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EE5342 – Semiconductor Device Modeling and Characterization Lecture 21 - Spring 2005

EE5342 – Semiconductor Device Modeling and Characterization Lecture 21 - Spring 2005. Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/. Gummel-Poon Static npn Circuit Model. Intrinsic Transistor. C. R C. I BR. B. R BB. I LC. I CC - I EC = {IS/Q B }*

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EE5342 – Semiconductor Device Modeling and Characterization Lecture 21 - Spring 2005

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  1. EE5342 – Semiconductor Device Modeling and CharacterizationLecture 21 - Spring 2005 Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/

  2. 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

  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= {½+[¼+(BFIBF/IKF + BRIBR/IKR)]1/2} (1 - vBC/VAF - vBE/VAR )-1 Gummel Poon npnModel Equations

  4. 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

  5. Reverse EarlyData for VAR • At a particular data point, an effective VAR value can be calculated VAReff = abs{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)

  6. 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)

  7. 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

  8. Forward EarlyData for VAF • At a particular data point, an effective VAF value can be calculated VAFeff = abs{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)

  9. 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)

  10. 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

  11. 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

  12. 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)

  13. 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)

  14. 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

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

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

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

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

  19. 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

  20. 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

  21. 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

  22. Forward ActiveHybrid-pi Circuit model Fig 9.33*

  23. Gummel PoonBase 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

  24. RB and RE from FG data

  25. RB and RE from FG data • In this case, the data were generated with • RB = 98.76 W, compare to 77.4 - 32.3 • RE = 1.432 W, compare to 32.3

  26. h11_vs_ib

  27. h11_vs_frequency

  28. h11_vs_1/ib

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