Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/ Semiconductor Device Modeling and Characterization EE5342, Lecture 19 Spring 2003 Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/ L19 25Mar03

Distributed resis- tance in a planar BJT emitter base collector reg 4 reg 3 reg 2 reg 1 coll. base & emitter contact regions The base current must flow lateral to the wafer surface Assume E & C cur-rents perpendicular Each region of the base adds a term of lateral res.  vBE diminishes as current flows L19 25Mar03

Simulation of 2- dim. current flow =  DV  Both sources have same current iB1 = iB. The effective value of the 2-dim. base resistance is Rbb’(iB) = DV/iB = RBBTh Distributed device is repr. by Q1, Q2, … Qn Area of Q is same as the total area of the distributed device. Both devices have the same vCE = VCC L19 25Mar03

Analytical solution for distributed Rbb Analytical solution and SPICE simulation both fit RBB = Rbmin + Rbmax/(1 + iB/IRB)aRB L19 25Mar03

Distributed base resistance function Normalized base resis-tance vs. current. (i) RBB/RBmax, (ii) RBBSPICE/RBmax, after fitting RBB and RBBSPICE to RBBTh (x) RBBTh/RBmax. FromAn Accurate Mathematical Model for the Intrinsic Base Resistance of Bipolar Transistors, by Ciubotaru and Carter, Sol.-St.Electr. 41, pp. 655-658, 1997. RBBTh = RBM + DR/(1+iB/IRB)aRB (DR = RB - RBM ) L19 25Mar03

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)) [1+144iB/(p2IRB)]1/2-1 z = (24/p2)(iB/IRB)1/2 Regarding (i) RBB and (x) RTh on previous slide, RBB = Rbmin + Rbmax/(1 + iB/IRB)aRB L19 25Mar03

Gummel-Poon Static npn Circuit Model Intrinsic Transistor RC B RBB ILC IBR ICC - IEC = {IS/QB}* {exp(vBE/NFVt)-exp(vBC/NRVt)} B’ ILE IBF RE E L19 25Mar03

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 L19 25Mar03

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 L19 25Mar03

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) L19 25Mar03

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) L19 25Mar03

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 L19 25Mar03

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) L19 25Mar03

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) L19 25Mar03

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 + - L19 25Mar03

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 L19 25Mar03

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)] L19 25Mar03

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) L19 25Mar03

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 L19 25Mar03

Region (e) fg Data Sensitivities Region e - ISE, NE iB = IBF + ILE = (IS/BF)expf(vBE/NFVt) + ISEexpf(vBE/NEVt) L19 25Mar03

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 L19 25Mar03

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 L19 25Mar03

Region (d) fg Data Sensitivities Region d - IS/BF, NF iB = IBF + ILE = (IS/BF)expf(vBE/NFVt) + ISEexpf(vBE/NEVt) L19 25Mar03

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 L19 25Mar03

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 ) L19 25Mar03

Region (c) fg Data Sensitivities Region c - IS/BF, NF, RB, RE iB = IBF + ILE = (IS/BF)expf(vBE/NFVt) + ISEexpf(vBE/NEVt) L19 25Mar03

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 + - L19 25Mar03

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 L19 25Mar03

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) L19 25Mar03