l9 february 151 semiconductor device modeling and characterization ee5342, lecture 9-spring 2005...
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L9 February 15 1
Semiconductor Device Modeling and CharacterizationEE5342, Lecture 9-Spring 2005
Professor Ronald L. [email protected]
http://www.uta.edu/ronc/
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• You must have a Gamma account– Go to the OIT webpage for a gamma account
• Use UNIX workstations in ELB2121. Input your account and password to login
The first interface looks like the figure below
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2. Right click mouse button Program Terminal
3. In the Terminal window, type: source /usr/local/iccap/00setup.iccap4. Type: iccap to run the program
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5. ICCAP interface looks like the figure below
Check out the following link to find documentation (user guide, reference manual and etc. ) for ICCAP http://eesof.tm.agilent.com/docs/iccap/orig_iccap_home.htm
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• Add source /usr/local/iccap/00setup.iccap into your .cshrc file.
Don’t need to type this line every time you login1. Right click mouse button Program Text Editor
2. Input the file name: .cshrc3. Add this line and save the file
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• Questions on UNIX?Check out the following link to find more information about UNIX (this resource has been helpful in past years)http://www.ee.surrey.ac.uk/Teaching/Unix/
• Hours of operation of ELB212 labMonday – Friday: 8:00am to 10:00pmSaturday – Sunday: 8:00am to 8:00pm
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MidTerm andProject Tests
• Project 1 assignment (draft) will be posted 2/15.– Project report to be used in doing– Project 1 Test on Thursday 3/10– Cover sheet will be posted as for MT
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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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Summary of Va > 0 current density eqns.• Ideal diode, Jsexpd(Va/(Vt))
– ideality factor,
• Recombination, Js,recexp(Va/(2Vt))– appears in parallel with ideal term
• High-level injection, (Js*JKF)
1/2exp(Va/(2Vt))
– SPICE model by modulating ideal Js term
• Va = Vext - J*A*Rs = Vext - Idiode*Rs
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1N ,
V2NV
t
aexp~
1N ,
VNV
t
aexp~
Vext
ln(J)
data Effect of Rs
2NR ,
VNRV
t
aexp~
VKF
Plot of typical Va > 0 current density equations
Sexta RAJ-VV
KFS JJln
recsJln ,
SJln
KFJln
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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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Spherical diodeBreakdown Voltage
1.0
10.0
100.0
1.00E+14 1.00E+15 1.00E+16 1.00E+17
Substrate Concentration (cm^-3)
Bre
ak
do
wn
Vo
lta
ge
(V
olt
)
rj = 0.1 micron
rj = 0.2 micron
rj = 0.5 micron
rj = 1.0 micron
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Summary of Va < 0 current density eqns.• Ideal diode: Js●expd{Va/(Vt)}
– ideality factor,
• Generation: Js,gen●√{Vbi – Va}
• Breakdown: JBV●exp{(BV + Va)/(BV)}
• BV and Gen are added to ideal term• Series resistance
– Va = Vext - J*A*Rs = Vext - Idiode*Rs
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Small-signal eqcircuit
CdiffCdep
l
rdiff
Cdiff and
Cdepl are both charged by
Va = VQ2/1
1
bi
ajojdepl V
VCCC
Va
diffdiffdiffQ
tdiff CrI
Vr ,
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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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Id = area(Ifwd - Irev) Ifwd = InrmKinj + IrecKgen Inrm = IS{exp [Vd/(NVt)] - 1}
Kinj = high-injection factorFor IKF > 0, Kinj = IKF/[IKF+Inrm)]1/2
otherwise, Kinj = 1
Irec = ISR{exp [Vd/(NR·Vt)] - 1}Kgen = ((1 - Vd/VJ)2 + 0.005)M/2
SPICE DiodeStatic Model Eqns.
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• Dinj– IS– N ~ 1– IKF, VKF, N ~ 1
• Drec– ISR– NR ~ 2
SPICE DiodeStatic Model
Vd
iD*RS
Vext = vD + iD*RS
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D DiodeGeneral 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 ParametersModel 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 ParametersModel 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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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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• 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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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.
L9 February 15 34
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. …
L9 February 15 38
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
L9 February 15 40
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)
L9 February 15 41
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)
L9 February 15 42
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.
L9 February 15 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.