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[Article](WuliHuaxueXuebao)ActaPhys.-Chim.Sin.,2009,25(3)463-469MarchReceived:September4,2008;Revised:November28,2008;PublishedonWeb:December31,2008.*Correspondingauthor.Email:Chen_c_f@163.com;Tel:+8610-89733200.(50601029、50771104)(106035)鬁EditorialofficeofActaPhysico-ChimicaSinica*((),102249)(Mott-Schottky(M-S)),M-S,、,//np,M-S.,,M-S,、.;Mott-Schottky;;O649;O646AnalysisoftheSpaceChargeCapacitanceofBipolarSemiconductorPassiveFilmsCHENChang-Feng*JIANGRui-JingZHANGGuo-AnZHENGShu-Qi(DepartmentofMaterialsScienceandEngineering,ChinaUniversityofPetroleum(Beijing),Beijing102249,P.R.China)AbstractMeasurementofthespacechargecapacitance(Mott-Schottky(M-S)plot)isanimportantmethodtostudysemiconductorpropertiesofpassivefilms.TheslopeofthelinearpartoftheM-Splotofabipolarsemiconductorpassivefilmshouldchangeinthedepletionregion.Auniformexpressionforthespacechargecapacitanceintheaccumulation,depletionandreversionregionswasestablished.Thespacechargecapacitanceofabipolarsemiconductorpassivefilmisregardedascapacitanceatthepassivefilm/solutioninterfaceandthenp-junctioncapacitanceattheouterlayerfilm/innerlayerfilminterfaceinseries.ThechangeofslopeforthelinearpartoftheM-Splottothebipolarpassivefilmiswellexplainedbythecalculatedresults.AnerrorwouldbeobtainedforthebipolarpassivefilmiftheflatpotentialandcarrierdensityaredetermineddirectlyfromthelinearzoneintheM-Splot.KeyWordsPassivefilm;Mott-Schottkyplot;Bipolar;SpacechargecapacitanceMott-Schottky(M-S),,(,)[1],(spacechargecapaci-tance,Csc)(measuredvoltage,Vm)[1],C-2sc=2eNdεε0A2(Vm-Vfb-kTe)(n)(1)C-2sc=-2eNaεε0A2(Vm-Vfb+kTe)(p)(2),Vfb(flatbandpotential),NdNa(donor)(accepter),ε,ε0,A,k463ActaPhys.-Chim.Sin.,2009Vol.25Boltaman,T,e.M-S,、,.M-S,(Vm)()[1](,,nppn)[1],,Vm＜Vfb,n,[1,2]Csc=e2Ndεε0A22kT2212e-eVskT2212(3)Vs,,Vs=Vm-Vfb.,Vm垌Vfb,n,[1,3]Csc=e2Naεε0A22kT2212e-eVskT2212(4)pn.[4-12],,,,//np[5-12],1,/,,M-S.np、,M-S.,M-S[8-17],.、,,M-S.1Poisson[1]:d2Vdx2=eεε0[Nd-Na+p(x)-n(x)](5),x.,n(x)p(x)Boltzmann[18,19]:n(x)=n0e-eVskT22(6a)p(x)=p0eeVskT22(6b)n0p0,n0=Nd,p0=Na.Gauss[1]:dVsdx=Qscεε0A(7)Qsc.(5):dVsdx=2eεε02212×(Nd-Na)Vs+n0kTee-eVskT+p0kTeeeVskT-(n0+p0)kTe2212(8)Guass(7):Qsc=(2eεε0A2)12×(Nd-Na)Vs+n0kTee-eVskT+p0kTeeeVskT-(n0+p0)kTe2212(9)dQscdV=Csc,Csc=eεε0A222212×1Fig.1SchematicdiagramofthebandenergyandspacechargestructuresofthepassivefilmwithdoublelayerCB:conductionband,VB:valenceband,Ef:Fermienergy,Cnp-n:capacitanceforn-typesemiconductorofthenp-junction,Cnp-p:capacitanceforp-typesemiconductorofthenp-junction,Cp:capacitanceofthep-typesemiconductoratpassivefilm/solutioninterface,Vd:built-inpotentialofthenp-junction,Vnp:appliedpotentialonthenp-junction,Vp:appliedpotentialonthep-typesemiconductoratpassivefilm/solutioninterface,Vfb:flatbandpotential;e:electroniccharge464No.3Nd-Na-n0e-eVskT+p0eeVskT(Nd-Na)Vs+n0kTee-eVskT+p0kTeeeVskT-(n0+p0)kTe2212(10)(10).(i)n,Nd垌Na,n0垌p0,(10)Csc=eNdεε0A2222121-e-eVskTVs+kTee-eVskT-kTe2212(11)Vs＞kTe,e-eVskT垲1,kTee-eVskT,(11)(1).(ii)n,Vs＜0,e-eVskT垌1,kTee-eVskT垌Vs、kTee-eVskT垌kTe,(11)(3).(iii)n,Nd垲Na,n0垲p0,(10)Csc=ep0εε0A222212eeVskT-1-Vs+kTeeeVskT-kTe2212(12)eeVskT垌1,kTeeeVskT垌Vs、kTeeeVskT垌kTe,(12)(4).2(1)、(3)、(4)(10)CscC-2scVs.,、,(10)(3)、(1)、(4).,(10)、.(10)(np).,,3(A),,,.(np)C-2sc-Vm,3(B),,,C-2sc-Vm.2npnpnp,1np,np[11,12,20],npVd,npCnp,(5)-(10)npnCnp-npCnp-pnpVnp,:1Cnp-n=eεε0A2222-12(Nnd-Nna)×Vnp-n+NndkTee-eVnp-nkT2+NnakTeeeVnp-nkT-(Nnd+Nna)kTe212Nnd-Nna-Nnde-eVnp-nkT+NnaeeVnp-nkT22(13)1Cnp-p=eεε0A2222-12(Npd-Npa)×Vnp-p+NpdkTee-eVnp-pkT2+NpakTeeeVnp-pkT-(Npd+Npa)kTe2122nCsc(A)C-2sc(B)VsFig.2Relationshipbetweenthespacechargecapacitancesofn-typesemiconductorelectrodesCsc(A)andC-2sc(B)andspacechargepotentialVscalculationparameters:Nd=2×1023m-3,Na=2×1013m-3,ε=15.6,A=1.13×10-4m2;Nd:donordensity,Na:acceptordensity,ε:relativedielectricconstant,A:electrodesurfacearea465ActaPhys.-Chim.Sin.,2009Vol.25Npd-Npa-Npde-eVnp-pkT+NpaeeVnp-pkT!(14),NndNnanpn;Npd、Npanpp,Vnp-nVnp-pnpnp.,npVnp,Vnp-Vd=Vnp-n-Vnp-p,npVd、VnpVnp-n、Vnp-p:Vnp-n=(Vnp-Vd)Npa(Npa+Nnd)(15)Vnp-p=-(Vnp-Vd)Nnd(Npa+Nnd)(16)(13)-(16),np1/C2np、1/C2np-n、1/C2np-pVnp,4,n1/C2-V.4,npnp,np1/C2np.,npnpnp,,.5np(Cnp)1/C2np-Vnp,53,np,np1/C2np-Vnp.3n()Na(A)()Nd(B)Fig.3Effectofminoritycarriers(acceptor)densityNa(A)andmajoritycarriers(donor)densityNd(B)onthespacechargecapacitancecalculationparameters:(A)Nd=2×1023m-3,(B)Na=2×1013m-3;ε=15.6,A=1.13×10-4m2,Vfb=-0.15V4np(NndNpa)1/C2-VnpFig.4Effectofdifferentconcentrationratiosofthemajoritycarriers(NndandNpa)onbothsidesofthenp-junctionon1/C2-Vnpplots(A)Nnd=Npa,(B)2Nnd=3Npa,(C)5Nnd=Npa;(a)1/C2np,(b)1/C2np-p,(c)1/C2np-n;calculationparameters:Nnd=2×1023m-3,Nna=Npd=1×1013m-3;ε=15.6,A=1.13×10-4m2,Vd=-0.3V;Cnp:capacitanceofthenp-junction,Nnd:donordensityforn-typesemiconductorofthenp-junction,Npa:acceptordensityforp-typesemiconductorofthenp-junction,Nna:acceptordensityforn-typesemiconductorofthenp-junction,Npd:donordensityforp-typesemiconductorofthenp-junction466No.33/1n-p,npCnp/pCp,Vm,、6.6,Vpp,Csc1Csc=1Cp+1Cnp=1Cp+1Cnp-n+1Cnp-p(17),1Cp=eεε0A2222-12(Npd-Npa)×(Vp-Vfb)+NpdkTee-e(Vp