Semiconductor Device Modeling and Characterization EE5342, Lecture 9-Spring 2002

1. Semiconductor Device Modeling and CharacterizationEE5342, Lecture 9-Spring 2002 Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/

2. Diode Switching • Consider the charging and discharging of a Pn diode • (Na > Nd) • Wd << Lp • For t < 0, apply the Thevenin pair VF and RF, so that in steady state • IF = (VF - Va)/RF, VF >> Va , so current source • For t > 0, apply VR and RR • IR = (VR + Va)/RR, VR >> Va, so current source

3. Diode switching(cont.) VF,VR >> Va F: t < 0 Sw RF R: t > 0 VF + RR D VR +

4. Diode chargefor t < 0 pn pno x xn xnc

5. Diode charge fort >>> 0 (long times) pn pno x xn xnc

6. Equationsummary

7. Snapshot for tbarely > 0 pn Total charge removed, Qdis=IRt pno x xn xnc

8. I(t) for diodeswitching ID IF ts ts+trr t - 0.1 IR -IR

9. Band model review (approx. to scale) metal n-type s/c p-type s/c Eo Eo Eo qcs ~ 4+V qcs ~ 4+V qfm ~ 4+V qfs,n qfs,p Ec Ec EFm EFn EFi EFi EFp Ev Ev

10. No disc in Eo Ex=0 in metal ==> Eoflat fBn=fm- cs = elec mtl to s/c barr Vbi=fBn-fn= fm-fs elect s/c to mtl barr Ideal metal to n-typebarrier diode (fm>fs,Va=0) metal n-type s/c Eo qcs qfm qVbi qfs,n qfBn Ec EFm EFn EFi Depl reg Ev qf’n

11. Ideal m to n s/c barr diode depletion width Ex r xd qNd x Q’d = qNdxd x xd -Em d (Sheet of neg chg on mtl)= -Q’d

12. Barrier transistion region, d Interface states above fo acc, p neutrl below fo dnr, n neutrl Ditd-> oo, qfBn=Eg- fo Fermi level “pinned” Ditd-> 0, qfBn=fm - c Goes to “ideal” case Real Schottkyband structure*

13. Fig 8.4* (a) Image charge and electric field lines at a metal-diel intf (b) Distortion of the potential barrier due to image forces with E=0 and (c) const E field

14. qVa = Efn - Efm Barrier for electrons from sc to m reduced toq(Vbi-Va) qfBn the same DR decr Ideal metal to n-typeSchottky (Va>0) metal n-type s/c Eo qcs qfm q(Vbi-Va) qfs,n qfBn Ec EFm EFn EFi Ev Depl reg qf’n

15. Ideal m to n s/c Schottky diode curr

16. D Diode General Form D<name> <(+) node> <(-) node> <model name> [area value] Examples DCLAMP 14 0 DMODD13 15 17 SWITCH 1.5 Model Form .MODEL <model name> 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) *$

17. Diode Model Parameters • Model Parameters (see .MODEL statement) • Description Unit Default • IS Saturation current amp 1E-14 • N Emission coefficient 1 • ISR Recombination current parameter amp 0 • NR Emission coefficient for ISR 1 • IKF High-injection “knee” current amp infinite • BV Reverse breakdown “knee” voltage volt infinite • IBV Reverse breakdown “knee” current amp 1E-10 • NBV Reverse breakdown ideality factor 1 • RS Parasitic resistance ohm 0 • TT Transit time sec 0 • CJO Zero-bias p-n capacitance farad 0 • VJ p-n potential volt 1 • M p-n grading coefficient 0.5 • FC Forward-bias depletion cap. coef, 0.5 • EG Bandgap voltage (barrier height) eV 1.11

18. Diode Model Parameters • Model Parameters (see .MODEL statement) • Description Unit Default • XTI IS temperature exponent 3 • TIKF IKF temperature coefficient (linear) °C-1 0 • TBV1 BV temperature coefficient (linear) °C-1 0 • TBV2 BV temperature coefficient (quadratic) °C-2 0 • TRS1 RS temperature coefficient (linear) °C-1 0 • TRS2 RS temperature coefficient (quadratic) °C-2 0 • T_MEASURED Measured temperature °C • T_ABS Absolute temperature °C • T_REL_GLOBAL Rel. to curr. Temp. °C • T_REL_LOCAL Relative to AKO model temperature °C • For information on T_MEASURED, T_ABS, T_REL_GLOBAL, and T_REL_LOCAL, see the .MODEL statement.

19. The diode is modeled as an ohmic resistance (RS/area) in series with an intrinsic diode. <(+) node> is the anode and <(-) node> 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 onlyVt = k·T/q (thermal voltage)k = Boltzmann’s constantq = electron charge T = analysis temperature (°K) Tnom = nom. temp. (set with TNOM option)

20. SPICE DiodeModel • Dinj • N~1, rd~N*Vt/iD • rd*Cd = TT = • Cdepl given by CJO, VJ and M • Drec • N~2, rd~N*Vt/iD • rd*Cd = ? • Cdepl =? t

21. DC Current Id = area(Ifwd - Irev)Ifwd = forward current = InrmKinj + IrecKgenInrm = normal current = IS(exp (Vd/(NVt))-1) Kinj = high-injection factor For: IKF > 0, Kinj = (IKF/(IKF+Inrm))1/2 otherwise, Kinj = 1 Irec = rec. cur. = ISR(exp (Vd/(NR·Vt))- 1) Kgen = generation factor = ((1-Vd/VJ)2+0.005)M/2Irev = reverse current = Irevhigh + IrevlowIrevhigh = IBVexp[-(Vd+BV)/(NBV·Vt)]Irevlow = IBVLexp[-(Vd+BV)/(NBVL·Vt)}

22. Vext-Va=iD*Rs low level injection ln iD ln(IKF) Effect ofRs ln[(IS*IKF) 1/2] Effect of high level injection ln(ISR) Data ln(IS) vD= Vext recomb. current VKF

23. References Semiconductor Device Modeling with SPICE, 2nd ed., by Massobrio and Antognetti, McGraw Hill, NY, 1993. MicroSim OnLine Manual, MicroSim Corporation, 1996.