Slide 1Slide 2Law of the junction: “Remember to follow the minority carriers”Law of the junction (cont.)Slide 5Slide 6Ideal Junction TheorySlide 8Slide 9Slide 10Slide 11Minority hole lifetimesMinority electron lifetimesExcess minority carrier distr fctnSlide 15Slide 16Minority carrier currentsSlide 18Slide 19Ideal diode equationIdeal diode equation (cont.)Slide 22Diffnt’l, one-sided diode cond. (cont.)Slide 24Slide 25Cap. of a (1-sided) short diode (cont.)Slide 27General time- constantGeneral time- constant (cont.)General time- constant (cont.)ReferencesEE 5340Semiconductor Device TheoryLecture 15 – Spring 2011Professor Ronald L. [email protected]://www.uta.edu/ronc©rlc L15-10Mar20112Forward Bias Energy Bands 1eppkT/EEexpnptaVV0nnFpFiiequilnon 1/exp 0taVVppFiFniequilnonennkTEEnnEvEcEFixnxnc-xpc-xp0q(Vbi-Va)EFPEFNqVaxImref, EFnImref, EFp©rlc L15-10Mar20113Law of the junction: “Rememberto follow the minority carriers”tbianppnatbinopoponoponotnopot2idatbiVV-Vexpnnpp ,0V when and,VV-expnnpp get to Invert .nnlnVpplnVnNNlnVV©rlc L15-10Mar20114Law of the junction (cont.)dnonapopppnnppopppopnnonnnonaNnn and Npp injection level- low Assume .pn and pn Assume .ppp ,nnn and ,nnn ,ppp So . 0V for nnot' eq.-non to Switched ----©rlc L15-10Mar20115Law of the junction (cont.) taptantatatbitbiaVV2ixppVV2ixnnVVno2iVVponoponVVnopoVV-Vpnennp also ,ennp Junction the of Law theennepnnp have We enn nda epp for So ---©rlc L15-10Mar2011ptapopntanonVV-pononoVV-Vpontbiaponnoxx at ,1VVexpnn sim. xx at ,1VVexppp so ,epp ,pepp giving VV-Vexpppp tbitbia----InjectionConditions6©rlc L15-10Mar2011Ideal JunctionTheoryAssumptions•Ex = 0 in the chg neutral reg. (CNR)•MB statistics are applicable•Neglect gen/rec in depl reg (DR)•Low level injection applies so that dnp < ppo for -xpc < x < -xp, and dpn < nno for xn < x < xnc•Steady State conditions7©rlc L15-10Mar2011Ideal Junction Theory (cont.)ppcnncnpxxx- ,Jq1dtdntn0and , xxx ,Jq1dtdptp0CNR the to Equation Continuity the applying and , 0tntp case, (static) state steady the In--8©rlc L15-10Mar2011Ideal JunctionTheory (cont.) ppcnnp2p2ncnppn2n2ppxnnxxxxx- for ,0Dndxndand ,xxx for ,0Dpdxpd giving dxdpqDJ anddxdnqDJ CNR, the in 0E Since9©rlc L15-10Mar2011Ideal JunctionTheory (cont.) )contacts( ,0xnxp and,1enxnpxp B.C. with.xxx- ,DeCexnxxx ,BeAexpSo .D L and D L DefinepcpncnVVpoppnonnppcLxLxpncnLxLxnpp2pnn2ntannpp10©rlc L15-10Mar20110.11.010.0100.01000.01.E+13 1.E+14 1.E+15 1.E+16 1.E+17 1.E+18 1.E+19 1.E+20Doping Concentration (cm^- 3)Dif usion Length, L (microns)electrons holesDiffusion Length model2imimminN36E5.4N18E7.71sec45L = (Dt)1/2 Diffusion Coeff. is Pierret* model11Minority hole lifetimesMark E. Law, E. Solley, M. Liang, and Dorothea E. Burk, “Self-Consistent Model of Minority-Carrier Lifetime, Diffusion Length, and Mobility, IEEE ELECTRON DEVICE LETTERS, VOL. 12, NO. 8, AUGUST 1991The parameters used in the fit are τo = 10 μs, Nref = 1×1017/cm2, and CA = 1.8×10-31cm6/s.2DAorefDopNCNN1 τττ©rlc L15-10Mar201112Minority electron lifetimesMark E. Law, E. Solley, M. Liang, and Dorothea E. Burk, “Self-Consistent Model of Minority-Carrier Lifetime, Diffusion Length, and Mobility, IEEE ELECTRON DEVICE LETTERS, VOL. 12, NO. 8, AUGUST 1991The parameters used in the fit are τo = 30 μs, Nref = 1×1017/cm2, and CA = 8.3×10-32 cm6/s.2DAorefDonNCNN1 τττ©rlc L15-10Mar201113©rlc L15-10Mar2011Excess minoritycarrier distr fctn 1eLWsinhLxxsinhnxn,xxW ,xxx- for and1eLWsinhLxxsinhpxp,xxW ,xxx FortataVVnpnpcpopppcpppcVVpnpncnonnncnncn14©rlc L15-10Mar2011Forward Bias Energy Bands 1eppkT/EEexpnptaVV0nnFpFiiequilnon 1/exp 0taVVppFiFniequilnonennkTEEnnEvEcEFixnxnc-xpc-xp0q(Vbi-Va)EFPEFNqVaxImref, EFnImref, EFp15©rlc L15-10Mar2011CarrierInjectionxn-xpc0ln(carrier conc)ln Naln Ndln niln ni2/Ndln ni2/Naxnc-xpx~Va/Vt~Va/Vt 1enxntaVVpopp 1epxptaVVnonn16©rlc L15-10Mar2011Minority carriercurrents 1eLWsinhLxxcoshLNDqnxxx- for ,qDxJ1eLWsinhLxxcoshLNDqnxxx for ,qDxJtaptanVVnpnpcnan2ippcdxndnnVVpnpncpdp2incndxpdpp17©rlc L15-10Mar2011Evaluating thediode current p/nn/pp/nd/ap/n2isp/snspsnsVVspnnpLWcothLNDqnJsdefinition with JJJ where1eJxJxJJthen DR, in gen/rec no gminAssuta18©rlc L15-10Mar2011Special cases forthe diode currentndp2isppan2isnnppnpdp2ispnan2isnnppnWNDqnJ and ,WNDqnJ LW or ,LW :diode ShortLNDqnJ and ,LNDqnJLW or ,LW :diode Long19©rlc L15-10Mar2011Ideal diodeequation•Assumptions:–low-level injection–Maxwell Boltzman statistics–Depletion approximation–Neglect gen/rec effects in DR–Steady-state solution only•Current dens, Jx = Js expd(Va/Vt)–where expd(x) = [exp(x) -1] 20©rlc L15-10Mar2011Ideal diodeequation (cont.)•Js = Js,p + Js,n = hole curr + ele currJs,p = qni2Dp coth(Wn/Lp)/(NdLp) = qni2Dp/(NdWn), Wn << Lp, “short” = qni2Dp/(NdLp), Wn >> Lp, “long”Js,n = qni2Dn coth(Wp/Ln)/(NaLn) = qni2Dn/(NaWp), Wp << Ln, “short” = qni2Dn/(NaLn), Wp >> Ln, “long”Js,n << Js,p when Na >> Nd21©rlc L15-10Mar2011Diffnt’l, one-sided diode
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