L9 February 15 1

Semiconductor Device Modeling and CharacterizationEE5342, Lecture 9-Spring 2005

Professor Ronald L. Carterronc@uta.edu

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.

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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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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.