1. Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/
Semiconductor Device Modeling and Characterization EE5342, Lecture 9-Spring 2004
Professor Ronald L. Carter
L9 February 17

2. You must have a Gamma account
See for your account and password information
Use UNIX workstations in ELB212
Input your account and password to login
The first interface looks like the figure below
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3. Right click mouse button  Program  Terminal
In the Terminal window, type:
source /usr/local/iccap/00setup.iccap
Type: iccap to run the program
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4. ICCAP interface looks like the figure below
Check out the following link to find documentation (user guide, reference manual and etc. ) for ICCAP
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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
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6. Hours of operation of ELB212 lab
Questions on UNIX?
Check out the following link to find more information about UNIX
Hours of operation of ELB212 lab
Monday – Friday: 8:00am to 10:00pm
Saturday – Sunday: 8:00am to 8:00pm
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7. MidTerm and Project Tests
Project 1 assignment (draft) was posted 2/15.
Project report to be used in doing
Project 1 Test on Thursday 3/11
Cover sheet will be posted as above
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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
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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
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10. Plot of typical Va > 0 current density equations
ln(J)
data
Effect of Rs
Vext
VKF
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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
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12. Spherical diode Breakdown Voltage
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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
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14. Small-signal eq circuit
Cdiff and Cdepl are both charged by
Va = VQ Va
Cdiff
rdiff
Cdepl
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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
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16. Diode switching (cont.)
VF,VR >> Va
F: t < 0 Sw RF
R: t > 0 VF + RR D VR +
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17. Diode charge for t < 0 pn
pno x xn
xnc
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18. Diode charge for t >>> 0 (long times)pn
pno x xn
xnc
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19. Equation summary
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20. Snapshot for t barely > 0pn
Total charge removed, Qdis=IRt
pno x xn
xnc
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21. I(t) for diode switchingID IF ts
ts+trr t
- 0.1 IR
-IR
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22. SPICE Diode Static Model Eqns.
Id = area(Ifwd - Irev) Ifwd = InrmKinj + IrecKgen Inrm = IS{exp [Vd/(NVt)] - 1}
Kinj = high-injection factor For IKF > 0, Kinj = IKF/[IKF+Inrm)]1/2 otherwise, Kinj = 1
Irec = ISR{exp [Vd/(NR·Vt)] - 1}
Kgen = ((1 - Vd/VJ) )M/2
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23. SPICE Diode Static Model
Vext = vD + iD*RS
Dinj IS
N ~ 1
IKF, VKF, N ~ 1
Drec
ISR
NR ~ 2
iD*RS Vd
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24. .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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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
FC Forward-bias depletion cap. coef, 0.5
EG Bandgap voltage (barrier height) eV 1.11
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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.
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27. 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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28. 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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29. 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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30. 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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31. 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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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.
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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.
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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 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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35. Static Model Eqns. Parameter Extraction
In the region where iD*RS >> Vd.
diD/Vd ~ 1/RSeff
dVd/diD  RSeff
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36. 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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37. diD/dVd - Numerical Differentiation
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38. dln(iD)/dVd - Numerical Differentiation
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39. Diode Par. Extraction
1/Reff iD
ISeff
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40. 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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41. 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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42. 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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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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