1. EE5342 – Semiconductor Device Modeling and Characterization Lecture 10 Spring 2010 Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/

2. vava vdvd L10 February 172 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: none –Cdepl: none SPICE Diode Model 

3. L10 February 173 ** 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 

4. L10 February 174 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) *$

5. Diode Equations** L10 February 175

6. Diode Equations for DC Current** L10 February 176

7. Diode Equations for Capacitance** L10 February 177

8. Physical basis for FC L10 February 178

9. 9 Diode Model Parameters ** 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

10. L10 February 1710 Diode Model Parameters ** 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.

11. L10 February 1711 v a = V ext ln i a 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 d = i a *R s

12. L10 February 1712 Interpreting a plot of the data for log(iD) vs. Vd In the region where Irec < Inrm < IKF, and iD*RS << Vd. iD ~ Inrm = IS  (exp (Vd/(N  Vt)) - 1) For N = 1 and Vt = 25.852 mV, the slope of the plot of log(iD) vs. Vd is evaluated as {dlog(iD)/dVd} = log (e)/(N  Vt) = 16.799 decades/V = 1decade/59.526mV

13. L10 February 1713 Static Model Eqns. Parameter Extraction In the region where Irec < Inrm < IKF, and iD*RS << Vd. iD ~ Inrm = IS  (exp (Vd/(N  Vt)) - 1) {diD/dVd}/iD = d[ln(iD)]/dVd = 1/(N  Vt) so N ~ {dVd/d[ln(iD)]}/Vt  N eff, and ln(IS) ~ ln(iD) - Vd/(N  Vt)  ln(IS eff ). Note: iD, Vt, etc., are normalized to 1A, 1V, resp.

14. L10 February 1714 Static Model Eqns. Parameter Extraction In the region where Irec > Inrm, and iD*RS << Vd. iD ~ Irec = ISR  (exp (Vd/(NR  Vt)) - 1) {diD/dVd}/iD = d[ln(iD)]/dVd ~ 1/(NR  Vt) so NR ~ {dVd/d[ln(iD)]}/Vt  N eff, & ln(ISR) ~ln(iD) -Vd/(NR  Vt )  ln(ISR eff ). Note: iD, Vt, etc., are normalized to 1A, 1V, resp.

15. L10 February 1715 Static Model Eqns. Parameter Extraction In the region where IKF > Inrm, and iD*RS << Vd. iD ~ [IS  IKF] 1/2  (exp (Vd/(2  N  Vt)) - 1) {diD/dVd}/iD = d[ln(iD)]/dVd ~ (2  N  Vt) -1 so 2N ~ {dVd/d[ln(iD)]}/Vt  2N eff, and ln(iD) -Vd/(NR  Vt)  ½ln(IS  IKF eff ). Note: iD, Vt, etc., are normalized to 1A, 1V, resp.

16. L10 February 1716 Static Model Eqns. Parameter Extraction In the region where iD*RS >> Vd. diD/Vd ~ 1/RS eff dVd/diD  RS eff

17. L10 February 1717 Getting Diode Data for Parameter Extraction The model used.model Dbreak D( Is=1e-13 N=1 Rs=.5 Ikf=5m Isr=.11n Nr=2) Analysis has V1 swept, and IPRINT has V1 swept iD, Vd data in Output

18. L10 February 1718 di D /dV d - Numerical Differentiation

19. L10 February 1719 dln(i D )/dV d - Numerical Differentiation

20. L10 February 1720 Diode Par. Extraction 1/Reff iD ISeff

21. L10 February 1721 Results of Parameter Extraction At Vd = 0.2 V, NReff = 1.97, ISReff = 8.99E-11 A. At Vd = 0.515 V, Neff = 1.01, ISeff = 1.35 E-13 A. At Vd = 0.9 V, RSeff = 0.725 Ohm Compare to.model Dbreak D( Is=1e-13 N=1 Rs=.5 Ikf=5m Isr=.11n Nr=2)

22. L10 February 1722 Hints for RS and NF parameter extraction In the region where v D > VKF. Defining v D = v Dext - i D *RS and I HLI = [IS  IKF] 1/2. i D = I HLI exp (v D /2NV t ) + ISRexp (v D /NRV t ) di D /di D = 1  (i D /2NV t )(dv Dext /di D - RS) + … Thus, for v D > VKF (highest voltages only)  plot i D -1 vs. (dv Dext /di D ) to get a line with  slope = (2NV t ) -1, intercept = - RS/(2NV t )

23. L10 February 1723 Application of RS to lower current data In the region where v D < VKF. We still have v D = v Dext - i D *RS and since. i D = ISexp (v D /NV t ) + ISRexp (v D /NRV t )  Try applying the derivatives for methods described to the variables i D and v D (using RS and v Dext ).  You also might try comparing the N value from the regular N extraction procedure to the value from the previous slide.

24. L10 February 1724 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.

25. L10 February 1725 Reverse bias (V a < 0), carr gen in DR (cont.)

26. L10 February 1726 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

27. L10 February 1727 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

28. L10 February 1728 Reverse bias junction breakdown

29. L10 February 1729 E crit for reverse breakdown (M&K**) Taken from p. 198, M&K** Casey Model for E crit

30. L10 February 1730 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

31. L10 February 1731 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

32. L10 February 1732 Diode Switching Consider the charging and discharging of a Pn diode –(N a > N d ) –W d << Lp –For t < 0, apply the Thevenin pair V F and R F, so that in steady state I F = (V F - V a )/R F, V F >> V a, so current source –For t > 0, apply V R and R R I R = (V R + V a )/R R, V R >> V a, so current source

33. L10 February 1733 Diode switching (cont.) + + VFVF VRVR D R RFRF Sw R: t > 0 F: t < 0 V F,V R >> V a

34. L10 February 1734 Diode charge for t < 0 xnxn x nc x pnpn p no

35. L10 February 1735 Diode charge for t >>> 0 (long times) xnxn x nc x pnpn p no

36. L10 February 1736 Equation summary

37. L10 February 1737 Snapshot for t barely > 0 xnxn x nc x pnpn p no Total charge removed, Q dis =I R t

38. L10 February 1738 I(t) for diode switching IDID t IFIF -I R tsts t s +t rr - 0.1 I R

39. L10 February 1739 References *Semiconductor Device Modeling with SPICE, 2nd ed., by Massobrio and Antognetti, McGraw Hill, NY, 1993. **OrCAD Pspice A/D Reference Guide, Copyright 1999, OrCAD, Inc.