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Semiconductor Device Modeling and Characterization EE5342, Lecture 12 Spring 2003. Professor Ronald L. Carter [email protected] http://www.uta.edu/ronc/. SPICE Diode Static Model. V ext = v D + i D *RS. Dinj IS N ~ 1 IKF, VKF, N ~ 1 Drec ISR NR ~ 2. i D *RS. V d. - PowerPoint PPT Presentation
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L12 20Feb03 1
Semiconductor Device Modeling and CharacterizationEE5342, Lecture 12Spring 2003
Professor Ronald L. [email protected]
http://www.uta.edu/ronc/
L12 20Feb03 2
• Dinj– IS– N ~ 1– IKF, VKF, N ~ 1
• Drec– ISR– NR ~ 2
SPICE DiodeStatic Model
Vd
iD*RS
Vext = vD + iD*RS
L12 20Feb03 3
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
L12 20Feb03 4
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
L12 20Feb03 5
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
L12 20Feb03 6
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)
L12 20Feb03 7
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)
L12 20Feb03 9
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)
L12 20Feb03 10
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
L12 20Feb03 11
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
L12 20Feb03 13
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 /
L12 20Feb03 14
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
L12 20Feb03 15
Junction Capacitance
• Let c = Cj/CJO• Calculate c(dVd/dc) = dVd/d[ln(c)]
= r• Confirm that a plot of r vs. Vd has
slope = -1/m, andintercept = VJ/m
L12 20Feb03 16
SPICE Diode A.C. Parameters
L12 20Feb03 17
Small signal diodeZ-parameter
RS
/gdCd)(Cjf41
gdRe{Z}
212222
1
/
L12 20Feb03 18
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
L12 20Feb03 19
IS(T) / IS=e(T/Tnom-1)·EG/(N·Vt)·(T/Tnom)XTI/N
ISR(T) / ISR= e(T/Tnom-1)·EG/(NR·Vt)·(T/Tnom)XTI/NR
IKF(T) / IKF = (1 + TIKF·(T-Tnom))BV(T) = BV·(1 + TBV1·(T-Tnom) + TBV2·(T-Tnom)2)RS(T) = RS·(1 + TRS1·(T-Tnom) + TRS2·(T-Tnom)2)VJ(T) = VJ·T/Tnom - 3·Vt·ln(T/Tnom)
- Eg(Tnom)·T/Tnom + Eg(T)Eg(T) = silicon bandgap energy
= 1.16 - .000702·T2/(T+1108)CJO(T) / CJO =
(1 + M·(.0004·(T-Tnom)+(1-VJ(T)/VJ)) )
SPICE Diode Temperature Eqs.1
L12 20Feb03 20
Project 2
• Project will be published in the next few days (check web page).
• Id vs. Vd (forward and reverse) data• Cj data• Z data• Extract parameters, e.g.: IS, N, IKF,
RS, ISR, NR, CJO, M, VJ, IBV, BV, etc.
L12 20Feb03 21
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.