Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/ EE5342 – Semiconductor Device Modeling and Characterization Lecture 15 March 08, 2010 Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/

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 L15 03/08/10

Gummel-Poon Model General Form QXXXXXXX NC NB NE <NS> MNAME <AREA> <OFF> <IC=VBE, VCE> <TEMP=T> Netlist Examples Q5 11 26 4 Q2N3904 IC=0.6, 5.0 Q3 5 2 6 9 QNPN .67 NC, NB and NE are the collector, base and emitter nodes NS is the optional substrate node; if unspecified, the ground is used. MNAME is the model name, AREA is the area factor, and TEMP is the temperature at which this device operates, and overrides the specification in the Analog Options dialog. L15 03/08/10

Gummel-Poon Static Model Gummel Poon Model Parameters (NPN/PNP) Adaptation of the integral charge control model of Gummel and Poon. Extends the original model to include effects at high bias levels. Simplifies to Ebers-Moll model when certain parameters not specified. Defined by parameters IS, BF, NF, ISE, IKF, NE determine forward characteristics IS, BR, NR, ISC, IKR, NC determine reverse characteristics VAF and VAR determine output conductance for for and rev RB(depends on iB), RC, and RE are also included L15 03/08/10

Gummel-Poon Static Par. NAME PARAMETER UNIT DEFAULT IS transport saturation current A 1.0e-16 BF ideal maximum forward beta - 100 NF forward current emission coef. - 1.0 VAF forward Early voltage V infinite ISE B-E leakage saturation current A 0 NE B-E leakage emission coefficient - 1.5 BR ideal maximum reverse beta - 1 NR reverse current emission coeff. - 1 VAR reverse Early voltage V infinite ISC B-C leakage saturation current A 0 NC B-C leakage emission coefficient - 2 EG energy gap (IS dep on T) eV 1.11 XTI temperature exponent for IS - 3 L15 03/08/10

Gummel-Poon Static Model Parameters NAME PARAMETER UNIT DEFAULT IKF corner for forward beta A infinite high current roll-off IKR corner for reverse beta A infinite RB zero bias base resistance W 0 IRB current where base resistance A infinite falls halfway to its min value RBM minimum base resistance W RB at high currents RE emitter resistance W 0 RC collector resistance W 0 TNOM parameter - meas. temperature °C 27 L15 03/08/10

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 } L15 03/08/10

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 = {½ +[¼ +(BF IBF/IKF + BR IBR/IKR)]1/2 } (1 - vBC/VAF - vBE/VAR )-1 L15 03/08/10

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 slide 23, RBB = Rbmin + Rbmax/(1 + iB/IRB)aRB L15 03/08/10

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 L15 03/08/10

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expf(vBE/NFVt)/BF + ISEexpf(vBE/NEVt) iC = bFIBF/QB = ISexpf(vBE/NFVt)/QB L15 03/08/10

Ideal F-G Data iC and iB (A) vs. vBE (V) N = 1  1/slope = 59.5 mV/dec

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 L15 03/08/10

Ideal R-G Data iE and iB (A) vs. vBE (V) N = 1  1/slope = 59.5 mV/dec

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 L15 03/08/10

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 L15 03/08/10

Analytical solution for distributed Rbb Analytical solution and SPICE simulation both fit RBB = Rbmin + Rbmax/(1 + iB/IRB)aRB L15 03/08/10

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 ) L15 03/08/10

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 L15 03/08/10

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) L15 03/08/10

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) L15 03/08/10

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 L15 03/08/10

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) L15 03/08/10

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) L15 03/08/10

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 + - L15 03/08/10

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 L15 03/08/10

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)] L15 03/08/10

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) L15 03/08/10

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 L15 03/08/10

Region (e) fg Data Sensitivities Region e - ISE, NE iB = IBF + ILE = (IS/BF)expf(vBE/NFVt) + ISEexpf(vBE/NEVt) L15 03/08/10

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 L15 03/08/10

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 L15 03/08/10

Region (d) fg Data Sensitivities Region d - IS/BF, NF iB = IBF + ILE = (IS/BF)expf(vBE/NFVt) + ISEexpf(vBE/NEVt) L15 03/08/10

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 L15 03/08/10

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 ) L15 03/08/10

Region (c) fg Data Sensitivities Region c - IS/BF, NF, RB, RE iB = IBF + ILE = (IS/BF)expf(vBE/NFVt) + ISEexpf(vBE/NEVt) L15 03/08/10

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 + - L15 03/08/10

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 L15 03/08/10

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) L15 03/08/10

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). L15 03/08/10