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EE 5340 Semiconductor Device Theory Lecture 22 – Spring 2011

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, J s expd(V a /( h V t )) ideality factor, h Recombination, J s,rec exp(V a /(2 h V t ))

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EE 5340 Semiconductor Device Theory Lecture 22 – Spring 2011

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

  2. 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

  3. 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)

  4. SPICE DiodeModel • 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 =? t

  5. Derivation Tips

  6. Gummel-Poon Staticnpn Circuit Model C RC IBR B RBB ILC ICC -IEC = IS(exp(vBE/NFVt - exp(vBC/NRVt)/QB B’ IBF ILE RE E

  7. Gummel-Poon Staticnpn Circuit Model Intrinsic Transistor C RC IBR B RBB ILC ICC -IEC = {IS/QB}* {exp(vBE/NFVt)-exp(vBC/NRVt)} IBF B’ ILE RE E

  8. 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} Gummel Poon npnModel Equations

  9. Charge componentsin the BJT **From Getreau, Modeling the Bipolar Transistor, Tektronix, Inc.

  10. Gummel PoonBase 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

  11. iC RC vBC - iB + + RB vBE - vBEx RE BJT CharacterizationForward Gummel 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

  12. iC and iB(A) vs. vBE (V) N = 1  1/slope = 59.5 mV/dec N = 2  1/slope = 119 mV/dec Ideal F-G Data

  13. RC vBCx vBC - iB + + RB vBE - RE iE BJT CharacterizationReverse Gummel 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

  14. iE and iB(A) vs. vBE (V) N = 1  1/slope = 59.5 mV/dec N = 2  1/slope = 119 mV/dec Ideal R-G Data Ie

  15. Ideal 2-terminalMOS capacitor/diode conducting gate, area = LW Vgate -xox SiO2 0 y 0 L silicon substrate tsub Vsub x

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

  17. Flat band condition (approx. scale) Al 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

  18. Equivalent 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 comb C’Ox C’D,extr

  19. 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

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