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Semiconductor Device Modeling and Characterization EE5342, Lecture 19 Spring 2003

Semiconductor Device Modeling and Characterization EE5342, Lecture 19 Spring 2003. Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/. The base current must flow lateral to the wafer surface Assume E & C cur-rents perpendicular.

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Semiconductor Device Modeling and Characterization EE5342, Lecture 19 Spring 2003

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  1. Semiconductor Device Modeling and CharacterizationEE5342, Lecture 19Spring 2003 Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/

  2. 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 coll. base & emitter contact regions reg 1 reg 2 reg 3 reg 4 emitter base collector Distributed resis-tance in a planar BJT

  3. 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 Both sources have same current iB1 = iB. The effective value of the 2-dim. base resistance is Rbb’(iB) = DV/iB = RBBTh  DV  = Simulation of 2-dim. current flow

  4. Analytical solutionfor distributed Rbb • Analytical solution and SPICE simulation both fit RBB = Rbmin + Rbmax/(1 + iB/IRB)aRB

  5. Distributed baseresistance 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 )

  6. Gummel PoonBase 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

  7. Gummel-Poon Staticnpn Circuit Model Intrinsic Transistor C RC IBR B RBB ILC ICC -IEC = {IS/QB}* {exp(vBE/NFVt)-exp(vBC/NRVt)} IBF B’ ILE RE E

  8. 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= {+ [+ (BFIBF/IKF + BRIBR/IKR)]1/2}  (1 - vBC/VAF - vBE/VAR )-1 Gummel Poon npnModel Equations

  9. Reverse Active Operation iE iB vEC vBC 0.2 < vEC < 5.0 0.7 < vBC < 0.9 VAR ParameterExtraction (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

  10. Reverse EarlyData 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)

  11. Reverse EarlyVAR 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)

  12. VAF ParameterExtraction (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

  13. Forward EarlyData 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)

  14. Forward EarlyVAf 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)

  15. iC RC vBC - iB + + RB vBE - vBEx RE BJT CharacterizationForward 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

  16. Sample fg data forparameter 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

  17. Definitions ofNeff 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)]

  18. Forward GummelData Sensitivities a 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)

  19. Region (b) fgData Sensitivities Region b - IS, NF, VAR, RB, RE iC = bFIBF/QB = ISexp(vBE/NFVt)  (1-vBC/VAF-vBE/VAR ){IKF terms}-1

  20. Region (e) fgData Sensitivities Region e - ISE, NE iB = IBF + ILE = (IS/BF)expf(vBE/NFVt) + ISEexpf(vBE/NEVt)

  21. Simple extractionof 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

  22. 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

  23. Region (d) fgData Sensitivities Region d - IS/BF, NF iB = IBF + ILE = (IS/BF)expf(vBE/NFVt) + ISEexpf(vBE/NEVt)

  24. Simple extractionof 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

  25. Region (a) fgData 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 )

  26. Region (c) fgData Sensitivities Region c - IS/BF, NF, RB, RE iB = IBF + ILE = (IS/BF)expf(vBE/NFVt) + ISEexpf(vBE/NEVt)

  27. RC vBCx vBC - iB + + RB vBE - RE iE BJT CharacterizationReverse 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

  28. Sample rg data forparameter 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

  29. Reverse GummelData Sensitivities 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 c vBCx = 0 a d e b iB iE iE(A),iB(A) vs. vBC(V)

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