EE143 – Ali Javey

Section 7: Diffusion

Jaeger Chapter 4

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Dopant Diffusion Sources(a) Gas Source: AsH3, PH3, B2H6

(b) Solid SourceBN Si BN Si

(c) Spin-on-glass SiO2+dopant oxide

(d) Liquid Source.

EE143 – Ali Javey

Fick’s First Law of Diffusion

t coefficiendiffusion =DxNDJ

EE143 – Vivek Subramanian Slide 4-4

Fick’s Second Law of Diffusion

devicesmodernin situationsmany in t trueisn'which

t,independen-ionconcentrat is D Assumes

Eqn. Continuity with LawFirst Combine :Diffusion of Law Second sFick'

dimension) one(in

flux particle theof divergence theof negative the toequal ision concentrat of increase of Rate

:Flux Particlefor Equation Continuity

2

2

xND

tN

xJ

tN

EE143 – Ali Javey

B,P

As

10-6

Au

Cu

kTE

O

A

eDD

Diffusion Coefficients of Impurities in Si

SubstitutionalDiffusers Interstitial

Diffusers

EE143 – Ali Javey

Diffusion Coefficients

re temperatuabsolute=TJ/K x101.38=constant sBoltzmann'=k

energy activationE

ipRelationsh Arrhenius exp

23-

A

kTEDD A

O

EE143 – Ali Javey

(a) Interstitial Diffusion

Diffusion Mechanisms in Si

10-6 cm2/secAu

Cu

Fast DiffusionExample: Cu, Fe, Li, H

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(b) Substitutional Diffusion

Diffusion Mechanisms in Si

(c) Interstitialcy DiffusionExample: Dopants in Si ( e.g. B, P,As,Sb)

EE143 – Vivek Subramanian Slide 4-9

Constant Source DiffusionComplementary Error Function Profiles

FunctionError ary Complement=erfctCoefficienDiffusion

ionConcentrat Surface

2, :Dose Total

2, :ionConcentrat

0

00

0

DN

DtNdttxNQ

DtxerfcNtxN

EE143 – Ali Javey

Limited Source DiffusionGaussian Profiles

ProfileGaussian tCoefficienDiffusion

ion Concentrat Surface

2exp

2exp,

:ionConcentrat

00

22

0

DDt

QNN

Dtx

DtQ

DtxNtxN

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Two Step Dopant Diffusion (1) Predeposition dopant gas

SiO2SiO2

Si

dose control

(2) Drive-in Turn off dopant gasor seal surface with oxide

SiO2SiO2

Si

SiO2

Doped Si region

profile control(junction depth;concentration)

Note: Predeposition by diffusion can also be replaced by a shallow implantation step.

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Predeposition Drive-in

Normalized Concentration versus depth

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Diffusion of Gaussian Implantation Profile

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istep

ieffective DtDtBudgetThermal

)()(Example

Dttotal of :

Well drive-in

and

S/D annealing

Temp (t)

time

welldrive-in

stepS/D

Annealstep

Temp (t)

time

welldrive-in

stepS/D

Annealstep

For a complete process flow, only those steps with high Dt values are important

Successive Diffusions: Thermal Budget

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Solid Solubility Limits

• There is a limit to the amount of a given impurity that can be “dissolved” in silicon (the Solid Solubility Limit)

• At high concentrations, all of the impurities introduced into silicon will not be electrically active

EE143 – Ali Javey

High Concentration Diffusion Effects

Log C(x)

x

Low conc profile:Erfc or gaussian

Log C(x)

x

J large

J small

High conc. profile:D gets largerwhen C(x) is large

* C(x) looks “flatter”at high conc. regions

1) E-Field Enhanced Diffusion2) Charged point defects enhanced diffusion

EE143 – Ali Javey

Electric-field EnhancementExample: Acceptor Diffusion

Na(x)

Na(x)=Na-(x)

p(x)

hole gradient

x

Hole diffusion tendency

E build-in

Complete acceptorionization at diffusion temperature

At thermal equilibrium, hole current =0Hole gradient creates build-inelectric field to counteract the hole diffusion tendency

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B-

+[p]holes tends to moveaway due to holeconcentration gradient

Ebuild-in

B- acceptorsexperiencean additionaldrift force

Enhanced Diffusion for B- acceptor atoms

Electric Field Enhancement

EE143 – Ali Javey

Asdiffusion

Uniform B conc in substrate

caused by Asconc gradient

B-

Electric Field Enhancement – Substrate Perturbation