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Semiconductor Device Modeling and Characterization EE5342, Lecture 12 Spring 2003

Semiconductor Device Modeling and Characterization EE5342, Lecture 12 Spring 2003. Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/. SPICE Diode Static Model. V ext = v D + i D *RS. Dinj IS N ~ 1 IKF, VKF, N ~ 1 Drec ISR NR ~ 2. i D *RS. V d.

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Semiconductor Device Modeling and Characterization EE5342, Lecture 12 Spring 2003

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  1. Semiconductor Device Modeling and CharacterizationEE5342, Lecture 12Spring 2003 Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/

  2. SPICE DiodeStatic Model Vext = vD + iD*RS • Dinj • IS • N ~ 1 • IKF, VKF, N ~ 1 • Drec • ISR • NR ~ 2 iD*RS Vd

  3. SPICE Diode DC Model Params.1 PARAMETER definition and units default value IS saturation current amp 1E-14 ISR recombination current parameter amp 0.0 IKF high-injection knee current amp infinite N emission coefficient 1.0 NR emission coefficient for isr 2.0 RS parasitic resistance ohm 0.0EG bandgap voltage (barrier height) eV 1.11 XTI IS temperature exponent 3.0 BV reverse breakdown knee voltage volt infinite IBV reverse breakdown knee current amp 1E-10 NBV reverse breakdown ideality factor 1.0

  4. SPICE Diode DC Model Eqns.1 Id = area·(Ifwd - Irev) Ifwd = forward current = Inrm·Kinj + Irec·Kgen Inrm = normal current = IS·(eVd/(N·Vt)-1) if: IKF > 0 then: Kinj = high-injection factor = (IKF/(IKF+Inrm))^1/2 else: Kinj = 1 Irec = recombination current = ISR·(eVd/(NR·Vt)-1) Kgen = generation factor = ((1-Vd/VJ)^2+0.005)M/2 Irev = reverse current = Irevhigh + Irevlow Irevhigh = IBV·e-(Vd+BV)/(NBV·Vt) Irevlow = IBVL·e-(Vd+BV)/(NBVL·Vt)

  5. ln(I) Plot of SPICE D.C. Va > 0 current equations data Effect of Rs Vext VKF

  6. Static Model Eqns.Parameter Extraction In any region we can approximate the i-V relationship as a single exponential. iD ~ Iseff(exp (Vd/(NeffVt)) - 1) {diD/dVd}/iD = d[ln(iD)]/dVd = 1/(NeffVt) so Neff = {dVd/d[ln(iD)]}/Vt , and ln(ISeff). = ln(iD) - Vd/(NVt). (Note treat iD, Vt, etc., as normalized to 1A, 1V, respectively)

  7. Diode Par.Extraction 1/Reff iD ISeff

  8. Results ofParameter 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)

  9. Hints for RS and NFparameter extraction In the region where vD > VKF. Defining vD = vDext - iD*RS and IHLI = [ISIKF]1/2. iD = IHLIexp (vD/2NVt) + ISRexp (vD/NRVt) diD/diD = 1  (iD/2NVt)(dvDext/diD - RS) + … Thus, for vD > VKF (highest voltages only) • plot iD-1vs. (dvDext/diD) to get a line with • slope = (2NVt)-1, intercept = - RS/(2NVt)

  10. SPICE Diode Capacitance Pars.1 PARAMETER definition and units default value TT transit time sec 0.0 CJO zero-bias p-n capacitance farad 0.0 M p-n grading coefficient 0.5 FC forward-bias depletion capacitance coeff 0.5 VJ p-n potential volt 1.0

  11. SPICE Diode Capacitance Eqns.1 Cd = Ct + area·Cj Ct = transit time capacitance = TT·Gd Gd = DC conductance = area * d (Inrm Kinj + Irec Kgen)/dVd Kinj = high-injection factor Cj = junction capacitance IF: Vd < FC·VJ Cj = CJO*(1-Vd/VJ)^(-M) IF: Vd > FC·VJ Cj = CJO*(1-FC)^(-1-M)·(1-FC·(1+M)+M·Vd/VJ)

  12. Junction Capacitance • A plot of [Cj]-1/Mvs. Vd hasSlope = -[(CJO)1/M/VJ]-1 vertical axis intercept = [CJO]-2 horizontal axis intercept = VJ Cj-1/M CJO-1/M Vd VJ

  13. Junction Width and Debye Length • LD estimates the transition length of a step-junction DR (concentrations Na and Nd with Neff = NaNd/(Na +Nd)). Thus, • For Va=0, & 1E13 <Na,Nd< 1E19 cm-3 13% <d< 28% => DA is OK

  14. Junction CapacitanceAdapted from Figure 1-16 in Text2 Cj = CJO/(1-Vd/VJ)^M Cj = CJO/(1-FC)^(1+M)* (1-FC·(1+M)+M·Vd/VJ) FC*VJ VJ

  15. Junction Capacitance • Let c = Cj/CJO • Calculate c(dVd/dc) = dVd/d[ln(c)] = r • Confirm that a plot of r vs. Vd has slope = -1/m, and intercept = VJ/m

  16. SPICE Diode A.C. Parameters

  17. Small signal diodeZ-parameter

  18. SPICE Diode Temperature Pars.1 PARAMETER definition and units default value XTI IS temperature exponent 3.0 TIKF ikf temperature coefficient (linear) °C -1 0.0 TRS1 rs temperature coefficient (linear) °C -1 0.0 TRS2 rs temperature coefficient (quadratic) °C -2 0.0 TBV1 bv temperature coefficient (linear) °C -1 0.0 TBV2 bv temperature coefficient (quadratic) °C -2 0.0 T_ABS absolute temperature °C T_MEASURED measured temperature °C T_REL_GLOBAL relative to current temperature °C T_REL_LOCAL Relative to AKO model temperature °C

  19. SPICE Diode Temperature Eqs.1 IS(T) / IS =e(T/Tnom-1)·EG/(N·Vt)·(T/Tnom)XTI/N ISR(T) / ISR = e(T/Tnom-1)·EG/(NR·Vt)·(T/Tnom)XTI/NR IKF(T) / IKF = (1 + TIKF·(T-Tnom)) BV(T) = BV·(1 + TBV1·(T-Tnom) + TBV2·(T-Tnom)2) RS(T) = RS·(1 + TRS1·(T-Tnom) + TRS2·(T-Tnom)2) VJ(T) = VJ·T/Tnom - 3·Vt·ln(T/Tnom) - Eg(Tnom)·T/Tnom + Eg(T) Eg(T) = silicon bandgap energy = 1.16 - .000702·T2/(T+1108) CJO(T) / CJO = (1 + M·(.0004·(T-Tnom)+(1-VJ(T)/VJ)) )

  20. Project 2 • Project will be published in the next few days (check web page). • Id vs. Vd (forward and reverse) data • Cj data • Z data • Extract parameters, e.g.: IS, N, IKF, RS, ISR, NR, CJO, M, VJ, IBV, BV, etc.

  21. 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.

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