L9 February 151 Semiconductor Device Modeling and Characterization EE5342, Lecture 9-Spring 2005 Professor Ronald L. Carter

L9 February 152 You must have a Gamma account –Go to the OIT webpage for a gamma account Use UNIX workstations in ELB212 1.Input your account and password to login The first interface looks like the figure below

L9 February Right click mouse button  Program  Terminal 3.In the Terminal window, type: source /usr/local/iccap/00setup.iccap 4.Type: iccap to run the program

L9 February ICCAP interface looks like the figure below  Check out the following link to find documentation (user guide, reference manual and etc. ) for ICCAP

L9 February 155 Add source /usr/local/iccap/00setup.iccap into your.cshrc file.  Don’t need to type this line every time you login 1.Right click mouse button  Program  Text Editor 2.Input the file name:.cshrc 3.Add this line and save the file

L9 February 156 Questions on UNIX? Check out the following link to find more information about UNIX (this resource has been helpful in past years) Hours of operation of ELB212 lab Monday – Friday: 8:00am to 10:00pm Saturday – Sunday: 8:00am to 8:00pm

L9 February 157 MidTerm and Project Tests Project 1 assignment (draft) will be posted 2/15. –Project report to be used in doing –Project 1 Test on Thursday 3/10 –Cover sheet will be posted as for MT

L9 February 158 Ideal diode equation (abrupt junction) Current dens, J x = J s expd(V a /V t ) –Where I = J*A & expd(x) = [exp(x) -1] J s = J s,p + J s,n = hole curr + ele curr –J s,p = qn i 2 D p coth(W n /L p )/(N d L p ), (x=x n ) –J s,n = qn i 2 D n coth(W p /L n )/(N a L n ), (x=-x p ) –Often J s,n N d –Or J s,n > J s,p when N a < N d Note {L/coth(W/L)} ≈ least of W or L

L9 February 159 Summary of V a > 0 current density eqns. Ideal diode, J s expd(V a /(  V t )) –ideality factor,  Recombination, J s,rec exp(V a /(2  V t )) –appears in parallel with ideal term High-level injection, (J s *J KF ) 1/2 exp(V a /(2  V t )) –SPICE model by modulating ideal J s term V a = V ext - J*A*R s = V ext - I diode *R s

L9 February 1510 V ext ln(J) data Effect of R s V KF Plot of typical V a > 0 current density equations

L9 February 1511 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

L9 February 1512 Spherical diode Breakdown Voltage

L9 February 1513 Summary of V a < 0 current density eqns. Ideal diode: J s ●expd{V a /(  V t )} –ideality factor,  Generation: J s,gen ●√{V bi – V a } Breakdown: J BV ●exp{(BV + V a )/(  BV )} BV and Gen are added to ideal term Series resistance –V a = V ext - J*A*R s = V ext - I diode *R s

L9 February 1514 Small-signal eq circuit C diff C depl r diff C diff and C depl are both charged by V a = V Q VaVa

L9 February 1515 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

L9 February 1516 Diode switching (cont.) + + VFVF VRVR D R RFRF Sw R: t > 0 F: t < 0 V F,V R >> V a

L9 February 1517 Diode charge for t < 0 xnxn x nc x pnpn p no

L9 February 1518 Diode charge for t >>> 0 (long times) xnxn x nc x pnpn p no

L9 February 1519 Equation summary

L9 February 1520 Snapshot for t barely > 0 xnxn x nc x pnpn p no Total charge removed, Q dis =I R t

L9 February 1521 I(t) for diode switching IDID t IFIF -I R tsts t s +t rr I R

L9 February 1522 Id = area  (Ifwd - Irev) Ifwd = Inrm  Kinj + Irec  Kgen Inrm = IS  {exp [Vd/(N  Vt)] - 1} Kinj = high-injection factor For IKF > 0, Kinj = IKF/[IKF+Inrm)]1/2 otherwise, Kinj = 1 Irec = ISR  {exp [Vd/(NR·Vt)] - 1} Kgen = ((1 - Vd/VJ) ) M/2 SPICE Diode Static Model Eqns.

L9 February 1523 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

L9 February 1524 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) *$

L9 February 1525 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

L9 February 1526 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.

L9 February 1527 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 

L9 February 1528 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 

L9 February 1529 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)}

L9 February 1530 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

L9 February 1531 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

L9 February 1532 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.

L9 February 1533 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.

L9 February 1534 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.

L9 February 1535 Static Model Eqns. Parameter Extraction In the region where iD*RS >> Vd. diD/Vd ~ 1/RS eff dVd/diD  RS eff

L9 February 1536 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

L9 February 1537 di D /dV d - Numerical Differentiation

L9 February 1538 dln(i D )/dV d - Numerical Differentiation

L9 February 1539 Diode Par. Extraction 1/Reff iD ISeff

L9 February 1540 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)

L9 February 1541 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 )

L9 February 1542 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.

L9 February 1543 References Semiconductor Device Modeling with SPICE, 2nd ed., by Massobrio and Antognetti, McGraw Hill, NY, MicroSim OnLine Manual, MicroSim Corporation, Device Electronics for Integrated Circuits, 2nd ed., by Muller and Kamins, John Wiley, New York, 1986.