Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/ Semiconductor Device Modeling and Characterization – EE5342 Lecture 27 – Spring 2011 Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/

The npn Gummel-Poon Static Model RC ICC - IEC = IS(exp(vBE/NFVt - exp(vBC/NRVt)/QB B RBB ILC IBR B’ ILE IBF RE E ©rlc L27-11Apr2011

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 L27-11Apr2011

Static Model Eqns. Parameter Extraction In the region where Irec < Inrm < IKF, and iD*RS << Vd. iD ~ Inrm = IS(exp (Vd/(NVt)) - 1) {diD/dVd}/iD = d[ln(iD)]/dVd = 1/(NVt) so N ~ {dVd/d[ln(iD)]}/Vt  Neff, and ln(IS) ~ ln(iD) - Vd/(NVt)  ln(ISeff). Note: iD, Vt, etc., are normalized to 1A, 1V, resp. ©rlc L27-11Apr2011

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BJT Characterization Reverse Gummel vBEx= 0 = vBE + iBRB - iERE vBCx = vBC +iBRB +(iB+iE)RC iB = IBR + ILC = (IS/BR)expf(vBC/NRVt) + ISCexpf(vBC/NCVt) iE = bRIBR/QB = ISexpf(vBC/NRVt) (1-vBC/VAF-vBE/VAR ) {IKR terms }-1 iE RC iB RE RB vBCx vBC vBE + - ©rlc L27-11Apr2011

Sample rg data for parameter extraction IS=10f Nr=1 Br=2 Isc=10p Nc=2 Ikr=.1m Vaf=100 Rc=5 Rb=100 iB data iE data iE, iB vs. vBCext ©rlc L27-11Apr2011

Reverse Gummel Data Sensitivities c Region a - IKRIS, RB, RC, NR, VAF Region b - IS, NR, VAF, RB, RC Region c - IS/BR, NR, RB, RC Region d - IS/BR, NR Region e - ISC, NC vBCx = 0 a d e iB b iE iE(A),iB(A) vs. vBC(V) ©rlc L27-11Apr2011

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 L27-11Apr2011