072101052SCM52182938EOEENLDINTHEBASEREGION3546561310210659MC1021040SCM401729237DINOPPPPNNPDLDTINTHECOLLECTORREGION1093121010659CM107241010115SCM1153162936COCCNLDTHECURRENTCOMPONENTSAREGIVENBYEQS20,21,22,AND230A103196107241010312911510201061A1010411107210625185210201061A101596A101596109040613465401020106114332197025905032195502590504219CPEPBBCNENEPCPEPIIIIEIIIEI5ATHEEMITTER,COLLECTOR,ANDBASECURRENTSAREGIVENBYA101041A101596A101606755CNBBENBCNCPCENEPEIIIIIIIIIIBWECANOBTAINTHEEMITTEREFFICIENCYANDTHEBASETRANSPORTFACTOR9938010606110596155EEPIIG110596110596155EPCPTIIAHENCE,THECOMMONBASEANDCOMMONEMITTERCURRENTGAINSARE31601993800000AABGAAT36CTOIMPROVEG,THEEMITTERHASTOBEDOPEDMUCHHEAVIERTHANTHEBASETOIMPROVETA,WECANMAKETHEBASEWIDTHNARROWER6WECANSKETCH0NNPXPCURVESBYUSINGACOMPUTERPROGRAM0002040608100002040608102012510W/LPISLARGERTHAN1500VM100MWFORAREVERSEBLOCKVOLTAGEOF120V,WECANCHOOSEAWIDTHSUCHTHATPUNCHTHROUGHOCCURS,IE,22SDPTWQNVTHUS,CM1096323DPTSQNVWWHENSWITCHINGOCCURS,121AATHATIS,60401LN5001JJWLPA5111063910255060LN440JJ49THEREFORE,250CMA1025254JJCM44410252101AREA253JIS28INTHE2NP2N1TRANSISTOR,THEBASEDRIVECURRENTREQUIREDTOMAINTAINCURRENTCONDUCTIONISKII121AINADDITION,THEBASEDRIVECURRENTAVAILABLETOTHE2NP2N1TRANSISTORWITHAREVERSEGATECURRENTISGAIII12ATHEREFORE,WHENUSEAREVERSEGATECURRENT,THECONDITIONTOOBTAINTURNOFFOFTHETHYRISTORISGIVENBY12IINOTETHATIFWEDEFINETHERATIOOFIATOIGASTURNOFFGAIN,THENTHEMAXIMUMTURNOFFGAINMAXBIS1212MAXA