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Semiconductor Device Modeling and Characterization EE5342, Lecture 16 -Sp 2002

Semiconductor Device Modeling and Characterization EE5342, Lecture 16 -Sp 2002. Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/. Gummel-Poon Static npn Circuit Model. C. RC. Intrinsic Transistor. IBR. B. RBB. ILC. I CC - I EC = IS ( exp(v BE /NFV t ) -

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Semiconductor Device Modeling and Characterization EE5342, Lecture 16 -Sp 2002

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  1. Semiconductor Device Modeling and CharacterizationEE5342, Lecture 16 -Sp 2002 Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/

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

  3. 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

  4. 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

  5. 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)

  6. Forward EarlyVAf 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)

  7. 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

  8. 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)

  9. 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)

  10. 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

  11. 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

  12. 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)]

  13. 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)

  14. 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

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

  16. 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

  17. 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

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

  19. 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

  20. 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

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

  22. 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

  23. 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

  24. Definitions ofNeff 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)]

  25. Reverse GummelData 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 b iB iE iE(A),iB(A) vs. vBC(V)

  26. Region (d) rgData Sensitivities Region d - BR, IS, NR iB = IBR + ILC = IS/BRexpf(vBC/NRVt) + ISCexpf(vBC/NCVt)

  27. Simple extractionof 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

  28. Region (b) rgData Sensitivities Region b - IS, NR, VAF, RB, RC iE = bRIBR/QB = ISexp(vBC/NRVt) (1-vBC/VAF-vBE/VAR ){IKR terms}-1

  29. Region (e) rgData Sensitivities Region e - ISC, NC iB = IBR + ILC = IS/BRexpf(vBC/NRVt) + ISCexpf(vBC/NCVt)

  30. Simple extractionof 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

  31. 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

  32. Region (c) rgData Sensitivities Region c - BR, IS, NR, RB, RC iB = IBR + ILC = IS/BRexpf(vBC/NRVt) + ISCexpf(vBC/NCVt)

  33. Region (a) rgData Sensitivities Region a - IKRIS, RB, RC, NR, VAF iE=bRIBR/QB~[ISIKR]1/2exp(vBC/NRVt) (1-vBC/VAF-vBE/VAR )

  34. RE-flyback dataextraction 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

  35. Extraction of REfrom refly data RE vCE/iB • Slope gives RE  7.1 Ohm • Model data assumed RE = 1 Ohm

  36. Extraction of RBMfrom refly data RBM (vBE - vCE)/iB • Slope gives RBM  108 Ohm • Model data assumed RB = RBM = 100 Ohm

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