Slide 1Project Discussion – Ideal Diode equationsProject Discussion – Ideal Diode Forward Current EquationsSPICE Diode ModelDerivation TipsGummel-Poon Static npn Circuit ModelGummel-Poon Static npn Circuit ModelGummel Poon npn Model EquationsCharge components in the BJTGummel Poon Base ResistanceBJT Characterization Forward GummelIdeal F-G DataBJT Characterization Reverse GummelIdeal R-G DataIdeal 2-terminal MOS capacitor/diodeBand models (approx. scale)Flat band condition (approx. scale)Equivalent circuit for Flat-BandReferencesEE 5340Semiconductor Device TheoryLecture 22 – Spring 2011Professor Ronald L. [email protected]://www.uta.edu/roncProject Discussion – Ideal Diode equations©rlc L22-12Apr20112•Ideal diode, Jsexpd(Va/(hVt))–ideality factor, h•Recombination, Js,recexp(Va/(2hVt))–appears in parallel with ideal term•High-level injection, (Js*JKF)1/2exp(Va/(2hVt))–SPICE model by modulating ideal Js term•Va = Vext - J*A*Rs = Vext - Idiode*RsProject Discussion – Ideal Diode Forward Current Equations©rlc L22-12Apr20113Id = area·(Ifwd - Irev)Ifwd = forward current = Inrm·Kinj + Irec·KgenInrm = normal current = IS·(eVd/(N·Vt)-1)if: IKF > 0then: Kinj = (IKF/(IKF+Inrm))1/2else: Kinj = 1Irec = recombination current = ISR·(eVd/(NR·Vt)-1)©rlc L22-12Apr20114•Dinj–N~1, rd~N*Vt/iD–rd*Cd = TT =–Cdepl given by CJO, VJ and M•Drec–N~2, rd~N*Vt/iD–rd*Cd = ?–Cdepl =?SPICE DiodeModeltDerivation Tips©rlc L22-12Apr20115  15.273ln1TEMPminDAjAjiddvNkqTT©rlc L22-12Apr20116Gummel-Poon Staticnpn Circuit ModelCEBB’ILCILEIBFIBR ICC - IEC =IS(exp(vBE/NFVt- exp(vBC/NRVt)/QBRCRERBB©rlc L22-12Apr20117Gummel-Poon Staticnpn Circuit ModelCEBB’ILCILEIBFIBRICC - IEC = {IS/QB}* {exp(vBE/NFVt)-exp(vBC/NRVt)}RCRERBBIntrinsicTransistor©rlc L22-12Apr20118Gummel Poon npnModel EquationsIBF = ISexpf(vBE/NFVt)/BFILE = ISEexpf(vBE/NEVt)IBR = ISexpf(vBC/NRVt)/BRILC = ISCexpf(vBC/NCVt)QB = (1 + vBC/VAF + vBE/VAR ) {½ + [¼ + (BFIBF/IKF + BRIBR/IKR)]1/2 }©rlc L22-12Apr20119Charge componentsin the BJT**From Getreau, Modeling the Bipolar Transistor, Tektronix, Inc.©rlc L22-12Apr201110Gummel PoonBase ResistanceIf IRB = 0, RBB = RBM+(RB-RBM)/QBIf IRB > 0RB = RBM + 3(RB-RBM)(tan(z)-z)/(ztan2(z)) [1+144iB/(p2IRB)]1/2-1 (24/p2)(iB/IRB)1/2z =From An Accurate Mathematical Model for the Intrinsic Base Resistance of Bipolar Transistors, by Ciubotaru and Carter, Sol.-St.Electr. 41, pp. 655-658, 1997.RBB = Rbmin + Rbmax/(1 + iB/IRB)aRB©rlc L22-12Apr201111BJT CharacterizationForward GummelvBCx= 0 = vBC + iBRB - iCRCvBEx = vBE +iBRB +(iB+iC)REiB = IBF + ILE = ISexpf(vBE/NFVt)/BF+ ISEexpf(vBE/NEVt)iC = bFIBF/QB =ISexpf(vBE/NFVt)/QB+-iCRCiBRERBvBExvBCvBE++--©rlc L22-12Apr201112Ideal F-G DataiC and iB (A) vs. vBE (V)N = 1  1/slope = 59.5 mV/decN = 2  1/slope = 119 mV/decBJ T I (A) vs. Vbe (V) for the G-P model Forward Gummel configuration (Vbcx=0)1.E-161.E-151.E-141.E-131.E-121.E-111.E-101.E-091.E-081.E-071.E-061.E-051.E-041.E-031.E-020.0 0.2 0.4 0.6 0.8I cI b©rlc L22-12Apr201113BJT CharacterizationReverse Gummel+-iERCiBRERBvBCxvBCvBE++--vBEx= 0 = vBE + iBRB - iEREvBCx = vBC +iBRB +(iB+iE)RCiB = IBR + ILC = ISexpf(vBC/NRVt)/BR+ ISCexpf(vBC/NCVt)iE = bRIBR/QB =ISexpf(vBC/NRVt)/QB©rlc L22-12Apr201114Ideal R-G DataiE and iB (A) vs. vBE (V)N = 1  1/slope = 59.5 mV/decN = 2  1/slope = 119 mV/decBJ T I (A) vs. Vbe (V) for the G-P model Forward Gummel configuration (Vbcx=0)1.E-161.E-151.E-141.E-131.E-121.E-111.E-101.E-091.E-081.E-071.E-061.E-051.E-041.E-031.E-020.0 0.2 0.4 0.6 0.8I cI bIe©rlc L22-12Apr201115Ideal 2-terminalMOS capacitor/diodex-xox0SiO2silicon substrateVgateVsubconducting gate,area = LWtsub0yL©rlc L22-12Apr201116Band models (approx. scale)EoEcEvqcox ~ 0.95 eVmetal silicon dioxide p-type s/cqfm= 4.1 eV for AlEoEFmEFpEoEcEvEFiqfs,pqcSi= 4.05eVEg,ox~ 8 eV©rlc L22-12Apr201117Flat band condition (approx. scale)Ec,OxEvAlSiO2p-Siq(fm-cox)= 3.15 eVEFmEFpEcEvEFiq(cox-cSi)=3.1eVEg,ox~8eVcond band-flat forVVV8.0 VeV8.0EETheneV85.0EEIfsgMSfpfmFBfpfmfpcqffp= 3.95eV©rlc L22-12Apr201118Equivalent circuitfor Flat-Band•Surface effect analogous to the extr Debye length = LD,extr = [eVt/(qNa)]1/2•Debye cap, C’D,extr = eSi/LD,extr•Oxide cap, C’Ox = eOx/xOx•Net C is the series combOxextr,Dtot'C1'C1'C1C’OxC’D,extr©rlc L22-12Apr201119References* Semiconductor Physics & Devices, by Donald A. Neamen, Irwin, Chicago, 1997.**Device Electronics for Integrated Circuits, 2nd ed., by Richard S. Muller and Theodore I. Kamins, John Wiley and Sons, New York,