Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/ Semiconductor Device Modeling and Characterization – EE5342 Lecture 24 – 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 L24-04Apr2011

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 L24-04Apr2011

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 L24-04Apr2011

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 L24-04Apr2011

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 L24-04Apr2011

Region (d) fg Data Sensitivities Region d - IS/BF, NF iB = IBF + ILE = (IS/BF)expf(vBE/NFVt) + ISEexpf(vBE/NEVt) ©rlc L24-04Apr2011

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 L24-04Apr2011

Region (a) fg Data Sensitivities Region a - IKFIS, RB, RE, NF, VAR iC = bFIBF/QB = ISexp(vBE/NFVt)  (1-vBC/VAF-vBE/VAR ){IKF terms }-1 If iC > IKF, then iC ~ [IS*IKF]1/2 exp(vBE/2NFVt)  (1-vBC/VAF-vBE/VAR ) ©rlc L24-04Apr2011

Region (c) fg Data Sensitivities Region c - IS/BF, NF, RB, RE iB = IBF + ILE = (IS/BF)expf(vBE/NFVt) + ISEexpf(vBE/NEVt) ©rlc L24-04Apr2011

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 L24-04Apr2011

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 L24-04Apr2011

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 L24-04Apr2011

Region (b) rg Data Sensitivities Region b - IS, NR, VAF, RB, RC iE = bRIBR/QB = ISexp(vBC/NRVt) (1-vBC/VAF-vBE/VAR ){IKR terms }-1 ©rlc L24-04Apr2011

Region (a) rg Data Sensitivities Region a - IKRIS, RB, RC, NR, VAF iE=bRIBR/QB~[ISIKR]1/2exp(vBC/2NRVt) (1-vBC/VAF-vBE/VAR ) ©rlc L24-04Apr2011

Region (e) rg Data Sensitivities Region e - ISC, NC iB = IBR + ILC = IS/BRexpf(vBC/NRVt) + ISCexpf(vBC/NCVt) ©rlc L24-04Apr2011

Region (d) rg Data Sensitivities Region d - BR, IS, NR iB = IBR + ILC = IS/BRexpf(vBC/NRVt) + ISCexpf(vBC/NCVt) ©rlc L24-04Apr2011

Region (c) rg Data Sensitivities Region c - BR, IS, NR, RB, RC iB = IBR + ILC = IS/BRexpf(vBC/NRVt) + ISCexpf(vBC/NCVt) ©rlc L24-04Apr2011

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 L24-04Apr2011