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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} - PowerPoint PPT Presentation
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L9 11Feb03 1
Semiconductor Device Modeling and CharacterizationEE5342, Lecture 9-Spring 2003
Professor Ronald L. [email protected]
http://www.uta.edu/ronc/
L9 11Feb03 2
Id = area(Ifwd - Irev) Ifwd = InrmKinj + IrecKgen Inrm = IS{exp [Vd/(NVt)] - 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
SPICE DiodeStatic Model Eqns.
L9 11Feb03 3
• Dinj– IS– N ~ 1– IKF, VKF, N ~ 1
• Drec– ISR– NR ~ 2
SPICE DiodeStatic Model
Vd
iD*RS
Vext = vD + iD*RS
L9 11Feb03 4
D DiodeGeneral FormD<name> <(+) node> <(-) node> <model name> [area value]ExamplesDCLAMP 14 0 DMODD13 15 17 SWITCH 1.5Model 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 0uTt=11.54n)*$
L9 11Feb03 5
Diode Model ParametersModel Parameters (see .MODEL statement)
Description UnitDefault
IS Saturation current amp 1E-14N Emission coefficient 1ISR Recombination current parameter amp 0NR Emission coefficient for ISR 1IKF High-injection “knee” current amp infiniteBV Reverse breakdown “knee” voltage volt infiniteIBV Reverse breakdown “knee” current amp 1E-10NBV Reverse breakdown ideality factor 1RS Parasitic resistance ohm 0TT Transit time sec 0CJO Zero-bias p-n capacitance farad 0VJ p-n potential volt 1M p-n grading coefficient 0.5FC Forward-bias depletion cap. coef, 0.5EG Bandgap voltage (barrier height) eV 1.11
L9 11Feb03 6
Diode Model ParametersModel Parameters (see .MODEL statement)
Description UnitDefault
XTI IS temperature exponent 3TIKF IKF temperature coefficient (linear) °C-1 0TBV1 BV temperature coefficient (linear) °C-1 0TBV2 BV temperature coefficient (quadratic) °C-2 0TRS1 RS temperature coefficient (linear) °C-1 0TRS2 RS temperature coefficient (quadratic) °C-2 0
T_MEASURED Measured temperature °CT_ABS Absolute temperature °CT_REL_GLOBAL Rel. to curr. Temp. °CT_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.
L9 11Feb03 7
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
L9 11Feb03 8
• 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 DiodeModel
L9 11Feb03 9
DC CurrentId = area(Ifwd - Irev) Ifwd = forward current = InrmKinj + IrecKgen Inrm = normal current = IS(exp ( Vd/(NVt))-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/2
Irev = reverse current = Irevhigh + Irevlow
Irevhigh = IBVexp[-(Vd+BV)/(NBV·Vt)]Irevlow = IBVLexp[-(Vd+BV)/(NBVL·Vt)}
L9 11Feb03 10
vD=Vext
ln iD
Data
ln(IKF)
ln(IS)
ln[(IS*IKF) 1/2]
Effect
of Rs
t
a
VNFV
exp~
t
a
VNRV
exp~
VKF
ln(ISR)
Effect of high level injection
low level injection
recomb. current
Vext-
Va=iD*Rs
t
a
VNV
2exp~
L9 11Feb03 11
Interpreting a plotof log(iD) vs. VdIn the region where Irec < Inrm < IKF, and iD*RS << Vd.
iD ~ Inrm = IS(exp (Vd/(NVt)) - 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)/(NVt) = 16.799 decades/V = 1decade/59.526mV
L9 11Feb03 12
Static Model Eqns.Parameter ExtractionIn the region where Irec < Inrm < IKF, and iD*RS << Vd.
iD ~ Inrm = IS(exp (Vd/(NVt)) - 1)
{diD/dVd}/iD = d[ln(iD)]/dVd = 1/(NVt)
so N ~ {dVd/d[ln(iD)]}/Vt = Neff,
and ln(IS) ~ ln(iD) - Vd/(NVt) = ln(ISeff).
Note: iD, Vt, etc., are normalized to 1A, 1V, resp.
L9 11Feb03 13
Static Model Eqns.Parameter ExtractionIn the region where Irec > Inrm, and iD*RS << Vd.
iD ~ Irec = ISR(exp (Vd/(NRVt)) - 1)
{diD/dVd}/iD = d[ln(iD)]/dVd ~ 1/(NRVt)
so NR ~ {dVd/d[ln(iD)]}/Vt = Neff,
& ln(ISR) ~ln(iD) -Vd/(NRVt)= ln(ISReff).
Note: iD, Vt, etc., are normalized to 1A, 1V, resp.
L9 11Feb03 14
Static Model Eqns.Parameter ExtractionIn the region where IKF > Inrm, and iD*RS << Vd.
iD ~ [ISIKF]1/2(exp (Vd/(2NVt)) - 1)
{diD/dVd}/iD = d[ln(iD)]/dVd ~ (2NVt)-1
so 2N ~ {dVd/d[ln(iD)]}/Vt = 2Neff,
and ln(iD) -Vd/(NRVt)= ln(ISIKFeff).
Note: iD, Vt, etc., are normalized to 1A, 1V, resp.
L9 11Feb03 15
Static Model Eqns.Parameter Extraction
In the region where iD*RS >> Vd.
diD/Vd ~ 1/RSeff
dVd/diD = RSeff
L9 11Feb03 16
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
L9 11Feb03 17
diD/dVd - Numerical Differentiation
Vd iD diD/ dVd(central diff erence)
Vd(n-1) iD(n-1) … etc. …
Vd(n) iD(n) (iD(n+1) - iD(n-1))/ (Vd(n+1) - Vd(n-1))
Vd(n+1) iD(n+1) (iD(n+2) - iD(n))/ (Vd(n+2) - Vd(n))
Vd(n+2) iD(n+2) … etc. …
L9 11Feb03 18
dln(iD)/dVd - Numerical Differentiation
Vd iD dln (iD)/ dVd (central diff erence)
Vd(n-1) iD(n-1) … etc. …
Vd(n) iD(n) ln (iD(n+1)/ iD(n-1))/ (Vd(n+1)-Vd(n-1))
Vd(n+1) iD(n+1) ln (iD(n+2)/ iD(n))/ (Vd(n+2) - Vd(n))
Vd(n+2) iD(n+2) … etc. …
L9 11Feb03 19
1.E-13
1.E-11
1.E-09
1.E-07
1.E-05
1.E-03
1.E-01
1.E+01
0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90
iD(A), Iseff(A), and 1/Reff(mho) vs. Vext(V)
Diode Par.Extraction 1
2345
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Neff vs. Vext
1/Reff
iD
ISeff
L9 11Feb03 20
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)
L9 11Feb03 21
Hints for RS and NFparameter extractionIn the region where vD > VKF. Defining
vD = vDext - iD*RS and IHLI = [ISIKF]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)
L9 11Feb03 22
Application of RS tolower current dataIn 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.
L9 11Feb03 23
References
Semiconductor Device Modeling with SPICE, 2nd ed., by Massobrio and Antognetti, McGraw Hill, NY, 1993.
MicroSim OnLine Manual, MicroSim Corporation, 1996.