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Understanding the NPN Gummel-Poon Model for Bipolar Junction Transistors in Semiconductor Devices

This lecture focuses on the NPN Gummel-Poon static model used for characterizing bipolar junction transistors (BJTs), detailing key equations and parameters such as the collector current (IC), base current (IB), thermal voltage (VT), and more. The session explores extraction techniques for parameters including saturation current (IS), injection efficiency (ISE), and current gain (BF), as well as sensitivities of various model regions. Practical extraction methods using measured data and the significance of parameter relationships are also discussed, providing a comprehensive understanding of BJT performance in electronic circuits.

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Understanding the NPN Gummel-Poon Model for Bipolar Junction Transistors in Semiconductor Devices

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  1. Semiconductor Device Modeling and Characterization – EE5342 Lecture 24 – 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. 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)

  5. 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

  6. 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

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

  8. 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

  9. 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 )

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

  11. 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

  12. 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

  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. 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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