1. Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/
Semiconductor Device Modeling and Characterization – EE5342 Lecture 13 – Spring 2011
Professor Ronald L. Carter

2. 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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3. Diode Equations***
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4. Diode Equations for DC Current**
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5. Diode Equations for Temperature Effects**
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6. Diode Equations for Capacitance**
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7. 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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8. 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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9. 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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10. 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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11. 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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12. Static Model Eqns. Parameter Extraction
In the region where iD*RS >> Vd.
diD/Vd ~ 1/RSeff
dVd/diD  RSeff
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13. 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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14. diD/dVd - Numerical Differentiation
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15. dln(iD)/dVd - Numerical Differentiation
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16. Diode Par. Extraction
1/Reff iD
ISeff
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17. 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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18. 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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19. 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 the N value from the regular N extraction procedure to the value from the previous slide.
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20. Reverse bias (Va<0) => carrier gen in DR
Va < 0 gives the net rec rate, U = -ni/2t0, t0 = mean min carr g/r l.t.
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21. Reverse bias (Va< 0), carr gen in DR (cont.)
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22. Reverse bias junction breakdown
Avalanche breakdown
Electric field accelerates electrons to sufficient energy to initiate multiplication of impact ionization of valence bonding electrons
field dependence shown on next slide
Heavily doped narrow junction will allow tunneling - see Neamen*, p. 274
Zener breakdown
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23. Reverse bias junction breakdown
Assume -Va = VR >> Vbi, so Vbi-Va-->VR
Since Emax~ 2VR/W = (2qN-VR/(e))1/2, and VR = BV when Emax = Ecrit (N- is doping of lightly doped side ~ Neff)
BV = e (Ecrit )2/(2qN-)
Remember, this is a 1-dim calculation
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24. Reverse bias junction breakdown
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25. Ecrit for reverse breakdown (M&K**)
Taken from p. 198, M&K**
Casey Model for Ecrit
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26. Junction curvature effect on breakdown
The field due to a sphere, R, with charge, Q is Er = Q/(4per2) for (r > R)
V(R) = Q/(4peR), (V at the surface)
So, for constant potential, V, the field, Er(R) = V/R (E field at surface increases for smaller spheres)
Note: corners of a jctn of depth xj are like 1/8 spheres of radius ~ xj
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27. 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
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28. 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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29. 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 (in the document Pspcref.pdf).
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30. 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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31. 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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32. 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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33. 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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34. 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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35. 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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36. 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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37. Physical basis for FC1
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38. Junction Width and Debye Length
LD estimates the transition length of a step-junction DR (concentrations Na and Nd with Neff = NaNd/(Na +Nd)). Thus,
For Va=0, & 1E13 < Na,Nd < 1E19 cm-3
13% < d < 28% => DA is OK
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39. References
1Semiconductor Device Modeling with SPICE, 2nd ed., by Massobrio and Antognetti, McGraw Hill, NY, 1993.
**OrCAD Pspice A/D Reference Guide, Copyright 1999, OrCAD, Inc.
***MicroSim OnLine Manual, MicroSim Corporation, 1996.
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