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Semiconductor Device Modeling and Characterization – EE5342 Lecture 12 – Spring 2011. Professor Ronald L. Carter [email protected] http://www.uta.edu/ronc/. SPICE Diode Model. Dinj 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. - PowerPoint PPT Presentation
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Semiconductor Device Modeling and
Characterization – EE5342 Lecture 12 – Spring 2011
Professor Ronald L. [email protected]
http://www.uta.edu/ronc/
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• Dinj– 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 =?
SPICE DiodeModel
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** 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 onlyVt = k·T/q (thermal voltage)
k = Boltzmann’s constantq = electron chargeT = analysis temperature (°K)Tnom = nom. temp. (set with TNOM option
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D Diode **General FormD<name> <(+) node> <(-) node> <model name> [area value]ExamplesDCLAMP 14 0 DMODD13 15 17 SWITCH 1.5Model Form.MODEL <model name> D [model parameters] .model D1N4148-X D(Is=2.682n N=1.836 Rs=.5664 Ikf=44.17m Xti=3 Eg=1.11 Cjo=4p M=.3333 Vj=.5 Fc=.5 Isr=1.565n Nr=2 Bv=100 Ibv=10 0uTt=11.54n)*$
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Diode Model Parameters **Model Parameters (see .MODEL statement)
Description UnitDefault
IS Saturation current amp 1E-14N Emission coefficient 1ISR Recombination current parameter amp 0NR Emission coefficient for ISR 1IKF High-injection “knee” current amp infiniteBV Reverse breakdown “knee” voltage volt infiniteIBV Reverse breakdown “knee” current amp 1E-10NBV Reverse breakdown ideality factor 1RS Parasitic resistance ohm 0TT Transit time sec 0CJO Zero-bias p-n capacitance farad 0VJ p-n potential volt 1M p-n grading coefficient 0.5FC Forward-bias depletion cap. coef, 0.5EG Bandgap voltage (barrier height) eV 1.11
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Diode Model Parameters **Model Parameters (see .MODEL statement)
Description UnitDefault
XTI IS temperature exponent 3TIKF IKF temperature coefficient (linear) °C-1 0TBV1 BV temperature coefficient (linear) °C-1 0TBV2 BV temperature coefficient (quadratic) °C-2 0TRS1 RS temperature coefficient (linear) °C-1 0TRS2 RS temperature coefficient (quadratic) °C-2 0
T_MEASURED Measured temperature °CT_ABS Absolute temperature °CT_REL_GLOBAL Rel. to curr. Temp. °CT_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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**DC CurrentId = area(Ifwd - Irev) Ifwd = forward current = InrmKinj + IrecKgen Inrm = normal current = IS(exp ( Vd/(NVt))-1)
Kinj = high-injection factorFor: IKF > 0, Kinj = (IKF/(IKF+Inrm))1/2otherwise, Kinj = 1
Irec = rec. cur. = ISR(exp (Vd/(NR·Vt))- 1)
Kgen = generation factor = ((1-Vd/VJ)2+0.005)M/2
Irev = reverse current = Irevhigh + Irevlow
Irevhigh = IBVexp[-(Vd+BV)/(NBV·Vt)]Irevlow = IBVLexp[-(Vd+BV)/(NBVL·Vt)}
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vD=Vext
ln iD
Data
ln(IKF)
ln(IS)
ln[(IS*IKF) 1/2]
Effect
of Rs
t
a
VNFV
exp~
t
a
VNRV
exp~
VKF
ln(ISR)
Effect of high level injection
low level injection
recomb. current
Vext-
Va=iD*Rs
t
a
VNV
2exp~
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Interpreting a plotof log(iD) vs. VdIn the region where Irec < Inrm < IKF, and iD*RS << Vd.
iD ~ Inrm = IS(exp (Vd/(NVt)) - 1)
For N = 1 and Vt = 25.852 mV, the slope of the plot of log(iD) vs. Vd is evaluated as
{dlog(iD)/dVd} = log (e)/(NVt) = 16.799 decades/V = 1decade/59.526mV
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Static Model Eqns.Parameter ExtractionIn the region where Irec < Inrm < IKF, and iD*RS << Vd.
iD ~ Inrm = IS(exp (Vd/(NVt)) - 1)
{diD/dVd}/iD = d[ln(iD)]/dVd = 1/(NVt)
so N ~ {dVd/d[ln(iD)]}/Vt Neff,
and ln(IS) ~ ln(iD) - Vd/(NVt) ln(ISeff).
Note: iD, Vt, etc., are normalized to 1A, 1V, resp.
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Static Model Eqns.Parameter ExtractionIn the region where Irec > Inrm, and iD*RS << Vd.
iD ~ Irec = ISR(exp (Vd/(NRVt)) - 1)
{diD/dVd}/iD = d[ln(iD)]/dVd ~ 1/(NRVt)
so NR ~ {dVd/d[ln(iD)]}/Vt Neff,
& ln(ISR) ~ln(iD) -Vd/(NRVt )
ln(ISReff).
Note: iD, Vt, etc., are normalized to 1A, 1V, resp.
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Static Model Eqns.Parameter ExtractionIn the region where IKF > Inrm, and iD*RS << Vd.
iD ~ [ISIKF]1/2(exp (Vd/(2NVt)) - 1)
{diD/dVd}/iD = d[ln(iD)]/dVd ~ (2NVt)-1
so 2N ~ {dVd/d[ln(iD)]}/Vt 2Neff,
and ln(iD) -Vd/(NRVt) ½ln(ISIKFeff).
Note: iD, Vt, etc., are normalized to 1A, 1V, resp.
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Static Model Eqns.Parameter Extraction
In the region where iD*RS >> Vd.
diD/Vd ~ 1/RSeff
dVd/diD RSeff
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Getting Diode Data forParameter 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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diD/dVd - Numerical Differentiation
Vd iD diD/ dVd(central diff erence)
Vd(n-1) iD(n-1) … etc. …
Vd(n) iD(n) (iD(n+1) - iD(n-1))/ (Vd(n+1) - Vd(n-1))
Vd(n+1) iD(n+1) (iD(n+2) - iD(n))/ (Vd(n+2) - Vd(n))
Vd(n+2) iD(n+2) … etc. …
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dln(iD)/dVd - Numerical Differentiation
Vd iD dln (iD)/ dVd (central diff erence)
Vd(n-1) iD(n-1) … etc. …
Vd(n) iD(n) ln (iD(n+1)/ iD(n-1))/ (Vd(n+1)-Vd(n-1))
Vd(n+1) iD(n+1) ln (iD(n+2)/ iD(n))/ (Vd(n+2) - Vd(n))
Vd(n+2) iD(n+2) … etc. …
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1.E-13
1.E-11
1.E-09
1.E-07
1.E-05
1.E-03
1.E-01
1.E+01
0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90
iD(A), Iseff(A), and 1/Reff(mho) vs. Vext(V)
Diode Par.Extraction 1
2345
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Neff vs. Vext
1/Reff
iD
ISeff
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Results ofParameter Extraction• At Vd = 0.2 V, NReff = 1.97,
ISReff = 8.99E-11 A.• At Vd = 0.515 V, Neff = 1.01,
ISeff = 1.35 E-13 A.• At Vd = 0.9 V, RSeff = 0.725 Ohm• Compare to
.model Dbreak D( Is=1e-13 N=1 Rs=.5 Ikf=5m Isr=.11n Nr=2)
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Hints for RS and NFparameter extractionIn the region where vD > VKF. Defining
vD = vDext - iD*RS and IHLI = [ISIKF]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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Application of RS tolower current dataIn 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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Reverse bias (Va<0)=> carrier gen in DR• Va < 0 gives the net rec rate,
U = -ni/, = mean min carr g/r l.t.
NNN/NNN and
qN
VV2W where ,
2Wqn
J
(const.) U- G where ,qGdxJ
dadaeff
eff
abi
0
igen
x
xgen
n
p
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Reverse bias (Va< 0),carr gen in DR (cont.)
gens
gen
gengensrev
JJJ
JSPICE
JJJJJ
or of largest the set then ,0
V when 0 since :note model
VV where ,
current generation the plus bias negative
for current diode ideal the of value The
current the to components two are there
bias, reverse ,)0V(V for lyConsequent
a
abi
ra
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Reverse biasjunction 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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Reverse biasjunction breakdown• Assume -Va = VR >> Vbi, so Vbi-Va--
>VR
• Since Emax~ 2VR/W =
(2qN-VR/())1/2, and VR = BV when
Emax = Ecrit (N- is doping of lightly
doped side ~ Neff)
BV = (Ecrit )2/(2qN-)
• Remember, this is a 1-dim calculation
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Reverse biasjunction breakdown
8/3
4/3
0
4/3
2/3
20
161/
1.1/ 120 so
,161/
1.1/ 60 gives *,***
usually , 2
D.A. theand diode sided-one a Assuming
EN
EqNVE
EN
EVBVCasey
BVqN
EBV
g
Sicrit
B
g
icritSi
i
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Ecrit for reverse breakdown (M&K**)
Taken from p. 198, M&K**
Casey Model for Ecrit
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Junction curvatureeffect on breakdown• The field due to a sphere, R, with
charge, Q is Er = Q/(4r2) for (r > R)
• V(R) = Q/(4R), (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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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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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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Diode switching(cont.)
+
+ VF
VR
DRR
RF
Sw
R: t > 0
F: t < 0
ItI s
F
FF R
VI0tI
VF,VR >>
Va
F
F
F
aFQ R
VR
VVI
0,t for
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Diode chargefor t < 0
xn xncx
pn
pno
Dp2W
,IWV,xqp'Q
2N
TR
TRFnFnndiff,p
D
2i
noV/V
noFn Nn
p ,epV,xp tF
dxdp
qDJ since ,qAD
Idxdp
ppp
F
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Diode charge fort >>> 0 (long times)
xn xncx
pn
pno
tF V/Vnon ep0t,xp
t,xp
sppp
S Jdxdp
qDJ since ,qADI
dxdp
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Equationsummary
Q discharge to flows
R/VI current, a 0, but small, t For
RV
I ,qAD
Idxdp
AJI ,AqD
I
JqD1
dxdp
RRR
F
FF
p
F
0t,F
ssp
s
,ppt,R
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Snapshot for tbarely > 0
xn xncx
pn
pno
p
F
qADI
dxdp
p
RqAD
Idxdp
tF V/Vnon ep0t,xp
0t,xp Total charge removed, Qdis=IRt
st,xp
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I(t) for diodeswitching
ID
t
IF
-IR
ts ts+trr
- 0.1 IR
sRdischarge
p
Rs
tIQ
constant, a is qAD
Idxdp
,tt 0 For
pnp
p2is L/WtanhL
DqnI
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References
*Semiconductor Device Modeling with SPICE, 2nd ed., by Massobrio and Antognetti, McGraw Hill, NY, 1993.
**MicroSim OnLine Manual, MicroSim Corporation, 1996.