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Semiconductor Device Modeling and Characterization – EE5342 Lecture 25 – Spring 2011

Semiconductor Device Modeling and Characterization – EE5342 Lecture 25 – Spring 2011. Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/. The npn Gummel-Poon Static Model. C. R C. I CC - I EC = IS ( exp(v BE /NFV t - exp(v BC /NRV t )/Q B. I BR. B. R BB. I LC.

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Semiconductor Device Modeling and Characterization – EE5342 Lecture 25 – Spring 2011

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  1. Semiconductor Device Modeling and Characterization – EE5342 Lecture 25 – Spring 2011 Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/

  2. The npn Gummel-Poon Static Model C RC ICC -IEC = IS(exp(vBE/NFVt - exp(vBC/NRVt)/QB IBR B RBB ILC 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) QB = (1 + vBC/VAF + vBE/VAR ) {½ + [¼ + (BFIBF/IKF + BRIBR/IKR)]1/2 } Gummel Poon npnModel Equations

  4. 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

  5. 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

  6. 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)

  7. 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

  8. 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 )

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

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

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

  12. 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

  13. 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

  14. 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

  15. Forward ActiveHybrid-pi Circuit model Fig 9.33*

  16. 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

  17. RB and RE from FG data

  18. 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

  19. h11_vs_ib

  20. h11_vs_frequency

  21. h11_vs_1/ib

  22. 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).

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