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

2. ©rlc L22- 30Mar2011 2 The npn Gummel-Poon Static Model C E B B’ I LC I LE I BF I BR I CC - I EC = IS(exp(v BE /NFV t - exp(v BC /NRV t )/Q B RCRC RERE R BB

3. ©rlc L22- 30Mar2011 3 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)   }

4. ©rlc L22- 30Mar2011 E-M model equations 4

5. ©rlc L22- 30Mar2011 Common emitter current gain,  F 5

6. ©rlc L22- 30Mar2011 6 Recombination/Gen Currents (FA)

7. ©rlc L22- 30Mar2011 7 npn Base-width mod. (Early Effect) Fig 9.15*

8. ©rlc L22- 30Mar2011 8 Base-width modulation (Early Effect, cont.) Fig 9.16*

9. ©rlc L22- 30Mar2011 9 Charge components in the BJT **From Getreau, Modeling the Bipolar Transistor, Tektronix, Inc.

10. ©rlc L22- 30Mar2011 10 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

11. ©rlc L22- 30Mar2011 11 Gummel-Poon Model General Form QXXXXXXX NC NB NE MNAME 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.

12. ©rlc L22- 30Mar2011 12 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

13. ©rlc L22- 30Mar2011 13 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.

14. ©rlc L22- 30Mar2011 14 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

15. ©rlc L22- 30Mar2011 15 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)    }

16. ©rlc L22- 30Mar2011 16 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

17. ©rlc L22- 30Mar2011 17 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

18. ©rlc L22- 30Mar2011 18 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

19. ©rlc L22- 30Mar2011 19 Making a diode from the GP BJT model C E B B’ I LC I LE I BF I BR I CC - I EC = IS(exp(v BE /NFV t - exp(v BC /NRV t )/Q B RCRC RERE R BB

20. ©rlc L22- 30Mar2011 20 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

21. ©rlc L22- 30Mar2011 21 BJT Characterization Forward Gummel v BCx = 0 = v BC + i B R B - i C R C v BEx = v BE +i B R B +(i B +i C )R E i B = I BF + I LE = IS  expf(v BE /NFV t )/BF + ISE  expf(v BE /NEV t ) i C =  F I BF /Q B = IS  expf (v BE /NFV t )/Q B iCiC RCRC iBiB RERE RBRB v BEx v BC v BE + + - -

22. ©rlc L22- 30Mar2011 22 Ideal F-G Data i C and i B (A) vs. v BE (V) N = 1  1/slope = 59.5 mV/dec N = 2  1/slope = 119 mV/dec

23. ©rlc L22- 30Mar2011 23 BJT Characterization Reverse Gummel iEiE RCRC iBiB RERE RBRB v BCx v BC v BE + + - - v BEx = 0 = v BE + i B R B - i E R E v BCx = v BC +i B R B +(i B +i E )R C i B = I BR + I LC = IS  expf(v BC /NRV t )/BR + ISC  expf(v BC /NCV t ) i E =  R I BR /Q B = IS  expf (v BC /NRV t )/Q B

24. ©rlc L22- 30Mar2011 24 Ideal R-G Data i E and i B (A) vs. v BE (V) N = 1  1/slope = 59.5 mV/dec N = 2  1/slope = 119 mV/dec Ie

25. ©rlc L22- 30Mar2011 25 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

26. ©rlc L22- 30Mar2011 26 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 

27. ©rlc L22- 30Mar2011 27 Analytical solution for distributed Rbb Analytical solution and SPICE simulation both fit R BB = R bmin + R bmax /(1 + i B /I RB )  RB

28. ©rlc L22- 30Mar2011 28 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. 655-658, 1997. R BBTh = R BM +  R/(1+i B /I RB )  RB (  R = R B - R BM )

29. ©rlc L22- 30Mar2011 29 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).