semiconductor device modeling and characterization ee5342, lecture 9-spring 2002

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Semiconductor Device Modeling and CharacterizationEE5342, Lecture 9-Spring 2002

Professor Ronald L. Carterronc@uta.edu

http://www.uta.edu/ronc/

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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 ,qAD

Idxdp

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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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Band model review (approx. to scale)

qm

~ 4+V

Eo

EF

mEFp

EFn

Eo

Ec

Ev

EFi

qs,n

qs ~

4+V

Eo

Ec

Ev

EFi

qs,p

metal n-type s/c p-type s/c

qs ~

4+V

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Ideal metal to n-typebarrier diode (m>s,Va=0)

EFn

Eo

Ec

Ev

EFi

qs,n

qs

n-type s/c

qm

EF

m

metal

qBn

qVbi

q’n

No disc in Eo

Ex=0 in metal ==> Eoflat

Bn=m- s =

elec mtl to s/c barr

Vbi=Bn-n=

m-s elect s/c

to mtl barr Depl reg

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Ideal m to n s/c barr diode depletion width

xd

x

qN

d

Q’d =

qNdxd

x

Ex

-Em d

d

mx qN

xE

dxdE

xd

(Sheet of neg chg on mtl)= -Q’d

dctsmnBnbi

d

'jsemi,nma

d

abid

N/NlnVV

xC , VVV ,

qN

VV2x

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Real Schottkyband structure*

• Barrier transistion region,

• Interface statesabove o acc, p neutrl

below o dnr, n neutrl

Dit -> oo, qBn= Eg- o

Fermi level “pinned”

Dit -> 0, qBn= m - Goes to “ideal” case

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Fig 8.4* (a) Image charge and electric field lines at a metal-diel intf (b) Distortion of the potential barrier due to image forces with E=0 and (c) const E field

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Ideal metal to n-typeSchottky (Va>0)

qVa = Efn - Efm

Barrier for electrons from sc to m reduced to q(Vbi-Va)

qBn the same

DR decr

EFn

Eo

Ec

Ev

EFi

qs,n

qs

n-type s/c

qm

EF

m

metal

qBn

q(Vbi-Va)

q’nDepl reg

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Ideal m to n s/c Schottky diode curr

t0B

2sT

tasmssm

tabiDsa

s,ntbiDs

mmmss,nssma

mmmss,nssm

V/expT*AJ

1V/VexpJJJJ so

,V/VVexpNn ,0V

constv ,V/VexpNn and

,qvnJqvnJ ,0V

qvnJ ,qvnJ

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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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References

Semiconductor Device Modeling with SPICE, 2nd ed., by Massobrio and Antognetti, McGraw Hill, NY, 1993.

MicroSim OnLine Manual, MicroSim Corporation, 1996.