1. Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/
EE5342 – Semiconductor Device Modeling and Characterization Lecture 10 - Spring 2004
Professor Ronald L. Carter
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2. Estimating Junction Capacitance Parameters
Following L29 – EE 5340 Fall 2003
If CJ = CJO {1 – Va/VJ}-M
Define y  {d[ln(CJ)]/dV}-1
A plot of
y = yi vs. Va = vi has
slope = -1/M, and
intercept = VJ/MF
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3. Derivatives Defined
The central derivative is defined as (following Lecture 14 and 11)
yi,Central = (vi+1 – vi-1)/(lnCi+1 – lnCi-1),
with vi = (vi+1 + vi-1)/2 Equation A1.1
The Forward derivative (as applied to the theory in L11 and L14) is defined in this case as
yi,Forward = (vi+1 – vi)/(lnCi+1 – lnCi),
with vi,eff = (vi+1 + vi-1)/2 Equation A1.2
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4. Data calculations
Table A1.1. Calculations of yi and vi for the Central and Forward derivatives for the data in Table 1. The yi and vi are defined in Equations A1.1 and A1.2.
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5. y vs. Va plots
Figure A1.3. The yi and vi values from the theory in L11 and L14 with associa-ted trend lines and slope, intercept and R^2 values.
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6. Comments on the data interpretation
It is clear the Central derivative gives the more reliable data as the R^2 value is larger.
M is the reciprocal of the magnitude of the slope obtained by a least squares fit (linear) plot of yi vs. Vi
VJ is the horizontal axis intercept (computed as the vertical axis intercept divided by the slope)
Cj0 is the vertical axis intercept of a least squares fit of Cj-1/M vs. V (must use the value of V for which the Cj was computed).
The computations will be shown later.
The results of plotting Cj-1/M vs. V for the M value quoted below are shown in Figure A1.4
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7. Calculating the parameters
(the data were generated using M = 0.389, thus we have a 0.77% error).
VJ = yi(vi=0)/slope =1.6326/ = 0.640
(the data were generated using fi = 0.648, thus we have a 1.24% error).
Cj0 = 1.539E30^-.392 = pF
(the data were generated using Cj0 = 1.68 pF, thus we have a 12.6% error)
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8. Linearized C-V plot
Figure A1.4. A plot of the data for Cj^-1/M vs. Va using the M value determined for this data (M = 0.392).
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9. Doping Profile
The data were equal-ly spaced (DV=0.1V), the central differ-ence was used, for V ≤ V ≤ 0.4V, which for Cj = e/x, corresponds to a range of 2.81E-5 cm ≤ x ≤ 8.99E-5 cm. These data are shown. The trend line is also shown for a linear fit. Since R^2 = 1.000, a linear N(x) relationship can be assumed.
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10. SPICE Diode Model t Dinj Drec 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
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11. Irec = rec. cur. = ISR(exp (Vd/(NR·Vt))- 1)
DC Current
Id = area(Ifwd - Irev) Ifwd = forward current = InrmKinj + IrecKgen Inrm = 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) )M/2 Irev = reverse current = Irevhigh + Irevlow Irevhigh = IBVexp[-(Vd+BV)/(NBV·Vt)] Irevlow = IBVLexp[-(Vd+BV)/(NBVL·Vt)}
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12. .MODEL <model name> D [model parameters]
D Diode
General Form
D<name> <(+) node> <(-) node> <model name> [area value]
Examples
DCLAMP DMOD D SWITCH 1.5
Model Form
.MODEL <model name> D [model parameters]
.model D1N4148-X D(Is=2.682n N= Rs= Ikf=44.17m Xti=3 Eg=1.11 Cjo=4p M= Vj=.5 Fc=.5 Isr=1.565n Nr=2 Bv=100 Ibv=10 0u
Tt=11.54n) *$
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13. 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
FC Forward-bias depletion cap. coef, 0.5
EG Bandgap voltage (barrier height) eV 1.11
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14. 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.
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15. In the following equations:
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 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)
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16. ln iD ln(IKF) ln[(IS*IKF) 1/2] ln(ISR) ln(IS) vD= Vext VKF
Vext-Va=iD*Rs
low level injection
ln iD
ln(IKF)
Effect of Rs
ln[(IS*IKF) 1/2]
Effect of high level injection
ln(ISR)
Data
ln(IS)
vD=
Vext
recomb. current
VKF
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17. 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
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18. 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.
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19. 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.
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20. 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 N ~ {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.
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21. Static Model Eqns. Parameter Extraction
In the region where iD*RS >> Vd.
diD/Vd ~ 1/RSeff
dVd/diD  RSeff
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22. 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
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23. diD/dVd - Numerical Differentiation
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24. dln(iD)/dVd - Numerical Differentiation
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25. Diode Par. Extraction
1/Reff iD
ISeff
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26. 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)
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27. Hints for RS and NF parameter 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-1 vs. (dvDext/diD) to get a line with
slope = (2NVt)-1, intercept = - RS/(2NVt)
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28. Application of RS to lower 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.
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29. 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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