l11 february 241 ee5342 – semiconductor device modeling and characterization lecture 11 - spring...
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EE5342 – Semiconductor Device Modeling and CharacterizationLecture 11 - Spring 2004
Professor Ronald L. [email protected]
http://www.uta.edu/ronc/
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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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PARAMETER definition and units default value
IS saturation current amp 1E-14ISR recombination current parameter amp 0.0IKF high-injection knee current amp infiniteN emission coefficient 1.0NR emission coefficient for isr 2.0RS parasitic resistance ohm 0.0EG bandgap voltage (barrier height) eV 1.11XTI IS temperature exponent 3.0BV reverse breakdown knee voltage volt infiniteIBV reverse breakdown knee current amp 1E-10NBV reverse breakdown ideality factor 1.0
SPICE Diode DC Model Params.1
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Id = area·(Ifwd - Irev)Ifwd = forward current
= Inrm·Kinj + Irec·KgenInrm = normal current = IS·(eVd/(N·Vt)-1)
if: IKF > 0then: Kinj = high-injection factor
= (IKF/(IKF+Inrm))^1/2else: Kinj = 1
Irec = recombination current = ISR·(eVd/(NR·Vt)-1)Kgen = generation factor = ((1-Vd/VJ)^2+0.005)M/2Irev = reverse current = Irevhigh + IrevlowIrevhigh = IBV·e-(Vd+BV)/(NBV·Vt)Irevlow = IBVL·e-(Vd+BV)/(NBVL·Vt)
SPICE Diode DC Model Eqns.1
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1N ,
V2NV
t
aexp~
1N ,
VNV
t
aexp~
Vext
ln(I)
data Effect of Rs
2NR ,
VNRV
t
aexp~
VKF
Plot of SPICE D.C. Va > 0 current equations
Sexta RI-VV
IKFISln
ISRln
ISln
IKFln
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Static Model Eqns.Parameter ExtractionIn any region we can approximate the i-V relationship as a single exponential.
iD ~ Iseff (exp (Vd/(NeffVt)) - 1)
{diD/dVd}/iD = d[ln(iD)]/dVd = 1/(NeffVt)
so Neff = {dVd/d[ln(iD)]}/Vt ,
and ln(ISeff). = ln(iD) - Vd/(NVt).
(Note treat iD, Vt, etc., as normalized to 1A, 1V, respectively)
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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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PARAMETER definition and units default value
TT transit time sec 0.0CJO zero-bias p-n capacitance farad 0.0M p-n grading coefficient 0.5FC forward-bias depletion capacitance coeff 0.5VJ p-n potential volt 1.0
SPICE Diode Capacitance Pars.1
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Cd = Ct + area·CjCt = transit time capacitance = TT·GdGd = DC conductance = area * d (Inrm Kinj + Irec Kgen)/dVdKinj = high-injection factor
Cj = junction capacitanceIF: Vd < FC·VJ Cj = CJO*(1-Vd/VJ)^(-M) IF: Vd > FC·VJ Cj = CJO*(1-FC)^(-1-M)·(1-FC·(1+M)+M·Vd/VJ)
SPICE Diode Capacitance Eqns.1
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Junction Capacitance
• A plot of [Cj]-1/M vs. Vd hasSlope = -[(CJO)1/M/VJ]-1
vertical axis intercept = [CJO]-2 horizontal axis intercept = VJ
Cj-1/M
VJVd
CJO-1/M
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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,
bi
efft
dabia
dDaD
VFC12
NV
N1
N1
VFCVWNLNL
*
• For Va=0, & 1E13 < Na,Nd < 1E19 cm-3
13% < < 28% => DA is OK
pnqVL tD / , qNVVW effdbi /
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Junction CapacitanceAdapted from Figure 1-16 in Text2
Cj = CJO/(1-Vd/VJ)^M
Cj = CJO/(1-FC)^(1+M)*(1-FC·(1+M)+M·Vd/VJ)
VJFC*VJ
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SPICE Diode A.C. Parameters
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SPICE Diode Static I-V
1.E-14
1.E-12
1.E-10
1.E-08
1.E-06
1.E-04
1.E-02
1.E+00
0.0 0.2 0.4 0.6 0.8 1.0
IS = 1.00E-14 N = 1.00 RS = 1.00Id
,ext
(A)
Vd,ext (V)
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Small signal diodeZ-parameter**
TT M, VJ, CJO, RS, N, IS, par SPICE
VJRSIV1CJOC
rg , TTgC
1VNRSIVexpISI
meas. V & I ,qkTV , IVNr
r)C(Crω1r{Z}Re
Mddj
1dddd
tddd
ddtdtd
s2
dj2d
2d
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SPICE Diode Re{Z}
1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
1.E+06
1.E+07
1.E+08
1.E+09
1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 1.E+08 1.E+09
Re{
Z}
(O
hm
s)
Frequency (Hz)
CJ0 = 1E-12
VJ = 0.75
M = 0.5
TT = 1E-9
(2TT)-11 A
100 pA
1 nA
10 nA
100 nA
10 A100 A
1 mA10 mA
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PARAMETER definition and units default value
XTI IS temperature exponent 3.0TIKF ikf temperature coefficient (linear) °C -1 0.0TRS1 rs temperature coefficient (linear) °C -1 0.0TRS2 rs temperature coefficient (quadratic) °C -2 0.0TBV1 bv temperature coefficient (linear) °C -1 0.0TBV2 bv temperature coefficient (quadratic) °C -2 0.0T_ABS absolute temperature °CT_MEASURED measured temperature °CT_REL_GLOBAL relative to current temperature °CT_REL_LOCAL Relative to AKO model temperature °C
SPICE Diode Temperature Pars.1
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SPICE Diode Temperature Eqs.1IS(T) / IS =exp(T/ Tnom-1)·EG/ (N·Vt)·(T/ Tnom) (̂XTI / N )
ISR(T) / ISR =exp(T/ Tnom-1)·EG/ (NR·Vt)·(T/ Tnom) (̂XTI / NR )
IKF(T) / IKF = (1 + TI KF·(T-Tnom))
BV(T) / BV = (1 + TBV1·(T-Tnom) + TBV2·(T-Tnom) 2̂)
RS(T) / RS = (1 + TRS1·(T-Tnom) + TRS2·(T-Tnom) 2̂)
VJ (T) / VJ =T/ Tnom - 3·Vt·ln(T/ Tnom) - Eg(Tnom)·T/ Tnom + Eg(T)
Eg(T) =1.16 - .000702·T 2̂/ (T+1108)
CJ O(T) / CJ O = {1+M[4E-4*(T-Tnom)+(1-VJ (T)/VJ )]}
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Corrections
IS(T) / IS =
exp{[Eg(Tn)/ Vtn - Eg(T)/ Vt]/ N}/ *(T/ Tnom) (̂XTI / NR)
ISR(T) / ISR =
exp{[Eg(Tn)/ Vtn - Eg(T)/ Vt]/ NR}/ *(T/ Tnom) (̂XTI / NR)
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References
1 OrCAD PSpice A/D Manual, Version 9.1, November, 1999, OrCAD, Inc.
2 Semiconductor Device Modeling with SPICE, 2nd ed., by Massobrio and Antognetti, McGraw Hill, NY, 1993.