1. Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/
Semiconductor Device Modeling and Characterization EE5342, Lecture 9 -Spring 2010
Professor Ronald L. Carter

2. Effect of carrier recombination in DR
The S-R-H rate (tno = tpo = to) is
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3. Effect of carrier rec. in DR (cont.)
For low Va ~ 10 Vt
In DR, n and p are still > ni
The net recombination rate, U, is still finite so there is net carrier recomb.
reduces the carriers available for the ideal diode current
adds an additional current component
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4. Effect of carrier rec. in DR (cont.)
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5. Effect of non- zero E in the CNR
This is usually not a factor in a short diode, but when E is finite -> resistor
In a long diode, there is an additional ohmic resistance (usually called the parasitic diode series resistance, Rs)
Rs = L/(nqmnA) for a p+n long diode.
L=Wn-Lp (so the current is diode-like for Lp and the resistive otherwise).
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6. High level injection effects
Law of the junction remains in the same form, [pnnn]xn=ni2exp(Va/Vt), etc.
However, now dpn = dnn become >> nno = Nd, etc.
Consequently, the l.o.t.j. reaches the limiting form dpndnn = ni2exp(Va/Vt)
Giving, dpn(xn) = niexp(Va/(2Vt)), or dnp(-xp) = niexp(Va/(2Vt)),
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7. High level inj effects (cont.)
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8. 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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9. Diode Diffusion and Recombination Currents
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10. Diode Diffusion and Recombination Currents – One Sided Diode
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11. Plot of typical Va > 0 current density equations
ln(J)
data
Effect of Rs
Vext
VKF
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12. 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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13. Project 1A – Diode parameters to use
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14. Tasks
Using PSpice or any simulator, plot the i-v curve for this diode, assuming Rth = 0, for several temperatures in the range 300 K < TEMP = TAMB < 304 K.
Using this data, determine what the i-v plot would be for Rth = 500 K/W.
Using this data, determine the maximum operating temperature for which the diode conductance is within 1% of the Rth = 0 value at 300 K.
Do the same for a 10% tolerance.
Propose a SPICE macro which would give the Rth = 500 K/W i-v relationship.
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15. Example
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16. Approaches
Phenomenological
Theoretical
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19. 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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20. .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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21. 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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22. 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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23. 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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24. 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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25. 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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26. 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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27. 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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28. 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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29. Static Model Eqns. Parameter Extraction
In the region where iD*RS >> Vd.
diD/Vd ~ 1/RSeff
dVd/diD  RSeff
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30. 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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31. diD/dVd - Numerical Differentiation
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32. dln(iD)/dVd - Numerical Differentiation
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33. Diode Par. Extraction
1/Reff iD
ISeff
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34. 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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35. 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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36. 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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37. 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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38. Reverse bias (Va< 0), carr gen in DR (cont.)
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39. 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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40. 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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41. Reverse bias junction breakdown
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42. Ecrit for reverse breakdown (M&K**)
Taken from p. 198, M&K**
Casey Model for Ecrit
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43. 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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44. 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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45. 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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46. Diode switching (cont.)
VF,VR >> Va
F: t < 0 Sw RF
R: t > 0 VF + RR D VR +
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47. Diode charge for t < 0 pn
pno x xn
xnc
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48. Diode charge for t >>> 0 (long times)pn
pno x xn
xnc
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49. Equation summary
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50. Snapshot for t barely > 0pn
Total charge removed, Qdis=IRt
pno x xn
xnc
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51. I(t) for diode switchingID IF ts
ts+trr t
- 0.1 IR
-IR
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52. 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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