Professor Ronald L. Carter

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Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/ Semiconductor Device Modeling and Characterization – EE5342 Lecture 22 – Spring 2011 Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/

The npn Gummel-Poon Static Model RC ICC - IEC = IS(exp(vBE/NFVt - exp(vBC/NRVt)/QB B RBB ILC IBR B’ ILE IBF RE E ©rlc L22-30Mar2011

Gummel Poon npn Model Equations 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 } ©rlc L22-30Mar2011

E-M model equations ©rlc L22-30Mar2011

Common emitter current gain, bF ©rlc L22-30Mar2011

Recombination/Gen Currents (FA) ©rlc L22-30Mar2011

npn Base-width mod. (Early Effect) Fig 9.15* ©rlc L22-30Mar2011

Base-width modulation (Early Effect, cont.) Fig 9.16* ©rlc L22-30Mar2011

Charge components in the BJT **From Getreau, Modeling the Bipolar Transistor, Tektronix, Inc. ©rlc L22-30Mar2011

Gummel-Poon Static npn Circuit Model Intrinsic Transistor RC B RBB ILC IBR ICC - IEC = {IS/QB}* {exp(vBE/NFVt)-exp(vBC/NRVt)} B’ ILE IBF RE E ©rlc L22-30Mar2011

Gummel-Poon Model General Form QXXXXXXX NC NB NE <NS> MNAME <AREA> <OFF> <IC=VBE, VCE> <TEMP=T> Netlist Examples Q5 11 26 4 Q2N3904 IC=0.6, 5.0 Q3 5 2 6 9 QNPN .67 NC, NB and NE are the collector, base and emitter nodes NS is the optional substrate node; if unspecified, the ground is used. MNAME is the model name, AREA is the area factor, and TEMP is the temperature at which this device operates, and overrides the specification in the Analog Options dialog. ©rlc L22-30Mar2011

Gummel-Poon Static Model Gummel Poon Model Parameters (NPN/PNP) Adaptation of the integral charge control model of Gummel and Poon. Extends the original model to include effects at high bias levels. Simplifies to Ebers-Moll model when certain parameters not specified. Defined by parameters IS, BF, NF, ISE, IKF, NE determine forward characteristics IS, BR, NR, ISC, IKR, NC determine reverse characteristics VAF and VAR determine output conductance for for and rev RB(depends on iB), RC, and RE are also included ©rlc L22-30Mar2011

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 coeff. - 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 ©rlc L22-30Mar2011

Gummel-Poon Static Model Parameters NAME PARAMETER UNIT DEFAULT IKF corner for forward beta A infinite high current roll-off IKR corner for reverse beta A infinite 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 ©rlc L22-30Mar2011

Gummel Poon npn Model Equations 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 } ©rlc L22-30Mar2011

Gummel Poon npn Model Equations 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 +(BF IBF/IKF + BR IBR/IKR)]1/2 } (1 - vBC/VAF - vBE/VAR )-1 ©rlc L22-30Mar2011

Gummel Poon Base 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 23, RBB = Rbmin + Rbmax/(1 + iB/IRB)aRB ©rlc L22-30Mar2011

Gummel Poon Base 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 ©rlc L22-30Mar2011

Making a diode from the GP BJT model C RC ICC - IEC = IS(exp(vBE/NFVt - exp(vBC/NRVt)/QB B RBB ILC IBR B’ ILE IBF RE E ©rlc L22-30Mar2011

Making a complete diode with G-P BJT RB = RC = 0 Set RE to the desired RS value Set ILE and NE to ISR and NR so this is the rec. current Set BR=BF>>1, ~1e8 so IBR, IBF are neglibigle Set ISC = 0 so ILC is = 0 Set IS to IS for diode so ICC-IEC is the injection curr. Set VAR = VAF = 0 IKF gives the desired high level injection, set IKR = 0 ©rlc L22-30Mar2011

BJT Characterization Forward Gummel iC RC iB RE RB vBEx vBC vBE + - 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 ©rlc L22-30Mar2011

Ideal F-G Data iC and iB (A) vs. vBE (V) N = 1  1/slope = 59.5 mV/dec ©rlc L22-30Mar2011

BJT Characterization Reverse Gummel iE RC iB RE RB vBCx vBC vBE + - 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 ©rlc L22-30Mar2011

Ideal R-G Data iE and iB (A) vs. vBE (V) N = 1  1/slope = 59.5 mV/dec ©rlc L22-30Mar2011

Distributed resis- tance in a planar BJT emitter base collector reg 4 reg 3 reg 2 reg 1 coll. base & emitter contact regions 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 ©rlc L22-30Mar2011

Simulation of 2- dim. current flow =  DV  Both sources have same current iB1 = iB. The effective value of the 2-dim. base resistance is Rbb’(iB) = DV/iB = RBBTh 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 ©rlc L22-30Mar2011

Analytical solution for distributed Rbb Analytical solution and SPICE simulation both fit RBB = Rbmin + Rbmax/(1 + iB/IRB)aRB ©rlc L22-30Mar2011

Distributed base resistance 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 ) ©rlc L22-30Mar2011

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). ©rlc L22-30Mar2011