EE 5340 Semiconductor Device Theory Lecture 22 – Spring 2011 Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc

Project Discussion – Ideal Diode equations 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*Rs ©rlc L22-12Apr2011

Project Discussion – Ideal Diode Forward Current Equations Id = area·(Ifwd - Irev) Ifwd = forward current = Inrm·Kinj + Irec·Kgen Inrm = normal current = IS·(eVd/(N·Vt)-1) if: IKF > 0 then: Kinj = (IKF/(IKF+Inrm))1/2 else: Kinj = 1 Irec = recombination current = ISR·(eVd/(NR·Vt)-1) ©rlc L22-12Apr2011

SPICE Diode Model t Dinj Drec 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 =? t ©rlc L22-12Apr2011

Derivation Tips ©rlc L22-12Apr2011

Gummel-Poon Static npn Circuit Model B RBB ILC IBR ICC - IEC = IS(exp(vBE/NFVt - exp(vBC/NRVt)/QB B’ ILE IBF RE E ©rlc L22-12Apr2011

Gummel-Poon Static npn Circuit Model Intrinsic Transistor RC B RBB ILC IBR ICC - IEC = {IS/QB}* {exp(vBE/NFVt)-exp(vBC/NRVt)} B’ ILE IBF RE E ©rlc L22-12Apr2011

Gummel Poon npn Model Equations IBF = ISexpf(vBE/NFVt)/BF ILE = ISEexpf(vBE/NEVt) IBR = ISexpf(vBC/NRVt)/BR ILC = ISCexpf(vBC/NCVt) QB = (1 + vBC/VAF + vBE/VAR )  {½ + [¼ + (BFIBF/IKF + BRIBR/IKR)]1/2 } ©rlc L22-12Apr2011

Charge components in the BJT **From Getreau, Modeling the Bipolar Transistor, Tektronix, Inc. ©rlc L22-12Apr2011

Gummel Poon Base Resistance If IRB = 0, RBB = RBM+(RB-RBM)/QB If IRB > 0 RB = RBM + 3(RB-RBM)(tan(z)-z)/(ztan2(z)) [1+144iB/(p2IRB)]1/2-1 z = (24/p2)(iB/IRB)1/2 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 L22-12Apr2011

BJT Characterization Forward Gummel iC RC iB RE RB vBEx vBC vBE + - vBCx= 0 = vBC + iBRB - iCRC vBEx = vBE +iBRB +(iB+iC)RE iB = IBF + ILE = ISexpf(vBE/NFVt)/BF + ISEexpf(vBE/NEVt) iC = bFIBF/QB = ISexpf(vBE/NFVt)/QB ©rlc L22-12Apr2011

Ideal F-G Data iC and iB (A) vs. vBE (V) N = 1  1/slope = 59.5 mV/dec ©rlc L22-12Apr2011

BJT Characterization Reverse Gummel iE RC iB RE RB vBCx vBC vBE + - vBEx= 0 = vBE + iBRB - iERE vBCx = vBC +iBRB +(iB+iE)RC iB = IBR + ILC = ISexpf(vBC/NRVt)/BR + ISCexpf(vBC/NCVt) iE = bRIBR/QB = ISexpf(vBC/NRVt)/QB ©rlc L22-12Apr2011

Ideal R-G Data iE and iB (A) vs. vBE (V) N = 1  1/slope = 59.5 mV/dec ©rlc L22-12Apr2011

Ideal 2-terminal MOS capacitor/diode conducting gate, area = LW Vgate -xox SiO2 y L silicon substrate tsub Vsub x ©rlc L22-12Apr2011

Band models (approx. scale) metal silicon dioxide p-type s/c Eo Eo Eo qcox ~ 0.95 eV qcSi= 4.05eV qfm= 4.1 eV for Al Ec qfs,p Eg,ox ~ 8 eV EFm Ec EFp EFi Ev Ev ©rlc L22-12Apr2011

Flat band condition (approx. scale) SiO2 p-Si q(fm-cox)= 3.15 eV q(cox-cSi)=3.1eV Ec,Ox qffp= 3.95eV EFm Ec Eg,ox~8eV EFi EFp Ev Ev ©rlc L22-12Apr2011

Equivalent circuit for 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 comb C’Ox C’D,extr ©rlc L22-12Apr2011

References * 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, 1986 ©rlc L22-12Apr2011