半导体器件模拟及数值分析

1.2.3.4.5.6.1.111.2•Shockley1949•1964H.K.Gummel•1969DPKennedyR.R.O’BrienJFET•1969JWSlotboomDC•CADDETMINIMOS1.1.1.31.1MOSGaAsMESFET1-31-31-21-21.()()1.121CAD2.1.21.321CAD2.1.422CAA2.3132FORTRANCMATLAB333.41•PN••••42••4.43••44•••44••••••••S••5.2.12.22.3εµMaxwellEDHBJρ2.1MaxwellMaxwell)4.1.2(0)3.1.2()2.1.2()1.1.2(=•∇=•∇=∂∂+=×∇∂∂=×∇BDJDJHB-Eρtotaltt(2.1.6)(2.1.5)HBEDµ==2.12.1.1Poisson==•∇)5.1.2()3.1.2(EDDερρε=•∇)(Eϕ−∇=Eρϕε−=∇•∇)(Poisson:)(−+−+−=adNNnpqρ•:,,Poisson:)(2−+−+−−=∇adNNnpqεϕ2.12.1.2)2.1.2(t∂∂+=×∇DJH0)(=∂∂+•∇=×∇•∇tDJH)3.1.2(ρ=•∇D0=∂∂+•∇tρJ:2.12.1.2JJnJp0)(=∂∂−∂∂++•∇tnqtpqpnJJ)(tnqtpq∂∂−•∇−=∂∂+•∇npJJ0=∂∂+•∇tρJ“”“”=-qR2.12.1.2RRqtnRqtp−•∇=∂∂−•∇−=∂∂npJJ112.12.1.3JnJpqµnµpnpφnφp.2.1.3.1pppnnnpqnqφµφµ∇−=∇−=JJ:−=−=)(exp)(expϕφφϕpinikTqnpkTqnn−=−=ipinnpqkTnnqkTlnlnϕφϕφpqDpqnqDnqpppnnn∇=∇+=-EJEJµµE=-∇ϕDn=nqkTµDp=pqkTµ,2.12.1.32.1.3.2(a)(b)2.1.(a)GaAs,(b)Si2.12.1.32.1.3.2Si0.1µmGaAs0.5µm∑−+∇−∇•−=∂∂'kr')},)P(f()',')P({f(ff1tfkkkkkkFkhfh=h/2πhPlanckPk,k’kk’υF2.12.1.32.1.3.2“+”“-”k∫±=kxkkxJdtfqt),,()()2(2),(3π)(1)(kkEk∇=hυE(k)2.12.1.4ρCTQκ(T)])([TTQtTC∇•∇=−∂∂•κρQ=Jn+Jp•E+R•Eg2.12.1.5ScngΓNτσAAiAmA=Ai+AmστNSAgncdtdS+−Γ=)(211ln21RRLAm=LR1R22.12.1.6MaxwellEnk0=2π/λλzβzHelmholtz02022=+∇EEkn)(exp),,(),,,(ztjEEEtzyxzyxβω−=E222/,/ββ−=∂∂−=∂∂zjz,0)(22022=−+∇EEβknT,22222//yxT∂∂+∂∂=∇2.1:ρϕε−=∇•∇)(RqtnRqtp−•∇=∂∂−•∇−=∂∂npJJ11στNSAgncdtdS+−Γ=)(0)(22022=−+∇EEβknT])([TTQtTC∇•∇=−∂∂•κρpqDpqnqDnqpppnnn∇=∇+=-EJEJµµ∑−+∇−∇•−=∂∂'kr')},)P(f()',')P({f(ff1tfkkkkkkFkh∫±=kxkkxJdtfqt),,()()2(2),(3π2.22.2.1,,−=−=)(exp)(expϕφφϕpieniekTqnpkTqnnnie++++=−+−+kTCNNNNNNqVTnnadadiie2lnlnexp)(0201Si:V1=9×10-3VN0=1017cm-3C=0.5Tni(T)Si2.22.2.12.2,Si1016101710181019102010210510152025nie/niND+NA(cm-3)1017cm-3,2.2pppnnnpqnqφµφµ∇−=∇−=JJ−=−=)(exp)(expϕφφϕpieniekTqnpkTqnn−=−=iepiennpqkTnnqkTlnlnϕφϕφ,2.2.1∇+∇=∇−∇+=ieppppiennnnnqkTpqpqDpqnqkTnqnqDnqlnlnµµµµ-EJEJiepiennqkTnqkTlnln∇+=∇−=EEEE,pqDpqnqDnqppppnnnn∇=∇+=-EJEJµµ2.22.2.2:EEd/)(υµ=1.~T-a2.~T3/2/N3.-4.~5.6.:ββγµµ/1))/(1()0/(0EcETT+−=γµ−+=)0/(0))600/exp(8.01(*319.2TTTVmEcαµµµµ)/(1minmaxmin0NrNt+−+=,2.22.2.22.1µmin(cm2/V.s)65.047.7µmax(cm2/V.s)1330.0495.0Nr(cm-3)8.5×10166.3×1016α0.720.76Vm(cm/s)1.1×1079.5×106γ2.422.2β2.02.0T0(K)3003001021031041051060200400600800100012001400Nt=1019cm-3Nt=1018cm-3Nt=1017cm-3Nt=1016cm-3ElectronMobility(cm2/V.s)ElectricField(V/cm)Nt=1015cm-3T=300K2.3300K2.22.2.2(a)(b)2.31000V/cm(a)(b)3003203403603804000200400600800100012001400Nt=1019cm-3Nt=1018cm-3Nt=1017cm-3Nt=1016cm-3ElectronMobility(cm2/V.s)Temperature(K)Nt=1015cm-3E=103V/cm3003203403603804000100200300400500Nt=1019cm-3Nt=1018cm-3Nt=1017cm-3Nt=1016cm-3HoleMobility(cm2/V.s)Temperature(K)Nt=1015cm-3E=103V/cm2.22.2.3SRHShockley-Read-Hall1.SRH)()(112ppnnnnpRnpieSRH+++−=ττn1p1n1=p1=nie1001−+=nnnNNττ1001−+=pppNNττSiτp0=τn0=0.5×10-6sN0n=N0p=5×1016cm-32.22.2.3SRHShockley-Read-Hall2.r3.-cncpSicn=2.8×10-31cm6.s-1cp=9.9×10-32cm6.s-1Rsp=r(np-nie2)RAUG=cnn(np-nie2)+cpp(np-nie2)2.22.2.3R=RSRH+RSP+RAUG+RSUR+RA4.SRHsnsp100~106cm/sδ(y)δ5.GA-RA=GA=αnnυn+αppυp)()(1)(1112yppsnnsnnpRnpieSURδ+++−=qqGppnnAJJαα+=−=mlpnEbAexp)(αα2.32.3.12.32.3.2MOSIpnφφερϕ)(2−=∇II0)(0)(2==•∇−=∇pnJJερϕIII0)()(2==•∇−=∇pnnJqRJερϕIV)()()()()(2pppnnnGRqJGRqJ−−=•∇−=•∇−=∇ερϕ2.32.3.312PN2313233PN34PN3536PN37PN33113.1PNxN(x)=Nd(x)-Na(x)(3.1)zz0~Lz3.1NP0L3.1PNx43123.1)4.3()()3.3(1)2.3(122npNqxRGxJqtpRGxJqtnpn−+−=∂∂−+∂∂−=∂∂−+∂∂=∂∂εϕ)8.3(0)7.3()6.3()5.3(=∂∂∂∂++=∂∂−∂∂−=∂∂−∂∂=xJtEJJJxpqxpqDJxnqxnqDJlpnpppnnnεϕµϕµ)9.3()()(2inipippnnnnpR+++−=ττ5313N(0)+p(0)–n(0)=0(3.10a)N(L)+p(L)–n(L)=0(3.10b)n(0)p(0)=ni2(3.10c)n(L)p(L)=ni2(3.10d)φn(0)=φp(0)=0(3.11a)φn(L)=φp(L)=VA(3.11b)VAPN3.1)12.3(ln)12.3(lnbnpqkTannqkTipin+=−=ϕφϕφ)13.3()(ln)()13.3()0(ln)0(bnLpqkTVLannqkTiAi−==ϕϕ63141.“”3.12.(1)LDiDnqkTL2ε=ε(2)ni(3)Vt(kT/q)(4)3.1(3.2)-(3.8)73143.13.1SixLD3.405×10-3cmtLD2/D04.483×10-4sϕVt0.025875VVAVt0.025875VElVt/LD7.295V/cmnpni1.45×1010cm-3N,Nd,Nani1.45×1010cm-3J,Jn,JpqD0ni/LD1.76×10-8A/cm2G,RD0ni/LD23.234×1013cm-3.s-1Dn,DpD00.025875cm2/sµn,µpD0/Vt1cm2/V.s83143.3.1)17.3()()16.3()15.3(22npNxRGxJtpRGxJtnpn−+−=∂∂−+∂∂−=∂∂−+∂∂=∂∂ϕ)22.3()1()1(1)21.3(0)20.3()19.3()()18.3()(+++−==∂∂∂∂++=∂∂−−=∂∂+∂∂−=∂∂−−=∂∂−∂∂−=pnnpRxJtEJJJxpxpxpJxnxnxnJnplpnppppnnnnττφµϕµφµϕµ(3.15)-(3.22)(3.2)-(3.9)93144.N(0)+p(0)–n(0)=0(3.23a)N(L)+p(L)–n(L)=0(3.23b)n(0)p(0)=1(3.23c)n(L)p(L)=1(3.23d)3.1)23.3()(ln)()23.3()0(ln)0(fLpVLenA−==ϕϕ103211♥♥MOS♥3.2113212f(x)0≤x≤LNN-1∆x=L/(N-1)xl3.2x1x2xl-1xlxl+1xN-1xNx0L∆x∆x∆x∆x3.2(3.24c)∆x∆x2∆xxffdxdfllxxl∆−≈+=1xffdxdfllxxl∆−≈−=1xffdxdfllxxl∆−≈−+=211123213d2f/dx2xl3.221111222//2/12/1xfffxxffxffxdxdfdxdfdxfdlllllllxxxxlll∆+−=∆∆−−∆−≈∆−≈+−−+=−+∆x2x1x2xl-1xlxl+1xN-1xNx0L∆x∆x∆x∆x3.2(3.25)13322PN“”PN3.30≤x≤LN’K=1K=N’N’1N’-1PNnpϕ3.2x=0M-1MM+1M+2x=L1K-1KK+13.3K+2×××××××N’h(M-1)h(M)h’(K)143233.2)26.3(0)26.3(0bRxJaRxJpn=+∂∂=−∂∂3.3)27.3(0)()(')1()(aKRKhMJMJnn=−−−)27.3(0)()(')1()(bKRKhMJMJpp=+−−)27.3()]()()([)1()1()()()