Semiconductor device modeling and characterization ee5342 lecture 9 spring 2003
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Semiconductor Device Modeling and Characterization EE5342, Lecture 9-Spring 2003. Professor Ronald L. Carter [email protected] http://www.uta.edu/ronc/. SPICE Diode Static Model Eqns. Id = area  (Ifwd - Irev) Ifwd = Inrm  Kinj + Irec  Kgen Inrm = IS  { exp [Vd/(N  Vt)] - 1}

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Semiconductor Device Modeling and Characterization EE5342, Lecture 9-Spring 2003

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Semiconductor device modeling and characterization ee5342 lecture 9 spring 2003

Semiconductor Device Modeling and CharacterizationEE5342, Lecture 9-Spring 2003

Professor Ronald L. Carter

[email protected]

http://www.uta.edu/ronc/


Spice diode static model eqns

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)]1/2otherwise, Kinj = 1

Irec = ISR{exp [Vd/(NR·Vt)] - 1}

Kgen = ((1 - Vd/VJ)2 + 0.005)M/2


Spice diode static model

SPICE DiodeStatic Model

Vext = vD + iD*RS

  • Dinj

    • IS

    • N ~ 1

    • IKF, VKF, N ~ 1

  • Drec

    • ISR

    • NR ~ 2

iD*RS

Vd


Semiconductor device modeling and characterization ee5342 lecture 9 spring 2003

DDiode

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)

*$


Semiconductor device modeling and characterization ee5342 lecture 9 spring 2003

  • Diode Model Parameters

  • Model Parameters (see .MODEL statement)

    • DescriptionUnitDefault

  • 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


  • Semiconductor device modeling and characterization ee5342 lecture 9 spring 2003

    • Diode Model Parameters

    • Model Parameters (see .MODEL statement)

      • DescriptionUnitDefault

  • XTIIS temperature exponent3

  • TIKFIKF temperature coefficient (linear)°C-10

  • TBV1BV temperature coefficient (linear)°C-10

  • TBV2BV temperature coefficient (quadratic)°C-20

  • TRS1RS temperature coefficient (linear)°C-10

  • TRS2RS temperature coefficient (quadratic)°C-20

  • 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.


  • Semiconductor device modeling and characterization ee5342 lecture 9 spring 2003

    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 chargeT = analysis temperature (°K)Tnom= nom. temp. (set with TNOM option)


    Spice diode model

    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


    Semiconductor device modeling and characterization ee5342 lecture 9 spring 2003

    DC Current

    Id = area(Ifwd - Irev)Ifwd = forward current = InrmKinj + IrecKgenInrm = normal current = IS(exp (Vd/(NVt))-1)Kinj = high-injection factorFor: IKF > 0, Kinj = (IKF/(IKF+Inrm))1/2otherwise, 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)}


    Semiconductor device modeling and characterization ee5342 lecture 9 spring 2003

    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


    Interpreting a plot of log id vs vd

    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


    Static model eqns parameter extraction

    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.


    Static model eqns parameter extraction1

    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.


    Static model eqns parameter extraction2

    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)=ln(ISIKFeff).

    Note: iD, Vt, etc., are normalized to 1A, 1V, resp.


    Static model eqns parameter extraction3

    Static Model Eqns.Parameter Extraction

    In the region where iD*RS >> Vd.

    diD/Vd ~ 1/RSeff

    dVd/diD = RSeff


    Getting diode data for parameter extraction

    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


    Di d dv d numerical differentiation

    diD/dVd - Numerical Differentiation


    D ln i d dv d numerical differentiation

    dln(iD)/dVd - Numerical Differentiation


    Diode par extraction

    Diode Par.Extraction

    1/Reff

    iD

    ISeff


    Results of parameter extraction

    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)


    Hints for rs and nf parameter extraction

    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)


    Application of rs to lower current data

    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 t0he N value from the regular N extraction procedure to the value from the previous slide.


    References

    References

    Semiconductor Device Modeling with SPICE, 2nd ed., by Massobrio and Antognetti, McGraw Hill, NY, 1993.

    MicroSim OnLine Manual, MicroSim Corporation, 1996.


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