Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/ EE5342 – Semiconductor Device Modeling and Characterization Lecture 11 February 22, 2010 Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/

SPICE Diode Model t Dinj va Drec vd 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 t L11 02/22/10

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) L11 02/22/10

.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) *$ L11 02/22/10

Diode Equations** L11 02/22/10

Diode Equations for DC Current** L11 02/22/10

Diode Equations for Temperature Effects** L11 02/22/10

Diode Equations for Capacitance** L11 02/22/10

Physical basis for FC L11 02/22/10

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 L10 February 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 L11 02/22/10

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 (in the document Pspcref.pdf). L11 02/22/10

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. L11 02/22/10

Reverse bias (Va< 0), carr gen in DR (cont.) L11 02/22/10

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 L11 02/22/10

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 L11 02/22/10

Reverse bias junction breakdown L11 02/22/10

Ecrit for reverse breakdown (M&K**) Taken from p. 198, M&K** Casey Model for Ecrit L11 02/22/10

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 L11 02/22/10

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 L11 02/22/10

SPICE Diode Static I-V Id,ext (A) Vd,ext (V) L11 02/22/10

Small signal diode Z-parameter**

SPICE Diode Re{Z} Re{Z} (Ohms) Frequency (Hz) (2pTT)-1 1 mA 10 mA CJ0 = 1E-12 VJ = 0.75 M = 0.5 TT = 1E-9 (2pTT)-1 1 mA 100 pA 1 nA 10 nA 100 nA 10 mA 100 mA L11 02/22/10

Small signal low and high freq. limits for Z-par.**

SPICE Diode Temp. Eqs.1 L11 02/22/10

Corrections in some versions of SPICE L11 02/22/10

SPICE Diode Temp. 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 L11 02/22/10

Thermal Resistance L11 02/22/10

Self-Heating Effects Id (A) Vd,ext = Vd + Id*RS 348K < TNOM < 300K 10 mW 20 mW 30 mW 40 mW 50 mW 60 mW 70 mW 80 mW Rth = 0 K/W , RS = 0.32 W Rth = 600 K/W, RS = 1 W L11 02/22/10

Self-Heating Effects SPICE models the IS, etc. the same for all power dissipations. The effect of diode self-heating is to increase the current at all voltages. In this case, an Rth of 600K/W gave nearly the same simulation as re-setting RS from 1 Ohm to 0.32 Ohm. The diode Tj is different at all curr. L11 02/22/10

PiN Diode PiN: Na >> Nint (= N-) & Nint << Nd Wi = Intrinsic region (metall.) width Em,P-T = Peak field mag. when xn = Wi Vbi = fi = Vtln(NaNd/ni2) Vbi,int = fi,int = Vtln(NaNint/ni2) VHL = Vtln(Nd/Nint), the offset at N+N- Vbi = Vbi,int + VHL VPT = applied voltage when xn = Wi L11 02/22/10

PiN Diode Depletion Fields Normalized Position, x’ = x/Wi Normalized Field, E/Em,P-T dx’p dx’n x’n -x’p L11 02/22/10

PiN Diode Depletion Conditions

CV data and N(x) calculation

Estimating Junction Capacitance Parameters Following L29 – EE 5340 Fall 2003 If CJ = CJO {1 – Va/VJ}-M Define y  {d[ln(CJ)]/dV}-1 A plot of y = yi vs. Va = vi has slope = -1/M, and intercept = VJ/MF L11 02/22/10

Derivatives Defined The central derivative is defined as (following Lecture 14 and 11) yi,Central = (vi+1 – vi-1)/(lnCi+1 – lnCi-1), with vi = (vi+1 + vi-1)/2 Equation A1.1 The Forward derivative (as applied to the theory in L11 and L14) is defined in this case as yi,Forward = (vi+1 – vi)/(lnCi+1 – lnCi), with vi,eff = (vi+1 + vi-1)/2 Equation A1.2 L11 02/22/10

Data calculations Table A1.1. Calculations of yi and vi for the Central and Forward derivatives for the data in Table 1. The yi and vi are defined in Equations A1.1 and A1.2. L11 02/22/10

y vs. Va plots Figure A1.3. The yi and vi values from the theory in L11 and L14 with associa-ted trend lines and slope, intercept and R^2 values. L11 02/22/10

Comments on the data interpretation It is clear the Central derivative gives the more reliable data as the R^2 value is larger. M is the reciprocal of the magnitude of the slope obtained by a least squares fit (linear) plot of yi vs. Vi VJ is the horizontal axis intercept (computed as the vertical axis intercept divided by the slope) Cj0 is the vertical axis intercept of a least squares fit of Cj-1/M vs. V (must use the value of V for which the Cj was computed). The computations will be shown later. The results of plotting Cj-1/M vs. V for the M value quoted below are shown in Figure A1.4 L11 02/22/10

Calculating the parameters (the data were generated using M = 0.389, thus we have a 0.77% error). VJ = yi(vi=0)/slope =1.6326/2.551 = 0.640 (the data were generated using fi = 0.648, thus we have a 1.24% error). Cj0 = 1.539E30^-.392 = 1.467 pF (the data were generated using Cj0 = 1.68 pF, thus we have a 12.6% error) L11 02/22/10

Linearized C-V plot Figure A1.4. A plot of the data for Cj^-1/M vs. Va using the M value determined for this data (M = 0.392). L11 02/22/10

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 L11 02/22/10

Diode switching (cont.) VF,VR >> Va F: t < 0 Sw RF R: t > 0 VF + RR D VR + L11 02/22/10

Diode charge for t < 0 pn pno x xn xnc L11 02/22/10

Diode charge for t >>> 0 (long times) pn pno x xn xnc L11 02/22/10

Equation summary L11 02/22/10

Snapshot for t barely > 0 pn Total charge removed, Qdis=IRt pno x xn xnc L11 02/22/10

I(t) for diode switching ID IF ts ts+trr t - 0.1 IR -IR L11 02/22/10

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. L11 02/22/10