Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/ Semiconductor Device Modeling and Characterization EE5342, Lecture 9 -Spring 2010 Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/

Effect of carrier recombination in DR The S-R-H rate (tno = tpo = to) is L09 February 15

Effect of carrier rec. in DR (cont.) For low Va ~ 10 Vt In DR, n and p are still > ni The net recombination rate, U, is still finite so there is net carrier recomb. reduces the carriers available for the ideal diode current adds an additional current component L09 February 15

Effect of carrier rec. in DR (cont.) L09 February 15

Effect of non- zero E in the CNR This is usually not a factor in a short diode, but when E is finite -> resistor In a long diode, there is an additional ohmic resistance (usually called the parasitic diode series resistance, Rs) Rs = L/(nqmnA) for a p+n long diode. L=Wn-Lp (so the current is diode-like for Lp and the resistive otherwise). L09 February 15

High level injection effects Law of the junction remains in the same form, [pnnn]xn=ni2exp(Va/Vt), etc. However, now dpn = dnn become >> nno = Nd, etc. Consequently, the l.o.t.j. reaches the limiting form dpndnn = ni2exp(Va/Vt) Giving, dpn(xn) = niexp(Va/(2Vt)), or dnp(-xp) = niexp(Va/(2Vt)), L09 February 15

High level inj effects (cont.) L09 February 15

Summary of Va > 0 current density eqns. Ideal diode, Jsexpd(Va/(hVt)) ideality factor, h Recombination, Js,recexp(Va/(2hVt)) appears in parallel with ideal term High-level injection, (Js*JKF)1/2exp(Va/(2hVt)) SPICE model by modulating ideal Js term Va = Vext - J*A*Rs = Vext - Idiode*Rs L09 February 15

Diode Diffusion and Recombination Currents L09 February 15

Diode Diffusion and Recombination Currents – One Sided Diode L09 February 15

Plot of typical Va > 0 current density equations ln(J) data Effect of Rs Vext VKF L09 February 15

SPICE Diode Model t Dinj Drec 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 L09 February 15

Project 1A – Diode parameters to use L09 February 15

Tasks Using PSpice or any simulator, plot the i-v curve for this diode, assuming Rth = 0, for several temperatures in the range 300 K < TEMP = TAMB < 304 K. Using this data, determine what the i-v plot would be for Rth = 500 K/W. Using this data, determine the maximum operating temperature for which the diode conductance is within 1% of the Rth = 0 value at 300 K. Do the same for a 10% tolerance. Propose a SPICE macro which would give the Rth = 500 K/W i-v relationship. L09 February 15

Example L09 February 15

Approaches Phenomenological Theoretical L09 February 15

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In the following equations: ** 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 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) L09 February 15

.MODEL <model name> D [model parameters] D Diode ** General Form D<name> <(+) node> <(-) node> <model name> [area value] Examples DCLAMP 14 0 DMOD D13 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) *$ L09 February 15

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 L09 February 15

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. L09 February 15

Irec = rec. cur. = ISR(exp (Vd/(NR·Vt))- 1) ** DC Current Id = area(Ifwd - Irev) Ifwd = forward current = InrmKinj + IrecKgen Inrm = 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/2 Irev = reverse current = Irevhigh + Irevlow Irevhigh = IBVexp[-(Vd+BV)/(NBV·Vt)] Irevlow = IBVLexp[-(Vd+BV)/(NBVL·Vt)} L09 February 15

ln iD ln(IKF) ln[(IS*IKF) 1/2] ln(ISR) ln(IS) vD= Vext VKF Vext-Va=iD*Rs low level injection ln iD ln(IKF) Effect of Rs ln[(IS*IKF) 1/2] Effect of high level injection ln(ISR) Data ln(IS) vD= Vext recomb. current VKF L09 February 15

Interpreting a plot of 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 L09 February 15

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  Neff, and ln(IS) ~ ln(iD) - Vd/(NVt)  ln(ISeff). Note: iD, Vt, etc., are normalized to 1A, 1V, resp. L09 February 15

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  Neff, & ln(ISR) ~ln(iD) -Vd/(NRVt )  ln(ISReff). Note: iD, Vt, etc., are normalized to 1A, 1V, resp. L09 February 15

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  2Neff, and ln(iD) -Vd/(NRVt)  ½ln(ISIKFeff). Note: iD, Vt, etc., are normalized to 1A, 1V, resp. L09 February 15

Static Model Eqns. Parameter Extraction In the region where iD*RS >> Vd. diD/Vd ~ 1/RSeff dVd/diD  RSeff L09 February 15

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 L09 February 15

diD/dVd - Numerical Differentiation L09 February 15

dln(iD)/dVd - Numerical Differentiation L09 February 15

Diode Par. Extraction 1/Reff iD ISeff L09 February 15

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) L09 February 15

Hints for RS and NF parameter 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-1 vs. (dvDext/diD) to get a line with slope = (2NVt)-1, intercept = - RS/(2NVt) L09 February 15

Application of RS to lower current data In the region where vD < VKF. We still have vD = vDext - iD*RS and since. iD = ISexp (vD/NVt) + ISRexp (vD/NRVt) Try applying the derivatives for methods described to the variables iD and vD (using RS and vDext). You also might try comparing the N value from the regular N extraction procedure to the value from the previous slide. L09 February 15

Reverse bias (Va<0) => carrier gen in DR Va < 0 gives the net rec rate, U = -ni/2t0, t0 = mean min carr g/r l.t. L09 February 15

Reverse bias (Va< 0), carr gen in DR (cont.) L09 February 15

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 L09 February 15

Reverse bias junction breakdown Assume -Va = VR >> Vbi, so Vbi-Va-->VR Since Emax~ 2VR/W = (2qN-VR/(e))1/2, and VR = BV when Emax = Ecrit (N- is doping of lightly doped side ~ Neff) BV = e (Ecrit )2/(2qN-) Remember, this is a 1-dim calculation L09 February 15

Reverse bias junction breakdown L09 February 15

Ecrit for reverse breakdown (M&K**) Taken from p. 198, M&K** Casey Model for Ecrit L09 February 15

Junction curvature effect on breakdown The field due to a sphere, R, with charge, Q is Er = Q/(4per2) for (r > R) V(R) = Q/(4peR), (V at the surface) So, for constant potential, V, the field, Er(R) = V/R (E field at surface increases for smaller spheres) Note: corners of a jctn of depth xj are like 1/8 spheres of radius ~ xj L09 February 15

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 L09 February 15

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 L09 February 15

Diode switching (cont.) VF,VR >> Va F: t < 0 Sw RF R: t > 0 VF + RR D VR + L09 February 15

Diode charge for t < 0 pn pno x xn xnc L09 February 15

Diode charge for t >>> 0 (long times) pn pno x xn xnc L09 February 15

Equation summary L09 February 15

Snapshot for t barely > 0 pn Total charge removed, Qdis=IRt pno x xn xnc L09 February 15

I(t) for diode switching ID IF ts ts+trr t - 0.1 IR -IR L09 February 15

References *Semiconductor Device Modeling with SPICE, 2nd ed., by Massobrio and Antognetti, McGraw Hill, NY, 1993. **MicroSim OnLine Manual, MicroSim Corporation, 1996. L09 February 15