1. Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/
EE5342 – Semiconductor Device Modeling and Characterization Lecture 11 February 22, 2010
Professor Ronald L. Carter

2. SPICE Diode Model t Dinj va Drec vd 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: none
Cdepl: none t
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3. 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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4. .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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5. Diode Equations**
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6. Diode Equations for DC Current**
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7. Diode Equations for Temperature Effects**
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8. Diode Equations for Capacitance**
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9. Physical basis for FC
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10. 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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11. 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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12. 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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13. 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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14. Reverse bias (Va< 0), carr gen in DR (cont.)
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15. 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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16. 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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17. Reverse bias junction breakdown
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18. Ecrit for reverse breakdown (M&K**)
Taken from p. 198, M&K**
Casey Model for Ecrit
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19. 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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20. 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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21. SPICE Diode Static I-V
Id,ext (A)
Vd,ext (V)
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22. Small signal diode Z-parameter**

23. SPICE Diode Re{Z} Re{Z} (Ohms) Frequency (Hz) (2pTT)-1 1 mA 10 mA
CJ0 = 1E-12
VJ = 0.75
M = 0.5
TT = 1E-9
(2pTT)-1
1 mA
100 pA
1 nA
10 nA
100 nA
10 mA
100 mA
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24. Small signal low and high freq. limits for Z-par.**

25. SPICE Diode Temp. Eqs.1
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26. Corrections in some versions of SPICE
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27. SPICE Diode Temp. Pars.1 PARAMETER definition and units default value
XTI IS temperature exponent 3.0
TIKF ikf temperature coefficient (linear) °C
TRS1 rs temperature coefficient (linear) °C
TRS2 rs temperature coefficient (quadratic) °C
TBV1 bv temperature coefficient (linear) °C
TBV2 bv temperature coefficient (quadratic) °C
T_ABS absolute temperature °C
T_MEASURED measured temperature °C
T_REL_GLOBAL relative to current temperature °C
T_REL_LOCAL Relative to AKO model temperature °C
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28. Thermal Resistance
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29. Self-Heating Effects Id (A) Vd,ext = Vd + Id*RS
348K < TNOM < 300K
10 mW
20 mW
30 mW
40 mW
50 mW
60 mW
70 mW
80 mW
Rth = 0 K/W , RS = 0.32 W
Rth = 600 K/W, RS = 1 W
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30. Self-Heating Effects
SPICE models the IS, etc. the same for all power dissipations.
The effect of diode self-heating is to increase the current at all voltages.
In this case, an Rth of 600K/W gave nearly the same simulation as re-setting RS from 1 Ohm to 0.32 Ohm.
The diode Tj is different at all curr.
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31. PiN Diode PiN: Na >> Nint (= N-) & Nint << Nd
Wi = Intrinsic region (metall.) width
Em,P-T = Peak field mag. when xn = Wi
Vbi = fi = Vtln(NaNd/ni2)
Vbi,int = fi,int = Vtln(NaNint/ni2)
VHL = Vtln(Nd/Nint), the offset at N+N-
Vbi = Vbi,int + VHL
VPT = applied voltage when xn = Wi
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32. PiN Diode Depletion Fields
Normalized Position, x’ = x/Wi
Normalized Field, E/Em,P-T
dx’p
dx’n
x’n
-x’p
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33. PiN Diode Depletion Conditions

34. CV data and N(x) calculation

35. 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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36. 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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37. 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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38. 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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39. 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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40. 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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41. 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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42. 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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43. Diode switching (cont.)
VF,VR >> Va
F: t < 0 Sw RF
R: t > 0 VF + RR D VR +
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44. Diode charge for t < 0 pn
pno x xn
xnc
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45. Diode charge for t >>> 0 (long times)pn
pno x xn
xnc
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46. Equation summary
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47. Snapshot for t barely > 0pn
Total charge removed, Qdis=IRt
pno x xn
xnc
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48. I(t) for diode switchingID IF ts
ts+trr t
- 0.1 IR
-IR
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49. References
*Semiconductor Device Modeling with SPICE, 2nd ed., by Massobrio and Antognetti, McGraw Hill, NY, 1993.
**OrCAD Pspice A/D Reference Guide, Copyright 1999, OrCAD, Inc.
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