L08 07Feb02 1

EE 4345 - SemiconductorElectronics Design ProjectSpring 2002 - Lecture 08

Professor Ronald L. Carterronc@uta.edu

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

L08 07Feb02 2

Dates for TechnologyProject Reports

12 Feb - TP1.1 Eyad Fanous Group12 Feb - TP1.2 Nam Nguyen Group14 Feb - TP1.3 Viet Tran - The Pentagonal Group14 Feb - TP1.4 Fares Alnajjar Group19 Feb - TP1.5 Carlos Garcia Group19 Feb - TP1.6 Robert Colville Group21 Feb - TP1.7 Jepsy Colon Group21 Feb - TP1.8 Preeti Yadav Group26 Feb - TP1.9 Peter Presby - Group 626 Feb - TP1.10 Derek Johnson Group

L08 07Feb02 3

npn BJT currents(F A region, ©RLC)

IC =JCAC

IB=-(IE+IC )

JnE JnC

IE =-JEAE

JRB=JnE-JnC

JpE

JGC

JRE JpC

L08 07Feb02 4

Ebers-Moll(npn injection model)

C

E

B

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1

expt

BC

R

S

R

ECV

VII

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�

t

BC

t

BES

ECCCCT

VVV

VI

III

exp

exp

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�

��

1

expt

BE

F

S

F

CCV

VII(common-emitter)

L08 07Feb02 5

� �� �

� �� �

� �

� �

eff,o

taieffavgrec

o

taimaxfpfna

fnfii

fifni

x

xeffavgrec

2V2/VexpnqWxqUJ

2V2/VexpnU ,EEqV w/

,kT/EEexpnp and ,kT/EEexpnn cesin

xqUqUdxJ curr, ecRn

p

�

��

�

���

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�� ��

Effect of carrierrec. in DR (cont.)

L08 07Feb02 6

High levelinjection effects• Law of the junction remains in the

same form, [pnnn]xn=ni2exp(Va/Vt), etc.

• However, now �pn = �nn become >> nno= Nd, etc.

• Consequently, the l.o.t.j. reaches thelimiting form �pn�nn = ni

2exp(Va/Vt)• Giving, �pn(xn) = niexp(Va/(2Vt)), or

�np(-xp) = niexp(Va/(2Vt)),

L08 07Feb02 7

High level injeffects (cont.)

� �� �

� � � �

� �KFKFKFsinj lh,s

ia

tid

tKFa

appdnna

tainj lh,sinj lh

VJJ ,JJJ :Note nNlnV2 or ,

nN

lnV2VV Thus

Nx-n or ,Nxp giving V of range the for important is This

V2/VexpJJ :is density current injection level-High

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L08 07Feb02 8

Summary of Va > 0current density eqns.• Ideal diode, Jsexpd(Va/(�Vt))

– ideality factor, �• Recombination, Js,recexp(Va/(2�Vt))

– appears in parallel with ideal term• High-level injection,

(Js*JKF)1/2exp(Va/(2�Vt))– SPICE model by modulating ideal Js term

• Va = Vext - J*A*Rs = Vext - Idiode*Rs

L08 07Feb02 9

Plot of typical Va > 0current density eqns.

Vext

ln J

data

ln(JKF)

ln(Js)

ln[(Js*JKF) 1/2]Effectof Rs

���

����

�� t

aV

Vexp~

���

����

�� taV2

Vexp~

VKF

ln(Jsrec)

Effect ofhigh levelinjection

low levelinjection

recomb. current

Vext-Vd=JARs

L08 07Feb02 10

Reverse bias (Va<0)=> carrier gen in DR• Va < 0 gives the net rec rate,

U = -ni/���, �� = mean min carr g/r l.t.

� �

� �

� � �

�

���

��

�

�

�

�� �

NNN/NNN and

qN

VV2W where ,2

WqnJ

(const.) U- G where ,qGdxJ

dadaeff

eff

abi

0

igen

x

xgen

n

p

L08 07Feb02 11

Reverse bias (Va< 0),carr gen in DR (cont.)

� �

gens

gen

gengensrev

JJJJSPICE

JJJJJ

or of largest the set then ,0

V when 0 since :note model

VV where , current generation the plus bias negative

for current diode ideal the of value Thecurrent the to components two are there

bias, reverse ,)0V(V for lyConsequent

a

abi

ra

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L08 07Feb02 12

Reverse biasjunction breakdown• Avalanche breakdown

– Electric field accelerates electrons tosufficient energy to initiatemultiplication of impact ionization ofvalence bonding electrons

– field dependence shown on next slide• Heavily doped narrow junction will

allow tunneling - see Neamen*, p. 274– Zener breakdown

L08 07Feb02 13

Ecrit for reversebreakdown (M&K**)

Taken from p. 198, M&K**

L08 07Feb02 14

Reverse biasjunction breakdown• Assume -Va = VR >> Vbi, so Vbi-Va-->VR

• Since Emax~ 2VR/W = (2qN-VR/(�))1/2,and VR = BV when Emax = Ecrit (N- isdoping of lightly doped side ~ Neff)

BV = ��(Ecrit )2/(2qN-)

• Remember, this is a 1-dim calculation

L08 07Feb02 15

Junction curvatureeffect on breakdown• The field due to a sphere, R, with

charge, Q is Er = Q/(4��r2) for (r > R)• V(R) = Q/(4��R), (V at the surface)• So, for constant potential, V, the

field, Er(R) = V/R (E field at surfaceincreases for smaller spheres)

Note: corners of a jctn of depth xj arelike 1/8 spheres of radius ~ xj

L08 07Feb02 16

BV for reversebreakdown (M&K**)

Taken fromFigure 4.13,p. 198, M&K**Breakdownvoltage of aone-sided, plan,silicon stepjunction showingthe effect ofjunctioncurvature.4,5

L08 07Feb02 17

D DiodeGeneral FormD<name> <(+) node> <(-) node> <modelname> [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=1.836Rs=.5664 Ikf=44.17m Xti=3 Eg=1.11Cjo=4p M=.3333 Vj=.5 Fc=.5Isr=1.565n Nr=2 Bv=100 Ibv=10 0uTt=11.54n)*$

L08 07Feb02 18

Diode Model 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

L08 07Feb02 19

Diode Model 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 0T_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 anodethrough the diode to the cathode. [area value] scalesIS, 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�

L08 07Feb02 21

• Dinj– key par: IS, N(~1)– rd=N*Vt/iD– rd*Cd = TT =– Cdepl given by CJO, VJ

and M– HLI: IKF, VKF

• Drec– param: ISR, NR(~2)– rd~NR*Vt/iD– rd*Cd = ?– Cdepl =?

SPICE DiodeStatic Model

Vd

iD*RS

Vext = vD + iD*RS

L08 07Feb02 22

DC CurrentId = area�(Ifwd - Irev) Ifwd = forward current = Inrm�Kinj + Irec�Kgen Inrm = normal current = IS�(exp ( Vd/(N�Vt))-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 = IBV�exp[-(Vd+BV)/(NBV·Vt)]Irevlow = IBVL�exp[-(Vd+BV)/(NBVL·Vt)}

L08 07Feb02 23

vD=Vext

ln iD

Data

ln(IKF)

ln(IS)

ln[(IS*IKF) 1/2]

Effectof Rs

���

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�

� t

aVNF

Vexp~

���

����

�

�� t

aVNR

Vexp~

VKF

ln(ISR)

Effect ofhigh levelinjection

low levelinjection

recomb. current

Vext-Va=iD*Rs

���

����

�

�� t

aVN

V2

exp~

L08 07Feb02 24

npn BJT currents(F A region, ©RLC)

IC =JCAC

IB=-(IE+IC )

JnE JnC

IE =-JEAE

JRB=JnE-JnC

JpE

JGC

JRE JpC

L08 07Feb02 25

Charge componentsin the BJT From Getreau, Modeling the

Bipolar Transistor,Tektronix, Inc.

L08 07Feb02 26

Gummel-Poon Staticnpn Circuit Model

C

E

BB’

ILC

ILE IBF

IBR ICC - IEC =IS(exp(vBE/NFVt

- exp(vBC/NRVt)/QB

RC

RE

RBB

L08 07Feb02 27

Gummel-PoonModelGeneral FormQXXXXXXX NC NB NE <NS> MNAME <AREA> <OFF> <IC=VBE,VCE> <TEMP=T>

Netlist Examples

Q5 11 26 4 Q2N3904 IC=0.6, 5.0

Q3 5 2 6 9 QNPN .67

NC, NB and NE are the collector, base and emitter nodes

NS is the optional substrate node; if unspecified, the ground is used.MNAME is the model name,AREA is the area factor, and TEMP is the temperature at which this device operates, and overridesthe specification in the Analog Options dialog.

L08 07Feb02 28

Gummel-PoonStatic ModelGummel Poon Model Parameters (NPN/PNP)

Adaptation of the integral charge control model of Gummel and Poon.

Extends the original model to include effects at high bias levels.

Simplifies to Ebers-Moll model when certain parameters not specified.

Defined by parameters

IS, BF, NF, ISE, IKF, NE determine forward characteristics

IS, BR, NR, ISC, IKR, NC determine reverse characteristics

VAF and VAR determine output conductance for for and rev

RB(depends on iB), RC, and RE are also included

L08 07Feb02 29

Gummel-Poon StaticModel Parametersname parameter units default areaIS transport saturation current A 1.0e-16 *BF ideal maximum forward beta - 100NF forward current emission coefficient - 1.0VAF forward Early voltage V infiniteISE B-E leakage saturation current A 0 *NE B-E leakage emission coefficient - 1.5BR ideal maximum reverse beta - 1NR reverse current emission coefficient - 1VAR reverse Early voltage V infiniteISC B-C leakage saturation current A 0 *NC B-C leakage emission coefficient - 2EG energy gap for temperature eV 1.11

effect on ISXTI temperature exponent for effect on IS - 3

L08 07Feb02 30

Gummel-Poon StaticModel Parametersname parameter units default areaIKF corner for forward beta A infinite *

high current roll-offIKR corner for reverse beta A infinite *

high current roll-offRB zero bias base resistance W 0 *IRB current where base resistance A infinite *

falls halfway to its min valueRBM minimum base resistance W RB *

at high currentsRE emitter resistance W 0 *RC collector resistance W 0 *TNOM parameter - meas. temperature °C 27

L08 07Feb02 31

Gummel Poon npnModel Equations

IBF = IS�expf(vBE/NFVt)/BF

ILE = ISE�expf(vBE/NEVt)

IBR = IS�expf(vBC/NRVt)/BR

ILC = ISC�expf(vBC/NCVt)

QB = (1 + vBC/VAF + vBE/VAR )��

{� + �� + (BF�IBF/IKF + BR�IBR/IKR)�����}

L08 07Feb02 32

Gummel PoonBase ResistanceIf IRB = 0, RBB = RBM+(RB-RBM)/QB

If IRB > 0RB = RBM + 3(RB-RBM)�(tan(z)-z)/(ztan2(z))

[�+���iB/(��IRB)]1/2-�(��/��)(iB/IRB)1/2

z =

Regarding (i) RBB and (x) RTh on slide 22,RBB = Rbmin + Rbmax/(1 + iB/IRB)�RB

L08 07Feb02 33

References

Semiconductor Device Modeling withSPICE, 2nd ed., by Massobrio andAntognetti, McGraw Hill, NY, 1993.

MicroSim OnLine Manual, MicroSimCorporation, 1996.

* Semiconductor Physics & Devices, byDonald A. Neamen, Irwin, Chicago,1997.