Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/ Semiconductor Device Modeling and Characterization – EE5342 Lecture 13 – Spring 2011 Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/

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 ©rlc L13-28Feb2011

Diode Equations*** ©rlc L13-28Feb2011

Diode Equations for DC Current** ©rlc L13-28Feb2011

Diode Equations for Temperature Effects** ©rlc L13-28Feb2011

Diode Equations for Capacitance** ©rlc L13-28Feb2011

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 ©rlc L13-28Feb2011

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 ©rlc L13-28Feb2011

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. ©rlc L13-28Feb2011

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. ©rlc L13-28Feb2011

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. ©rlc L13-28Feb2011

Static Model Eqns. Parameter Extraction In the region where iD*RS >> Vd. diD/Vd ~ 1/RSeff dVd/diD  RSeff ©rlc L13-28Feb2011

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 ©rlc L13-28Feb2011

diD/dVd - Numerical Differentiation ©rlc L13-28Feb2011

dln(iD)/dVd - Numerical Differentiation ©rlc L13-28Feb2011

Diode Par. Extraction 1/Reff iD ISeff ©rlc L13-28Feb2011

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) ©rlc L13-28Feb2011

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) ©rlc L13-28Feb2011

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. ©rlc L13-28Feb2011

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. ©rlc L13-28Feb2011

Reverse bias (Va< 0), carr gen in DR (cont.) ©rlc L13-28Feb2011

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 ©rlc L13-28Feb2011

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 ©rlc L13-28Feb2011

Reverse bias junction breakdown ©rlc L13-28Feb2011

Ecrit for reverse breakdown (M&K**) Taken from p. 198, M&K** Casey Model for Ecrit ©rlc L13-28Feb2011

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 ©rlc L13-28Feb2011

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 ©rlc L13-28Feb2011

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 ©rlc L13-28Feb2011

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). ©rlc L13-28Feb2011

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 ©rlc L13-28Feb2011

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 ©rlc L13-28Feb2011

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. ©rlc L13-28Feb2011

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. ©rlc L13-28Feb2011

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 ©rlc L13-28Feb2011

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) ©rlc L13-28Feb2011

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). ©rlc L13-28Feb2011

Physical basis for FC1 ©rlc L13-28Feb2011

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 ©rlc L13-28Feb2011

References 1Semiconductor Device Modeling with SPICE, 2nd ed., by Massobrio and Antognetti, McGraw Hill, NY, 1993. **OrCAD Pspice A/D Reference Guide, Copyright 1999, OrCAD, Inc. ***MicroSim OnLine Manual, MicroSim Corporation, 1996. ©rlc L13-28Feb2011