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Semiconductor Device Modeling and Characterization EE5342, Lecture 15 -Sp 2002

Semiconductor Device Modeling and Characterization EE5342, Lecture 15 -Sp 2002. Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/. Charge components in the BJT. From Getreau, Modeling the Bipolar Transistor , Tektronix, Inc. Gummel-Poon Static npn Circuit Model. C. R C.

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Semiconductor Device Modeling and Characterization EE5342, Lecture 15 -Sp 2002

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  1. Semiconductor Device Modeling and CharacterizationEE5342, Lecture 15 -Sp 2002 Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/

  2. Charge componentsin the BJT From Getreau, Modeling the Bipolar Transistor, Tektronix, Inc.

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

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

  5. Gummel-Poon Static Par. NAME PARAMETER UNIT DEFAULT IS transport saturation current A 1.0e-16 BF ideal maximum forward beta - 100 NF forward current emission coef. - 1.0 VAF forward Early voltage V infinite ISE B-E leakage saturation current A 0 NE B-E leakage emission coefficient - 1.5 BR ideal maximum reverse beta - 1 NR reverse current emission coefficient - 1 VAR reverse Early voltage V infinite ISC B-C leakage saturation current A 0 NC B-C leakage emission coefficient - 2 EG energy gap (IS dep on T) eV 1.11 XTI temperature exponent for IS - 3

  6. Gummel-Poon StaticModel Parameters NAME PARAMETER UNIT DEFAULT IKF corner for forward beta A infinite high current roll-off IKR corner for reverse beta A infinite high current roll-off RB zero bias base resistance W 0 IRB current where base resistance A infinite falls halfway to its min value RBM minimum base resistance W RB at high currents RE emitter resistance W 0 RC collector resistance W 0 TNOM parameter - meas. temperature °C 27

  7. 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 ) { + [ + (BFIBF/IKF + BRIBR/IKR)]1/2} Gummel Poon npnModel Equations

  8. Gummel PoonBase Resistance If IRB = 0, RBB = RBM+(RB-RBM)/QB If IRB > 0 RB = RBM + 3(RB-RBM)(tan(z)-z)/(ztan2(z)) [1+144iB/(p2IRB)]1/2-1 z = (24/p2)(iB/IRB)1/2 Regarding (i) RBB and (x) RTh on slide 22, RB = RBM + DR/(1+iB/IRB)aRB ,DR = RB - RBM

  9. 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expf(vBE/NFVt)/BF + ISEexpf(vBE/NEVt) iC = bFIBF/QB = ISexpf(vBE/NFVt)/QB

  10. iC and iB (A) vs. vBE (V) N = 1  1/slope = 59.5 mV/dec N = 2  1/slope = 119 mV/dec Ideal F-G Data

  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expf(vBC/NRVt)/BR + ISCexpf(vBC/NCVt) iE = bRIBR/QB = ISexpf(vBC/NRVt)/QB

  12. iE and iB (A) vs. vBE (V) N = 1  1/slope = 59.5 mV/dec N = 2  1/slope = 119 mV/dec Ideal R-G Data Ie

  13. The base current must flow lateral to the wafer surface Assume E & C cur-rents perpendicular Each region of the base adds a term of lateral res. vBE diminishes as current flows coll. base & emitter contact regions reg 1 reg 2 reg 3 reg 4 emitter base collector Distributed resis-tance in a planar BJT

  14. Distributed device is repr. by Q1, Q2, … Qn Area of Q is same as the total area of the distributed device. Both devices have the same vCE = VCC Both sources have same current iB1 = iB. The effective value of the 2-dim. base resistance is Rbb’(iB) = DV/iB = RBBTh  DV  = Simulation of 2-dim. current flow

  15. Analytical solutionfor distributed Rbb • Analytical solution and SPICE simulation both fit RBB = Rbmin + Rbmax/(1 + iB/IRB)aRB

  16. Distributed baseresistance function Normalized base resis-tance vs. current. (i) RBB/RBmax, (ii) RBBSPICE/RBmax, after fitting RBB and RBBSPICE to RBBTh (x) RBBTh/RBmax. FromAn Accurate Mathematical Model for the Intrinsic Base Resistance of Bipolar Transistors, by Ciubotaru and Carter, Sol.-St.Electr. 41, pp. 655-658, 1997. RBBTh = RBM + DR/(1+iB/IRB)aRB (DR = RB - RBM )

  17. Gummel PoonBase Resistance If IRB = 0, RBB = RBM+(RB-RBM)/QB If IRB > 0 RB = RBM + 3(RB-RBM)(tan(z)-z)/(ztan2(z)) [1+144iB/(p2IRB)]1/2-1 z = (24/p2)(iB/IRB)1/2 Regarding (i) RBB and (x) RTh on previous slide, RBB = Rbmin + Rbmax/(1 + iB/IRB)aRB

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

  19. 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

  20. 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

  21. 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)

  22. 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

  23. 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)

  24. 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

  25. 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)

  26. 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

  27. 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

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

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

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

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