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Semiconductor Device Modeling and CharacterizationEE5342, Lecture 12Spring 2003

Professor Ronald L. Carterronc@uta.edu

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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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

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SPICE Diode A.C. Parameters

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Small signal diodeZ-parameter

RS

/gdCd)(Cjf41

gdRe{Z}

212222

1

/

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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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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

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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.

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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.