L11 February 241 EE5342 – Semiconductor Device Modeling and Characterization Lecture 11 - Spring 2004 Professor Ronald L. Carter

L11 February 242 Dinj –IS –N ~ 1 –IKF, VKF, N ~ 1 Drec –ISR –NR ~ 2 SPICE Diode Static Model VdVd i D *RS V ext = v D + i D *RS

L11 February 243 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 SPICE Diode DC Model Params. 1

L11 February 244 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)^ )M/2 Irev = reverse current = Irevhigh + Irevlow Irevhigh = IBV·e-(Vd+BV)/(NBV·Vt) Irevlow = IBVL·e-(Vd+BV)/(NBVL·Vt) SPICE Diode DC Model Eqns. 1

L11 February 245 V ext ln(I) data Effect of R s VKF Plot of SPICE D.C. V a > 0 current equations

L11 February 246 Static Model Eqns. Parameter Extraction In any region we can approximate the i-V relationship as a single exponential. iD ~ Is eff  (exp (Vd/(N eff  Vt)) - 1) {diD/dVd}/iD = d[ln(iD)]/dVd = 1/(N eff  Vt) so N eff = {dVd/d[ln(iD)]}/Vt, and ln(IS eff ). = ln(iD) - Vd/(N  Vt). (Note treat iD, Vt, etc., as normalized to 1A, 1V, respectively)

L11 February 247 Diode Par. Extraction 1/Reff iD ISeff

L11 February 248 Results of Parameter Extraction At Vd = 0.2 V, NReff = 1.97, ISReff = 8.99E-11 A. At Vd = V, Neff = 1.01, ISeff = 1.35 E-13 A. At Vd = 0.9 V, RSeff = Ohm Compare to.model Dbreak D( Is=1e-13 N=1 Rs=.5 Ikf=5m Isr=.11n Nr=2)

L11 February 249 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) y plot i D -1 vs. (dv Dext /di D ) to get a line with y slope = (2NV t ) -1, intercept = - RS/(2NV t )

L11 February 2410 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 SPICE Diode Capacitance Pars. 1

L11 February 2411 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) SPICE Diode Capacitance Eqns. 1

L11 February 2412 Junction Capacitance A plot of [Cj] -1/M vs. V d has Slope = -[(CJO) 1/M /VJ] -1 vertical axis intercept = [CJO] -2 horizontal axis intercept = VJ Cj -1/M VJ VdVd CJO -1/M

L11 February 2413 Junction Width and Debye Length L D estimates the transition length of a step-junction DR (concentrations N a and N d with N eff = N a N d /(N a +N d )). Thus, For V a =0, & 1E13 < N a,N d < 1E19 cm -3 13% DA is OK

L11 February 2414 Junction Capacitance Adapted from Figure 1-16 in Text 2 Cj = CJO/(1-Vd/VJ)^M Cj = CJO/(1-FC)^(1+M)* (1-FC·(1+M)+M·Vd/VJ) VJFC*VJ

L11 February 2415 SPICE Diode A.C. Parameters

L11 February 2416 SPICE Diode Static I-V Id,ext (A) Vd,ext (V)

L11 February 2417 Small signal diode Z-parameter**

L11 February 2418 SPICE Diode Re{Z} Re{Z} (Ohms) Frequency (Hz) CJ0 = 1E-12 VJ = 0.75 M = 0.5 TT = 1E-9 (2  TT) -1 1  A 100 pA 1 nA 10 nA 100 nA 10  A 100  A 1 mA 10 mA

L11 February 2419 PARAMETER definition and units default value XTI IS temperature exponent 3.0 TIKF ikf temperature coefficient (linear) °C TRS1 rs temperature coefficient (linear) °C TRS2 rs temperature coefficient (quadratic) °C TBV1 bv temperature coefficient (linear) °C TBV2 bv temperature coefficient (quadratic) °C 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 SPICE Diode Temperature Pars. 1

L11 February 2420 SPICE Diode Temperature Eqs. 1

L11 February 2421 Corrections

L11 February 2422 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.