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Semiconductor Device Modeling and Characterization EE5342, Lecture 20 Spring 2003

This lecture notes cover the Gummel-Poon static NPN circuit model, which is crucial for semiconductor device modeling and characterization. The content details intrinsic transistor equations, including collector current (IC), base current (IB), and emitter current (IE) calculations. It discusses parameter extraction methods, such as IS, NR, and VAF sensitivity analysis based on reverse Gummel data. The notes provide example data sets for practical understanding, allowing students to grasp the model's application in evaluating transistor performance through empirical data.

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Semiconductor Device Modeling and Characterization EE5342, Lecture 20 Spring 2003

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  1. Semiconductor Device Modeling and CharacterizationEE5342, Lecture 20Spring 2003 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= {+ [+ (BFIBF/IKF + BRIBR/IKR)]1/2}  (1 - vBC/VAF - vBE/VAR )-1 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. Definitions ofNeff and ISeff • In a region where iC or iB is approxi-mately a single exponential term, then iE or iB ~ ISeffexp (vBCext /(NReffVt) where Neff={dvBCext/d[ln(i)]}/Vt, and ISeff = exp[ln(i) - vBCext/(NeffVt)]

  7. 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)

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

  9. 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

  10. 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

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

  12. 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

  13. 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

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

  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. 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

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

  18. 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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