Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/ Semiconductor Device Modeling and Characterization EE5342, Lecture 16 -Sp 2002 Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/ L16 07Mar02

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 L16 07Mar02

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 L16 07Mar02

VAF Parameter Extraction (fEarly) 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 Forward Active Operation iC iB vCE vBE 0.2 < vCE < 5.0 0.7 < vBE < 0.9 L16 07Mar02

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) L16 07Mar02

Forward Early VAf extraction VAFeff = iC/[iC/vBC]vBE VAF was set at 100V for this data When vBC = 0 vBE=0.75VAR=101.2 vBE=0.85VAR=101.0 vBE = 0.75 V vBE = 0.85 V VAFeff(V) vs. vCE (V) L16 07Mar02

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 L16 07Mar02

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) L16 07Mar02

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) L16 07Mar02

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exp(vBE/NFVt)/BF + ISEexpf(vBE/NEVt) iC = bFIBF/QB = ISexp(vBE/NFVt)  (1-vBC/VAF-vBE/VAR ) {IKF terms }-1 L16 07Mar02

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 L16 07Mar02

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)] L16 07Mar02

Forward Gummel Data Sensitivities vBCx = 0 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 c iC b d iB e iC(A),iB(A) vs. vBE(V) L16 07Mar02

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 L16 07Mar02

Region (e) fg Data Sensitivities Region e - ISE, NE iB = IBF + ILE = (IS/BF)expf(vBE/NFVt) + ISEexpf(vBE/NEVt) L16 07Mar02

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 L16 07Mar02

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 L16 07Mar02

Region (d) fg Data Sensitivities Region d - IS/BF, NF iB = IBF + ILE = (IS/BF)expf(vBE/NFVt) + ISEexpf(vBE/NEVt) L16 07Mar02

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 L16 07Mar02

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 L16 07Mar02

Region (c) fg Data Sensitivities Region c - IS/BF, NF, RB, RE iB = IBF + ILE = (IS/BF)expf(vBE/NFVt) + ISEexpf(vBE/NEVt) L16 07Mar02

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 + - L16 07Mar02

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 L16 07Mar02

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 (vBCext /(NReffVt) where Neff = {dvBCext/d[ln(i)]}/Vt, and ISeff = exp[ln(i) - vBCext/(NeffVt)] L16 07Mar02

Reverse Gummel Data Sensitivities c vBCx = 0 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 a d e iB b iE iE(A),iB(A) vs. vBC(V) L16 07Mar02

Region (d) rg Data Sensitivities Region d - BR, IS, NR iB = IBR + ILC = IS/BRexpf(vBC/NRVt) + ISCexpf(vBC/NCVt) L16 07Mar02

Simple extraction of BR from data Data set used Br = 2 Extraction gives max iE/iB = 1.7 for 0.48 V < vBC < 0.55V 1.13A < iE < 14.4A Minimum value of Neff =1 for same range iE/iB vs. iE L16 07Mar02

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 L16 07Mar02

Region (e) rg Data Sensitivities Region e - ISC, NC iB = IBR + ILC = IS/BRexpf(vBC/NRVt) + ISCexpf(vBC/NCVt) L16 07Mar02

Simple extraction of IS, ISC from data Data set used IS = 10fA ISC = 10pA Min ISeff for iE data = 9.96E-15 for vBC = 0.200 Max ISeff value for iB data is 8.44E-12 for vBC = 0.200 iB data iE data ISeff vs. vBCext L16 07Mar02

Simple extraction of NR, NC from rg data Data set used Nr = 1 Nc = 2 Flat Neff region from iE data = 1.00 for 0.195 < vBC < 0.375 Max Neff value from iB data is 1.914 for 0.195 < vBC < 0.205 iB data iE data NEeff vs. vBCext L16 07Mar02

Region (c) rg Data Sensitivities Region c - BR, IS, NR, RB, RC iB = IBR + ILC = IS/BRexpf(vBC/NRVt) + ISCexpf(vBC/NCVt) L16 07Mar02

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 ) L16 07Mar02

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 L16 07Mar02

Extraction of RE from refly data RE  vCE/iB Slope gives RE  7.1 Ohm Model data assumed RE = 1 Ohm L16 07Mar02

Extraction of RBM from refly data RBM  (vBE - vCE)/iB Slope gives RBM  108 Ohm Model data assumed RB = RBM = 100 Ohm L16 07Mar02