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EE143 – Fall 2016Microfabrication Technologies

Lecture 8: DiffusionReading: Jaeger Chapter 4

Prof. Ming C. Wu

wu@eecs.berkeley.edu

511 Sutardja Dai Hall (SDH)

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

(b) Solid Source BN Si BN Si

(c) Spin-­on-­glass SiO2+dopant oxide

(d) Liquid Source.

ceramic wafer of boron nitride

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3

Fick’s First Law of Diffusion

t coefficiendiffusion =DxNDJ¶¶

-=

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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

¶¶

¶¶

¶¶

¶¶

=

-=

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5

B,P

As

Au

Cu

kTE

O

A

eDD-

=

Diffusion Coefficients of Impurities in Si

SubstitutionalDiffusers Interstitial

Diffusers

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Diffusion Coefficients

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

energy activationE

ipRelationsh Arrhenius exp

23-A =

÷øö

çèæ-=kTEDD A

O

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(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)

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Constant Source DiffusionComplementary Error Function Profiles

( )

( )

FunctionError ary Complement=erfctCoefficienDiffusion

ionConcentrat Surface

2, :Dose Total

2, :ionConcentrat

0

00

0

==

==

÷ø

öçè

æ=

ò¥

DN

DtNdxtxNQ

DtxerfcNtxN

p

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Limited Source DiffusionGaussian Profiles

( )

ProfileGaussian tCoefficienDiffusion

ion Concentrat Surface

2exp

2exp,

:ionConcentrat

00

22

0

=

==

úúû

ù

êêë

é÷ø

öçè

æ-=úúû

ù

êêë

é÷ø

öçè

æ-=

DDtQNN

Dtx

DtQ

DtxNtxN

p

p

6

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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 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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å=istep

ieffective DtDtBudgetThermal

)()(

Example: Dttotal for Well drive-in and S/D annealing

Temp

time

welldrive-­instep

S/DAnnealstep

Temp

time

welldrive-­instep

S/DAnnealstep

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

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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

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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 tend to moveaway due to holeconcentration gradient

Ebuild-­in

B-­ acceptorsexperiencean additionaldrift force

Enhanced Diffusion for B-­ acceptor atoms

Electric Field Enhancement

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Asdiffusion

Uniform B conc in substrate

caused by Asconc gradient

B-­

Electric Field Enhancement – Substrate Perturbation

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Example : High Concentration Arsenic diffusion profile becomes “box-­like”

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Summary of High-­Concentration Diffusion

• If doping conc < ni:– Use constant diffusivity solutions– (profile is erfc or half-­gaussian)

• If doping conc > ni:– Solution requires numerical techniques

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Transient Enhanced Diffusion (TED)Dopant Implantation

Sisubstrate

Implantationinduced excesspoint defects

x

C(x)no annealing

900oC, several sec (TED)Extremely rapid diffusion due to excess point defects

Implantation createslarge number of excess Siinterstitials and vacancies.(1000X than thermal process).After several seconds of annealing, the excess point defects recombine.

900oC, several minutes(After excess point defects recombine. slower diffusion)

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Diffusion: p-­n Junction Formation

÷÷ø

öççè

æ=

÷÷ø

öççè

æ=

=

0

B1-

B

0

NNerfc 2 :profileFunction Error

NNln 2 :ProfileGaussian

doping) type-nout cancels doping type-p e. (i. zero ision concentrat

impuritynet the wherepoint at the occursjunction n -P

DepthJunction calMetallurgi

Dtx

Dtx

xx

j

j

j

j

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Sheet Resistance

Square]per [Ohms ResistanceSheet =t

R

WLR

WL

tR

tWA

S

S

r

r

=

÷øö

çèæ=÷

øö

çèæ÷øö

çèæ=

•=

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Resistivity vs. Doping

r =s-1 = q µnn + µp p( )[ ]-1

n- type : r @ qµn ND -NA( )[ ]-1

p- type : r @ qµp NA -ND( )[ ]-1

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Resistivity Measurement: Four-­Point Probe

tMeasuremen Resistance TerminalFour

/square][ 53.42ln

t>> sfor m]-[ 2ln

s>>for t m]-[ 2

W@==

W=

W=

IV

IV

tR

IVtIVs

Spr

pr

pr

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Impurity Profiling withSecondary Ion Mass Spectroscopy (SIMS)