Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/ EE5342 – Semiconductor Device Modeling and Characterization Lecture 20 - Spring 2004 Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/ L20 April 01

Charge components in the BJT From Getreau, Modeling the Bipolar Transistor, Tektronix, Inc. L20 April 01

Gummel-Poon Static npn Circuit Model Intrinsic Transistor C’ B RBB ILC IBR B’ ILE IBF E’ RE E L20 April 01

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 } L20 April 01

Gummel Poon Base Resistance If IRB = 0, RBB = RBM+(RB-RBM)/QB If IRB > 0 RB = RBM + 3(RB-RBM)(tan(z)-z)/(ztan2(z)) Regarding (i) RBB and (x) RTh on previous slide, RBB = Rbmin + Rbmax/(1 + iB/IRB)aRB L20 April 01

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 L20 April 01

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) L20 April 01

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) L20 April 01

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 L20 April 01

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) L20 April 01

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) L20 April 01

BJT Characterization Forward Gummel iC RC iB RE RBB 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)  (1-vBC/VAF-vBE/VAR ) {IKF terms }-1 vBE = vBEx –iBRBB -(iB+iC)RE L20 April 01

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, iB vs. vBEext iC data iB data L20 April 01

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)] L20 April 01

Forward Gummel Data Sensitivities iC(A),iB(A) vs. vBEx(V) vBE = vBEx - iBRB - (iB+iC)RE Region a – (IKFIS)1/2, RB, RE, NF, VAR, (slight RC) Region b - IS, NF, VAR, slight (RB, RE) Region c - IS/BF, NF, RB, RE, (no IKF, slight RC) Region d - IS/BF, NF, (slight RB, RE) Region e - ISE, NE iC vBCx = 0 iB a b c d e L20 April 01

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 In this region expect to be able to estimate Neff ~ N at some point, and ISeff ~ IS at the same point. For vBEx small, VAR effects can be negl. L20 April 01

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 ) L20 April 01

Region (e) fg Data Sensitivities Region e - ISE, NE iB = IBF + ILE = (IS/BF)expf(vBE/NFVt) + ISEexpf(vBE/NEVt) In this region, ILE > IBF, so expect to be able to estimate Neff ~ NE at some point, and ISeff ~ ISE at the same point. There are no VAR effects. L20 April 01

Region (d) fg Data Sensitivities Region d - IS/BF, NF iB = IBF + ILE = (IS/BF)expf(vBE/NFVt) + ISEexpf(vBE/NEVt) In this region, ILE < IBF expect to be able to estimate Neff ~ N at some point, and ISeff ~ IS at the same point. There are no VAR effects but at high vBE, there are RBB and RE effects (RC much less). L20 April 01

Region (c) fg Data Sensitivities Region c - IS/BF, NF, RB, RE, (no IKF), (RC) iB = IBF + ILE = (IS/BF)expf(vBE/NFVt) + ISEexpf(vBE/NEVt) In this region, assuming iB ~ IBF, can take derivatives like ∂iB/∂iB  1 to form functions of RBB and RE for estimation. There are no VAR or IKF effects but at high vBE, there are slight RC effects). L20 April 01

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 L20 April 01

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 L20 April 01

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 L20 April 01

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 L20 April 01

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 + - L20 April 01

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 L20 April 01

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) L20 April 01

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) L20 April 01

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 L20 April 01

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 ) L20 April 01

Region (e) rg Data Sensitivities Region e - ISC, NC iB = IBR + ILC = IS/BRexpf(vBC/NRVt) + ISCexpf(vBC/NCVt) L20 April 01

Region (d) rg Data Sensitivities Region d - BR, IS, NR iB = IBR + ILC = IS/BRexpf(vBC/NRVt) + ISCexpf(vBC/NCVt) L20 April 01

Region (c) rg Data Sensitivities Region c - BR, IS, NR, RB, RC iB = IBR + ILC = IS/BRexpf(vBC/NRVt) + ISCexpf(vBC/NCVt) L20 April 01

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 L20 April 01

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 L20 April 01

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 L20 April 01

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 L20 April 01

Extraction of RE from refly data RE  vCE/iB Slope gives RE  7.1 Ohm Model data assumed RE = 1 Ohm L20 April 01

Extraction of RBM from refly data RBM  (vBE - vCE)/iB Slope gives RBM  108 W Model data assumed RB = RBM = 100 Ohm L20 April 01

BJT Project 2 Project 2 is in the “Example” files under bjt models. Look at the file bjtPr2.mdl in the /examples/model_files/bjt directory on gamma. The assignment is to extract (using only procedures you develop) the static parameters for the npn bjt. L20 April 01

References * Modeling the Bipolar Transistor, by Ian Getreau, Tektronix, Inc., (out of print). ** IC-CAP Modeling Reference - Measurement, Modeling and Simulation of Electronic Components and Circuits, Agilent Technologies, May 2000. L20 April 01