L19 March 291 EE5342 – Semiconductor Device Modeling and Characterization Lecture 19 - Spring 2005 Professor Ronald L. Carter

L19 March 292 Project 1 I-V

L19 March 293 Project 1 C-V

L19 March 294 Project 1 Z-parameters

L19 March 295 Project 1 Circuit and Parameters

L19 March 296 Values chosen for SPICE parameters

L19 March 297 The limiting values of Re{Z}, with corner frequency, effective total capacitance and transit time (both raw and adjusted to include rd,inj only).

L19 March 298 Charge components in the BJT From Getreau, Modeling the Bipolar Transistor, Tektronix, Inc.

L19 March 299 Gummel-Poon Static npn Circuit Model C E B B’ I LC I LE I BF I BR I CC - I EC = {IS/Q B }* {exp(v BE /NFV t )- exp(v BC /NRV t )} RCRC RERE R BB Intrinsic Transistor

L19 March 2910 Gummel-Poon Model General Form QXXXXXXX NC NB NE MNAME Netlist Examples Q Q2N3904 IC=0.6, 5.0 Q 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.

L19 March 2911 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 i B ), RC, and RE are also included

L19 March 2912 NAMEPARAMETERUNITDEFAULT IStransport saturation currentA1.0e-16 BFideal maximum forward beta-100 NFforward current emission coef.-1.0 VAFforward Early voltageVinfinite ISEB-E leakage saturation currentA0 NEB-E leakage emission coefficient-1.5 BRideal maximum reverse beta-1 NRreverse current emission coeff.-1 VARreverse Early voltageVinfinite ISCB-C leakage saturation currentA0 NCB-C leakage emission coefficient-2 EGenergy gap (IS dep on T)eV1.11 XTItemperature exponent for IS-3 Gummel-Poon Static Par.

L19 March 2913 Gummel-Poon Static Model Parameters NAMEPARAMETERUNITDEFAULT IKFcorner for forward betaAinfinite high current roll-off IKRcorner for reverse betaAinfinite high current roll-off RBzero bias base resistanceW0 IRBcurrent where base resistanceAinfinite falls halfway to its min value RBMminimum base resistanceWRB at high currents REemitter resistanceW0 RCcollector resistanceW0 TNOM parameter - meas. temperature°C27

L19 March 2914 Gummel Poon npn Model Equations I BF = IS  expf(v BE /NFV t )/BF I LE = ISE  expf(v BE /NEV t ) I BR = IS  expf(v BC /NRV t )/BR I LC = ISC  expf(v BC /NCV t ) Q B = (1 + v BC /VAF + v BE /VAR )  {½ +  ¼ + (BF  IBF/IKF + BR  IBR/IKR)    }

L19 March 2915 Gummel Poon npn Model Equations I BF = IS expf(v BE /NFV t )/BF I LE = ISE expf(v BE /NEV t ) I BR = IS expf(v BC /NRV t )/BR I LC = ISC expf(v BC /NCV t ) I CC - I EC = IS(exp(v BE /NFV t - exp(v BC /NRV t )/Q B Q B = {½ +  ¼ +(BF IBF/IKF + BR IBR/IKR)  1/2  }  (1 - v BC /VAF - v BE /VAR ) -1

L19 March 2916 Gummel Poon Base Resistance If IRB = 0, R BB = R BM +(R B -R BM )/Q B If IRB > 0 R B = R BM + 3(R B -R BM )  (tan(z)-z)/(ztan 2 (z)) [  +  i B /(   IRB)] 1/2 -  (  /   )(i B /IRB) 1/2 z = Regarding (i) R BB and (x) R Th on slide 23, R BB = R bmin + R bmax /(1 + i B /I RB )  RB

L19 March 2917 If IRB = 0, R BB = R BM +(R B -R BM )/Q B If IRB > 0 R B = R BM + 3(R B -R BM )  (tan(z)-z)/(ztan 2 (z)) [  +  i B /(   IRB)] 1/2 -  Gummel Poon Base Resistance (  /   )(i B /IRB) 1/2 z = Regarding (i) R BB and (x) R Th on previous slide, R BB = R bmin + R bmax /(1 + i B /I RB )  RB

L19 March 2918 emitter base collector reg 4reg 3reg 2reg 1 coll. base & emitter contact regions Distributed resis- tance in a planar BJT 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.  v BE diminishes as current flows

L19 March 2919 Simulation of 2- dim. current flow Distributed device is repr. by Q 1, Q 2, … Q n Area of Q is same as the total area of the distributed device. Both devices have the same v CE = VCC Both sources have same current i B1 = i B. The effective value of the 2-dim. base resistance is R bb’ (i B ) =  V/i B = R BBTh =   V 

L19 March 2920 Analytical solution for distributed Rbb Analytical solution and SPICE simulation both fit R BB = R bmin + R bmax /(1 + i B /I RB )  RB

L19 March 2921 Distributed base resistance function Normalized base resis- tance vs. current. (i) R BB /R Bmax, (ii) R BBSPICE /R Bmax, after fitting R BB and R BBSPICE to R BBTh (x) R BBTh /R Bmax. FromAn Accurate Mathematical Model for the Intrinsic Base Resistance of Bipolar Transistors, by Ciubotaru and Carter, Sol.- St.Electr. 41, pp , R BBTh = R BM +  R/(1+i B /I RB )  RB (  R = R B - R BM )

L19 March 2922 References * Modeling the Bipolar Transistor, by Ian Getreau, Tektronix, Inc., (out of print).