Semiconductor Device Modeling and Characterization – EE5342 Lecture 12 – Spring 2011 Professor Ronald L. Carter

©rlc L12-25Feb20112 Dinj –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 =? SPICE Diode Model 

©rlc L12-25Feb20113 ** The diode is modeled as an ohmic resistance (RS/area) in series with an intrinsic diode. is the anode and 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 

©rlc L12-25Feb20114 DDiode ** General Form D [area value] Examples DCLAMP 14 0 DMOD D SWITCH 1.5 Model Form. MODEL 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) *$

©rlc L12-25Feb20115 Diode Model Parameters ** Model Parameters (see.MODEL statement) DescriptionUnit Default ISSaturation currentamp1E-14 NEmission coefficient1 ISRRecombination current parameteramp0 NREmission coefficient for ISR1 IKFHigh-injection “knee” currentampinfinite BVReverse breakdown “knee” voltagevoltinfinite IBVReverse breakdown “knee” currentamp1E-10 NBVReverse breakdown ideality factor1 RSParasitic resistanceohm0 TTTransit timesec0 CJOZero-bias p-n capacitancefarad0 VJp-n potentialvolt1 Mp-n grading coefficient0.5 FCForward-bias depletion cap. coef,0.5 EGBandgap voltage (barrier height)eV1.11

©rlc L12-25Feb20116 Diode Model Parameters ** Model Parameters (see.MODEL statement) DescriptionUnit Default XTIIS temperature exponent3 TIKFIKF temperature coefficient (linear)°C -1 0 TBV1BV temperature coefficient (linear)°C -1 0 TBV2BV temperature coefficient (quadratic)°C -2 0 TRS1RS temperature coefficient (linear)°C -1 0 TRS2RS temperature coefficient (quadratic)°C -2 0 T_MEASUREDMeasured temperature°C T_ABSAbsolute temperature°C T_REL_GLOBALRel. to curr. Temp.°C T_REL_LOCALRelative to AKO model temperature °C For information on T_MEASURED, T_ABS, T_REL_GLOBAL, and T_REL_LOCAL, see the.MODEL statement.

©rlc L12-25Feb20117 ** DC Current I d = area  ( I fwd - I rev) I fwd = forward current = I nrm  Kinj + I rec  Kgen I nrm = normal current = IS  (exp ( Vd/(N  Vt))-1) Kinj = high-injection factor For: IKF > 0, Kinj = (IKF/(IKF+ I nrm)) 1/2 otherwise, Kinj = 1 I rec = rec. cur. = ISR  (exp (Vd/(NR·Vt))- 1) Kgen = generation factor = ((1-Vd/VJ) ) M/2 I rev = reverse current = I rev high + I rev low I rev high = IBV  exp[-(Vd+BV)/(NBV·Vt)] I rev low = IBVL  exp[-(Vd+BV)/(NBVL·Vt)}

©rlc L12-25Feb20118 vD= V ext ln iD Data ln(IKF) ln(IS) ln[(IS*IKF) 1/2 ] Effect of R s V KF ln(ISR) Effect of high level injection low level injection recomb. current V ext -V a =iD*R s

©rlc L12-25Feb20119 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 = mV, the slope of the plot of log(iD) vs. Vd is evaluated as {dlog(iD)/dVd} = log (e)/(N  Vt) = decades/V = 1decade/59.526mV

©rlc L12-25Feb 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  N eff, and ln(IS) ~ ln(iD) - Vd/(N  Vt)  ln(IS eff ). Note: iD, Vt, etc., are normalized to 1A, 1V, resp.

©rlc L12-25Feb 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  N eff, & ln(ISR) ~ln(iD) -Vd/(NR  Vt )  ln(ISR eff ). Note: iD, Vt, etc., are normalized to 1A, 1V, resp.

©rlc L12-25Feb 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  2N eff, and ln(iD) -Vd/(NR  Vt)  ½ln(IS  IKF eff ). Note: iD, Vt, etc., are normalized to 1A, 1V, resp.

©rlc L12-25Feb Static Model Eqns. Parameter Extraction In the region where iD*RS >> Vd. diD/Vd ~ 1/RS eff dVd/diD  RS eff

©rlc L12-25Feb 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 L12-25Feb di D /dV d - Numerical Differentiation

©rlc L12-25Feb dln(i D )/dV d - Numerical Differentiation

©rlc L12-25Feb Diode Par. Extraction 1/Reff iD ISeff

©rlc L12-25Feb 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)

©rlc L12-25Feb 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)  plot i D -1 vs. (dv Dext /di D ) to get a line with  slope = (2NV t ) -1, intercept = - RS/(2NV t )

©rlc L12-25Feb Application of RS to lower current data In the region where v D < VKF. We still have v D = v Dext - i D *RS and since. i D = ISexp (v D /NV t ) + ISRexp (v D /NRV t )  Try applying the derivatives for methods described to the variables i D and v D (using RS and v Dext ).  You also might try comparing the N value from the regular N extraction procedure to the value from the previous slide.

©rlc L12-25Feb Reverse bias (V a carrier gen in DR V a < 0 gives the net rec rate, U = -n i /  ,   = mean min carr g/r l.t.

©rlc L12-25Feb Reverse bias (V a < 0), carr gen in DR (cont.)

©rlc L12-25Feb 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 L12-25Feb Reverse bias junction breakdown Assume -V a = V R >> V bi, so V bi -V a -->V R Since E max ~ 2V R /W = (2qN - V R /(  )) 1/2, and V R = BV when E max = E crit (N - is doping of lightly doped side ~ N eff ) BV =  (E crit ) 2 /(2qN - ) Remember, this is a 1-dim calculation

©rlc L12-25Feb Reverse bias junction breakdown

©rlc L12-25Feb E crit for reverse breakdown (M&K**) Taken from p. 198, M&K** Casey Model for E crit

©rlc L12-25Feb Junction curvature effect on breakdown The field due to a sphere, R, with charge, Q is E r = Q/(4  r 2 ) for (r > R) V(R) = Q/(4  R), (V at the surface) So, for constant potential, V, the field, E r (R) = V/R (E field at surface increases for smaller spheres) Note: corners of a jctn of depth x j are like 1/8 spheres of radius ~ x j

©rlc L12-25Feb 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 L12-25Feb Diode Switching Consider the charging and discharging of a Pn diode –(N a > N d ) –W d << Lp –For t < 0, apply the Thevenin pair V F and R F, so that in steady state I F = (V F - V a )/R F, V F >> V a, so current source –For t > 0, apply V R and R R I R = (V R + V a )/R R, V R >> V a, so current source

©rlc L12-25Feb Diode switching (cont.) + + VFVF VRVR D R RFRF Sw R: t > 0 F: t < 0 V F,V R >> V a

©rlc L12-25Feb Diode charge for t < 0 xnxn x nc x pnpn p no

©rlc L12-25Feb Diode charge for t >>> 0 (long times) xnxn x nc x pnpn p no

©rlc L12-25Feb Equation summary

©rlc L12-25Feb Snapshot for t barely > 0 xnxn x nc x pnpn p no Total charge removed, Q dis =I R t

©rlc L12-25Feb I(t) for diode switching IDID t IFIF -I R tsts t s +t rr I R

©rlc L12-25Feb References *Semiconductor Device Modeling with SPICE, 2nd ed., by Massobrio and Antognetti, McGraw Hill, NY, **MicroSim OnLine Manual, MicroSim Corporation, 1996.