1. L08 07Feb021 EE 4345 - Semiconductor Electronics Design Project Spring 2002 - Lecture 08 Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/

2. L08 07Feb022 Dates for Technology Project Reports 12 Feb - TP1.1 Eyad Fanous Group 12 Feb - TP1.2 Nam Nguyen Group 14 Feb - TP1.3 Viet Tran - The Pentagonal Group 14 Feb - TP1.4 Fares Alnajjar Group 19 Feb - TP1.5 Carlos Garcia Group 19 Feb - TP1.6 Robert Colville Group 21 Feb - TP1.7 Jepsy Colon Group 21 Feb - TP1.8 Preeti Yadav Group 26 Feb - TP1.9 Peter Presby - Group 6 26 Feb - TP1.10 Derek Johnson Group

3. L08 07Feb023 npn BJT currents (F A region, ©RLC ) I C = J C A C I B =-(I E +I C ) J nE J nC I E = -J E A E J RB =J nE -J nC J pE J GC J RE J pC

4. L08 07Feb024 Ebers-Moll (npn injection model) C E B (common-emitter)

5. L08 07Feb025 Effect of carrier rec. in DR (cont.)

6. L08 07Feb026 High level injection effects Law of the junction remains in the same form, [p n n n ] x n =n i 2 exp (V a /V t ), etc. However, now  p n =  n n become >> n no = N d, etc. Consequently, the l.o.t.j. reaches the limiting form  p n  n n = n i 2 exp(V a /V t ) Giving,  p n (x n ) = n i exp(V a /(2V t )), or  n p (-x p ) = n i exp(V a /(2V t )),

7. L08 07Feb027 High level inj effects (cont.)

8. L08 07Feb028 Summary of V a > 0 current density eqns. Ideal diode, J s expd(V a /(  V t )) –ideality factor,  Recombination, J s,rec exp(V a /(2  V t )) –appears in parallel with ideal term High-level injection, (J s *J KF ) 1/2 exp(V a /(2  V t )) –SPICE model by modulating ideal J s term V a = V ext - J*A*R s = V ext - I diode *R s

9. L08 07Feb029 Plot of typical V a > 0 current density eqns. V ext ln J data ln(J KF ) ln(J s ) ln[(J s *J KF ) 1/2 ] Effect of R s V KF ln(J srec ) Effect of high level injection low level injection recomb. current V ext -V d =JAR s

10. L08 07Feb0210 Reverse bias (V a carrier gen in DR V a < 0 gives the net rec rate, U = -n i /  ,   = mean min carr g/r l.t.

11. L08 07Feb0211 Reverse bias (V a < 0), carr gen in DR (cont.)

12. L08 07Feb0212 Reverse bias junction breakdown Avalanche breakdown –Electric field accelerates electrons to sufficient energy to initiate multiplication of impact ionization of valence bonding electrons –field dependence shown on next slide Heavily doped narrow junction will allow tunneling - see Neamen*, p. 274 –Zener breakdown

13. L08 07Feb0213 E crit for reverse breakdown (M&K**) Taken from p. 198, M&K**

14. L08 07Feb0214 Reverse bias junction breakdown Assume -V a = V R >> V bi, so V bi -V a -->V R Since E max ~ 2V R /W = (2qN - V R /(  )) 1/2, and V R = BV when E max = E crit (N - is doping of lightly doped side ~ N eff ) BV =  (E crit ) 2 /(2qN - ) Remember, this is a 1-dim calculation

15. L08 07Feb0215 Junction curvature effect on breakdown The field due to a sphere, R, with charge, Q is E r = Q/(4  r 2 ) for (r > R) V(R) = Q/(4  R), (V at the surface) So, for constant potential, V, the field, E r (R) = V/R (E field at surface increases for smaller spheres) Note: corners of a jctn of depth x j are like 1/8 spheres of radius ~ x j

16. L08 07Feb0216 BV for reverse breakdown (M&K**) Taken from Figure 4.13, p. 198, M&K** Breakdown voltage of a one-sided, plan, silicon step junction showing the effect of junction curvature. 4,5

17. L08 07Feb0217 DDiode General Form D [area value] Examples DCLAMP 14 0 DMOD D13 15 17 SWITCH 1.5 Model Form. MODEL D [model parameters].model D1N4148-X D(Is=2.682n N=1.836 Rs=.5664 Ikf=44.17m Xti=3 Eg=1.11 Cjo=4p M=.3333 Vj=.5 Fc=.5 Isr=1.565n Nr=2 Bv=100 Ibv=10 0u Tt=11.54n) *$

18. L08 07Feb0218 Diode Model Parameters (see.MODEL statement) DescriptionUnit Default ISSaturation currentamp1E-14 NEmission coefficient1 ISRRecombination current parameteramp0 NREmission coefficient for ISR1 IKFHigh-injection “knee” currentampinfinite BVReverse breakdown “knee” voltagevoltinfinite IBVReverse breakdown “knee” currentamp1E-10 NBVReverse breakdown ideality factor1 RSParasitic resistanceohm0 TTTransit timesec0 CJOZero-bias p-n capacitancefarad0 VJp-n potentialvolt1 Mp-n grading coefficient0.5 FCForward-bias depletion cap. coef,0.5 EGBandgap voltage (barrier height)eV1.11

19. L08 07Feb0219 Diode Model Parameters (see.MODEL statement) DescriptionUnit Default XTIIS temperature exponent3 TIKFIKF temperature coefficient (linear)°C -1 0 TBV1BV temperature coefficient (linear)°C -1 0 TBV2BV temperature coefficient (quadratic)°C -2 0 TRS1RS temperature coefficient (linear)°C -1 0 TRS2RS temperature coefficient (quadratic)°C -2 0 T_MEASUREDMeasured temperature°C T_ABSAbsolute temperature°C T_REL_GLOBALRel. to curr. Temp.°C T_REL_LOCALRelative to AKO model temperature °C For information on T_MEASURED, T_ABS, T_REL_GLOBAL, and T_REL_LOCAL, see the.MODEL statement.

20. L08 07Feb0220 The diode is modeled as an ohmic resistance (RS/area) in series with an intrinsic diode. is the anode and is the cathode. Positive current is current flowing from the anode through the diode to the cathode. [area value] scales IS, ISR, IKF,RS, CJO, and IBV, and defaults to 1. IBV and BV are both specified as positive values. In the following equations: Vd= voltage across the intrinsic diode only Vt= k·T/q (thermal voltage) k = Boltzmann’s constant q = electron charge T = analysis temperature (°K) Tnom= nom. temp. (set with TNOM option 

21. L08 07Feb0221 Dinj –key par: IS, N(~1) –rd=N*Vt/iD –rd*Cd = TT = –Cdepl given by CJO, VJ and M –HLI: IKF, VKF Drec –param: ISR, NR(~2) –rd~NR*Vt/iD –rd*Cd = ? –Cdepl =? SPICE Diode Static Model VdVd i D *RS V ext = v D + i D *RS

22. L08 07Feb0222 DC Current I d = area  ( I fwd - I rev) I fwd = forward current = I nrm  Kinj + I rec  Kgen I nrm = normal current = IS  (exp ( Vd/(N  Vt))-1) Kinj = high-injection factor For: IKF > 0, Kinj = (IKF/(IKF+ I nrm)) 1/2 otherwise, Kinj = 1 I rec = rec. cur. = ISR  (exp (Vd/(NR·Vt))- 1) Kgen = generation factor = ((1-Vd/VJ) 2 +0.005) M/2 I rev = reverse current = I rev high + I rev low I rev high = IBV  exp[-(Vd+BV)/(NBV·Vt)] I rev low = IBVL  exp[-(Vd+BV)/(NBVL·Vt)}

23. L08 07Feb0223 vD= V ext ln iD Data ln(IKF) ln(IS) ln[(IS*IKF) 1/2 ] Effect of R s V KF ln(ISR) Effect of high level injection low level injection recomb. current V ext -V a =iD*R s

24. L08 07Feb0224 npn BJT currents (F A region, ©RLC ) I C = J C A C I B =-(I E +I C ) J nE J nC I E = -J E A E J RB =J nE -J nC J pE J GC J RE J pC

25. L08 07Feb0225 Charge components in the BJT From Getreau, Modeling the Bipolar Transistor, Tektronix, Inc.

26. L08 07Feb0226 Gummel-Poon Static npn Circuit 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

27. L08 07Feb0227 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.

28. L08 07Feb0228 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

29. L08 07Feb0229 Gummel-Poon Static Model Parameters nameparameterunitsdefaultarea IStransport saturation currentA1.0e-16* BFideal maximum forward beta-100 NFforward current emission coefficient-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 coefficient-1 VARreverse Early voltageVinfinite ISCB-C leakage saturation currentA0* NCB-C leakage emission coefficient-2 EGenergy gap for temperatureeV1.11 effect on IS XTItemperature exponent for effect on IS-3

30. L08 07Feb0230 Gummel-Poon Static Model Parameters nameparameterunitsdefaultarea 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

31. L08 07Feb0231 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 )  {  +   + (BF  IBF/IKF + BR  IBR/IKR)    }

32. L08 07Feb0232 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 22, R BB = R bmin + R bmax /(1 + i B /I RB )  RB

33. L08 07Feb0233 References Semiconductor Device Modeling with SPICE, 2nd ed., by Massobrio and Antognetti, McGraw Hill, NY, 1993. MicroSim OnLine Manual, MicroSim Corporation, 1996. * Semiconductor Physics & Devices, by Donald A. Neamen, Irwin, Chicago, 1997.