Semiconductor Device Modeling & Characterization Lecture 18 Professor Ronald L. Carter ronc@uta.edu Spring 2001 L18 March 15

Gummel-Poon Static npn Circuit Model Intrinsic Transistor B RBB ILC IBR ICC - IEC = IS(exp(vBE/NFVt) - exp(vBC/NRVt)/QB B’ ILE IBF RE E L18 March 15

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) ICC - IEC = IS(exp(vBE/NFVt - exp(vBC/NRVt)/QB QB = { + [ + (BFIBF/IKF + BRIBR/IKR)]1/2 }  (1 - vBC/VAF - vBE/VAR )-1 L18 March 15

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 + - L18 March 15

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) L18 March 15

Region (a) rg Data Sensitivities Region a - IKRIS, RB, RC, NR, VAF iE=bRIBR/QB~[ISIKR]1/2exp(vBC/NRVt) (1-vBC/VAF-vBE/VAR ) L18 March 15

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 L18 March 15

Region (c) rg Data Sensitivities Region c - BR, IS, NR, RB, RC iB = IBR + ILC = IS/BRexpf(vBC/NRVt) + ISCexpf(vBC/NCVt) L18 March 15

Region (d) rg Data Sensitivities Region d - BR, IS, NR iB = IBR + ILC = IS/BRexpf(vBC/NRVt) + ISCexpf(vBC/NCVt) L18 March 15

Region (e) rg Data Sensitivities Region e - ISC, NC iB = IBR + ILC = IS/BRexpf(vBC/NRVt) + ISCexpf(vBC/NCVt) L18 March 15

RE-flyback data extraction of RE RE  vCE/iB (from IC-CAP Modeling Reference, p. 6-37) RBM  (vBE - vCE)/iB (adapted by RLC from IC-CAP Modeling Reference, p. 6-39) o.c. Qintr vCE RBB B’ vBE E’ iB RE L18 March 15

Extraction of RE from refly data RE  vCE/iB Slope gives RE  7.1 Ohm Model data assumed RE = 1 Ohm L18 March 15

Extraction of RBM from refly data RBM  (vBE - vCE)/iB Slope gives RBM  108 Ohm Model data assumed RB = RBM = 100 Ohm L18 March 15

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 L18 March 15

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)] L18 March 15

Simple extraction of NF, NE from fg data iB 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 iC data NEeff vs. vBEext L18 March 15

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 L18 March 15

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 L18 March 15