Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/ Semiconductor Device Modeling and Characterization – EE5342 Lecture 23 – Spring 2011 Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/

Linking current E-M circuit model ©rlc L23-01Apr2011

E-M model equations ©rlc L23-01Apr2011

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 L23-01Apr2011

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 L23-01Apr2011

Common emitter current gain, bF ©rlc L23-01Apr2011

Recombination/Gen Currents (FA) ©rlc L23-01Apr2011

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 L23-01Apr2011

Ideal F-G Data iC and iB (A) vs. vBE (V) N = 1  1/slope = 59.5 mV/dec ©rlc L23-01Apr2011

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 L23-01Apr2011

Ideal R-G Data iE and iB (A) vs. vBE (V) N = 1  1/slope = 59.5 mV/dec ©rlc L23-01Apr2011

VAR Parameter Extraction (rEarly) iE = - IEC = (IS/QB)exp(vBC/NRVt), where ICC = 0, and QB-1 = (1-vBC/VAF-vBE/VAR ) {IKR terms }-1, so since vBE = vBC - vEC, VAR ~ iE/[iE/vBE]vBC iE iB vEC vBC 0.2 < vEC < 5.0 0.7 < vBC < 0.9 Reverse Active Operation ©rlc L23-01Apr2011

Reverse Early Data for VAR At a particular data point, an effective VAR value can be calculated VAReff = iE/[iE/vBE]vBC The most accurate is at vBE = 0 (why?) vBC = 0.85 V vBC = 0.75 V iE(A) vs. vEC (V) ©rlc L23-01Apr2011

Reverse Early VAR extraction VAReff = iE/[iE/vBE]vBC VAR was set at 200V for this data When vBE = 0 vBC = 0.75VAR=200.5 vBC = 0.85VAR=200.2 vBC = 0.75 V vBC = 0.85 V VAReff(V) vs. vEC (V) ©rlc L23-01Apr2011

VAF Parameter Extraction (fEarly) Forward Active Operation iC = ICC = (IS/QB)exp(vBE/NFVt), where ICE = 0, and QB-1 = (1-vBC/VAF-vBE/VAR )* {IKF terms }-1, so since vBC = vBE - vCE, VAF ~ iC/[iC/vBC]vBE iC iB vCE vBE 0.2 < vCE < 5.0 0.7 < vBE < 0.9 ©rlc L23-01Apr2011

Forward Early Data for VAF At a particular data point, an effective VAF value can be calculated VAFeff = iC/[iC/vBC]vBE The most accurate is at vBC = 0 (why?) vBE = 0.85 V vBE = 0.75 V iC(A) vs. vCE (V) ©rlc L23-01Apr2011

Forward Early VAf extraction VAFeff = iC/[iC/vBC]vBE VAF was set at 100V for this data When vBC = 0 vBE = 0.75VAF=101.2 vBE = 0.85VAF=101.0 vBE = 0.75 V vBE = 0.85 V VAFeff(V) vs. vCE (V) ©rlc L23-01Apr2011

BJT Characterization Forward Gummel vBCx= 0 = vBC + iBRB - iCRC vBEx = vBE +iBRB +(iB+iC)RE iB = IBF + ILE = ISexp(vBE/NFVt)/BF + ISEexpf(vBE/NEVt) iC = bFIBF/QB = ISexp(vBE/NFVt)  (1-vBC/VAF-vBE/VAR ) {IKF terms }-1 iC RC iB RE RB vBEx vBC vBE + - ©rlc L23-01Apr2011

Sample fg data for parameter extraction IS = 10f NF = 1 BF = 100 Ise = 10E-14 Ne = 2 Ikf = .1m Var = 200 Re = 1 Rb = 100 iC data iB data iC, iB vs. vBEext ©rlc L23-01Apr2011

Definitions of Neff and ISeff In a region where iC or iB is approxi-mately a single exponential term, then iC or iB ~ ISeffexp (vBEext /(NFeffVt) where Neff = {dvBEext/d[ln(i)]}/Vt, and ISeff = exp[ln(i) - vBEext/(NeffVt)] ©rlc L23-01Apr2011

Forward Gummel Data Sensitivities Region a - IKFIS, RB, RE, NF, VAR Region b - IS, NF, VAR, RB, RE Region c - IS/BF, NF, RB, RE Region d - IS/BF, NF Region e - ISE, NE vBCx = 0 c iC b d iB e iC(A),iB(A) vs. vBE(V) ©rlc L23-01Apr2011

Region (b) fg Data Sensitivities Region b - IS, NF, VAR, RB, RE iC = bFIBF/QB = ISexp(vBE/NFVt)  (1-vBC/VAF-vBE/VAR ){IKF terms }-1 ©rlc L23-01Apr2011

Region (e) fg Data Sensitivities Region e - ISE, NE iB = IBF + ILE = (IS/BF)expf(vBE/NFVt) + ISEexpf(vBE/NEVt) ©rlc L23-01Apr2011

Simple extraction of IS, ISE from data Data set used IS = 10f ISE = 10E-14 Flat ISeff for iC data = 9.99E-15 for 0.230 < vD < 0.255 Max ISeff value for iB data is 8.94E-14 for vD = 0.180 iC data iB data ISeff vs. vBEext ©rlc L23-01Apr2011

Simple extraction of NF, NE from fg data Data set used NF=1 NE=2 Flat Neff region from iC data = 1.00 for 0.195 < vD < 0.390 Max Neff value from iB data is 1.881 for 0.180 < vD < 0.181 iB data iC data NEeff vs. vBEext ©rlc L23-01Apr2011

Region (d) fg Data Sensitivities Region d - IS/BF, NF iB = IBF + ILE = (IS/BF)expf(vBE/NFVt) + ISEexpf(vBE/NEVt) ©rlc L23-01Apr2011

Simple extraction of BF from data Data set used BF = 100 Extraction gives max iC/iB = 92 for 0.50 V < vD < 0.51 V 2.42A < iD < 3.53A Minimum value of Neff =1 for slightly lower vD and iD iC/iB vs. iC ©rlc L23-01Apr2011

References 1 OrCAD PSpice A/D Manual, Version 9.1, November, 1999, OrCAD, Inc. 2 Semiconductor Device Modeling with SPICE, 2nd ed., by Massobrio and Antognetti, McGraw Hill, NY, 1993. * Semiconductor Physics & Devices, by Donald A. Neamen, Irwin, Chicago, 1997. ** Modeling the Bipolar Transistor, by Ian Getreau, Tektronix, Inc., (out of print). ©rlc L23-01Apr2011