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Semiconductor Device Modeling and Characterization EE5342, Lecture 9-Spring 2005

Semiconductor Device Modeling and Characterization EE5342, Lecture 9-Spring 2005. Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/. You must have a Gamma account Go to the OIT webpage for a gamma account Use UNIX workstations in ELB212

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Semiconductor Device Modeling and Characterization EE5342, Lecture 9-Spring 2005

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  1. Semiconductor Device Modeling and CharacterizationEE5342, Lecture 9-Spring 2005 Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/

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

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

  4. ICCAP interface looks like the figure below • Check out the following link to find documentation (user guide, reference manual and etc. ) for ICCAP http://eesof.tm.agilent.com/docs/iccap/orig_iccap_home.htm

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

  6. Questions on UNIX? Check out the following link to find more information about UNIX (this resource has been helpful in past years) http://www.ee.surrey.ac.uk/Teaching/Unix/ • Hours of operation of ELB212 lab Monday – Friday: 8:00am to 10:00pm Saturday – Sunday: 8:00am to 8:00pm

  7. MidTerm andProject 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

  8. Ideal diode equation (abrupt junction) • Current dens, Jx = Js expd(Va/Vt) • Where I = J*A & expd(x) = [exp(x) -1] • Js = Js,p + Js,n = hole curr + ele curr • Js,p = qni2Dp coth(Wn/Lp)/(NdLp), (x=xn) • Js,n = qni2Dn coth(Wp/Ln)/(NaLn), (x=-xp) • Often Js,n < Js,p when Na > Nd • Or Js,n > Js,p when Na < Nd • Note {L/coth(W/L)} ≈ least of W or L

  9. 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

  10. ln(J) Plot of typical Va > 0 current density equations data Effect of Rs Vext VKF

  11. 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

  12. Spherical diodeBreakdown Voltage

  13. Summary of Va < 0 current density eqns. • Ideal diode: Js●expd{Va/(hVt)} • ideality factor, h • Generation: Js,gen●√{Vbi – Va} • Breakdown: JBV●exp{(BV + Va)/(hBV)} • BV and Gen are added to ideal term • Series resistance • Va = Vext - J*A*Rs = Vext - Idiode*Rs

  14. Small-signal eqcircuit Cdiff and Cdepl are both charged by Va = VQ Va rdiff Cdepl Cdiff

  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

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

  17. Diode chargefor t < 0 pn pno x xn xnc

  18. Diode charge fort >>> 0 (long times) pn pno x xn xnc

  19. Equationsummary

  20. Snapshot for tbarely > 0 pn Total charge removed, Qdis=IRt pno x xn xnc

  21. I(t) for diodeswitching ID IF ts ts+trr t - 0.1 IR -IR

  22. SPICE DiodeStatic Model Eqns. Id = area(Ifwd - Irev) Ifwd = InrmKinj + IrecKgen Inrm = IS{exp [Vd/(NVt)] - 1} Kinj = high-injection factorFor IKF > 0, Kinj = IKF/[IKF+Inrm)]1/2 otherwise, Kinj = 1 Irec = ISR{exp [Vd/(NR·Vt)] - 1} Kgen = ((1 - Vd/VJ)2 + 0.005)M/2

  23. SPICE DiodeStatic Model Vext = vD + iD*RS • Dinj • IS • N ~ 1 • IKF, VKF, N ~ 1 • Drec • ISR • NR ~ 2 iD*RS Vd

  24. D Diode General Form D<name> <(+) node> <(-) node> <model name> [area value] Examples DCLAMP 14 0 DMODD13 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) *$

  25. 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

  26. 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.

  27. 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 onlyVt = k·T/q (thermal voltage)k = Boltzmann’s constantq = electron charge T = analysis temperature (°K) Tnom = nom. temp. (set with TNOM option)

  28. SPICE DiodeModel • 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 =? t

  29. DC Current Id = area(Ifwd - Irev)Ifwd = forward current = InrmKinj + IrecKgenInrm = 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/2Irev = reverse current = Irevhigh + IrevlowIrevhigh = IBVexp[-(Vd+BV)/(NBV·Vt)]Irevlow = IBVLexp[-(Vd+BV)/(NBVL·Vt)}

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

  31. Interpreting a plotof 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

  32. 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.

  33. 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.

  34. 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.

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

  36. Getting Diode Data forParameter 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

  37. diD/dVd - Numerical Differentiation

  38. dln(iD)/dVd - Numerical Differentiation

  39. Diode Par.Extraction 1/Reff iD ISeff

  40. Results ofParameter 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)

  41. Hints for RS and NFparameter 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-1vs. (dvDext/diD) to get a line with • slope = (2NVt)-1, intercept = - RS/(2NVt)

  42. Application of RS tolower 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.

  43. References Semiconductor Device Modeling with SPICE, 2nd ed., by Massobrio and Antognetti, McGraw Hill, NY, 1993. MicroSim OnLine Manual, MicroSim Corporation, 1996. Device Electronics for Integrated Circuits, 2nd ed., by Muller and Kamins, John Wiley, New York, 1986.

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