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1-2003

Optical properties of materials for 157 nm

lithography

Anatoly Bourov

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Recommended Citation

Optical Properti

e

s of I'vlaterials

for

157 nm

Lithograph

y

by

Ana

toly

Bourov

BS Physics,

RIT

A thesis

submitt

ed in p

artia

l

fulfillm

ent of the

requirements

for the

degree

of Mas

ter of Science

in the

De

pa

rtment of rvIicro

e

l

## ectronic

En

ginee

ring

Rochester Institute

of Tec

hnology

August, 2003

The

disse

rtation

of Anatoly Bourov is approved

:

Prof. Bru

ce W. Smith

Prof. D

a

le Ewbank

Date

8-1-

**0**

**0**

3

Prof. Mi

chael J

ackson

D

ate

Rochester Institute

of Technology,

Rochester

,

NY

THESIS RELEASE PERI

'vIlSSION

## ROCHESTER

INSTITUTE

OF TECHNOLOGY

D

EPARTI

'vIENT 0 F Microelectronic EN G

INEERIN

G

Title of Thesis:

Optical Properties of Materials for 157

nm

Lithography

I

,

Anatoly Bourov, h

e

reby grant permission to

'Wa

ll

ace Memorial

Library of

R.I.T. to reproduce my thesis in whole or in part

.

Any reproduction will not be

for

commercial

## use or profit.

Optical Properties

of

Materials

for

157

nm

Lithography

by

Anatoly

Bourov

Submitted

to the

Department

ofMicroelectronic

Engineering

in

partialfulfillment

ofthe

requirementsfor

the

Master

ofScience

Degree

at

the

Rochester Institute

ofTechnology

Abstract

A

survey

of optical properties of sputtered materialsin

the

spectral range of145

nmto

800

nmhas been

performed.The

optical constants n andk have been

measured

## using

ellipsometrictechniques.

Four

combination materialshave been

created withthe

properties suitablefor

applicationin

Attenuated

Phase

Shift

Mask

(APSM)

manufacturing.The four

combination materialshave

alsobeen

To Rose

of

Sharon

Daly,

whose

incessant nagging

made completion

Contents

Acronyms

viiSymbols

ix

Elements

andCompounds

xi1

Introduction

1

1.1

Evaluating Microlithography

Process

. .1

1.1.1

## Attenuated Phase

Shift

Mask

. . ...3

1.2

Dielectric

constantmodeling

... ... ...4

1.2.1

Lorentz Oscillator

.... . .5

1.2.2

Free

electron plasma . .... ...6

1.2.3

Cauchy

approximation . . . . ...7

1.3

Effective Medium Models

. . .8

1.3.1

Wiener Bounds

. . ....8

1.3.2

Effective Media Approaches

. . . .121.4

Fresnel

equations ... .14

1.5

Phase Shift

andTransmission

... . . . .161.6

Modeling

ofComposite

APSM

materials . .17

2

Experimental

18

2.1

Thin

film deposition

... . .18

2.1.1

Capacitatively

Coupled

Glow

discharge

plasma18

2.1.2

## Sputtering

.... . . .19

2.1.3

Reactive

sputtering

using

RF

power source20

2.1.4

Single

target

mode vs.Dual

target

mode . ...21

2.1.5

Deposition

ofComposite Materials

.22

CONTENTS

m2.2.1

Profilometry

24

2.2.2

Spectrophotometry

... .24

2.2.3

Ellipsometry

. .... . .26

Results

27

3.1

Materials

Database

....27

3.2

Composite Materials

32

3.2.1

Analysis

32

3.3

Summary

ofMeasured

Films'Properties

at157

nm ....32

3.4

Conclusions

.34

List

of

Figures

1.1

Progress

oflithography

systems'

resolution. .

2

1.2

An illustration

of## the working

principle ofAPSM.

. . .3

1.3

Representation

offield-induced

dipole

moment.5

1.4

A

periodicassembly

ofdisparate layers.

9

1.5

An

example ofthe

Wiener bounds for

two

materials11

1.6

An

example ofthe

EMA

model.14

1.7

Diagram

of electricfield

notation usedfor TM-polarization

set ofFresnel

equations. . .15

1.8

Notation

usedin

the

calculation ofthe

modeledtransmission.

.16

2.1

A

typical

sputtering

chamber setup.19

2.2

Dual

target

chambersetup,

withboth

targets

on atthe

sametime.

21

2.3

## The data

usedfor

power calibrationin

the

composite mode ofsputtering. . ... . .

23

2.4

A

schematic representation ofa profilometer scan. ...25

2.5

Example

of a spectrophotometry measurement. ...25

3.1

An

example plot ofthe

experimentaland modeled^

valuesfor CrOx. 29

3.2

An

example plot ofthe

experimental and modeledA

valuesfor

CrOx.

... ...29

3.3

An

example plot ofthe

optical properties ofCrOx.

. . . .30

3.4

The dielectric

constant ofCrOx.

. . .30

3.5

A

summary

plot ofthe

dielectric

constant at157

nm. . ...31

3.6

Transmission

for

the

final APSM

candidate materials. . .33

A.l

XPS

spectrum ofNb-based APSM

film,

taken

atthe

surface . .38

A. 2

XPS

spectrum ofNb-based APSM

film,

## taken

at14

nm underthe

surface. ... ... ... ...

39

A. 3

XPS

spectrum ofMo-based APSM

film,

taken

atthe

surface. ...40

LIST

OF FIGURES

A.4

XPS

spectrum ofMo-based APSM

film,

taken

at14

nm underthe

surface. . . .41

A. 5

XPS

spectrum ofCr-based APSM

film,

taken

atthe

surface. .42

A. 6

XPS

spectrum ofCr-based

APSM

film,

taken

at14

nm underthe

List

of

Tables

3.1

## A list

of materials surveyed ...28

3.2

List

of composite materialsdeposited.

. .33

A.l

Summary

of materialfractions

in

manufacturedAPSM

films

as measuredby

XPS. The

ratio of respective metalto

Si is

given.37

Acronyms

CD Critical dimension. The

smallestfeature

presentin the

objectto

be

imaged.

OPC Optical

Proximity

Correction.

A

technique that

correctsfor

non-ideality

of

the

imaging

systemby

pre-distorting

the

object.OD Optical

Density

is

the

log

ofthe

attenuation## factor

of an optical component.VUV Vacuum Ultra Violet.

VUV defines

the

spectral region of wavelengthvalues

between 15

nm and185

nm.DUV

Deep

Ultra Violet. Spectral

region of wavelength valuesbetween 185

nmand

300

nm.RET

Resolution Enhancement Technique.

A

method ofovercoming

the theo

retical resolution

limit

of a conventional opticalimaging

system.APSM Attenuated Phase Shift Mask. The

type

of mask usedin

## microlithogra-phy that

produces enhanced aerialimage

contrast.MSE

Mean

Square Error. The

indicator

of aquality

offit.

VASE Variable Angle Spectroscopic Ellipsometry:

Thin

film

characterizationtechnique

that

allows accurate measurement of optical constants n andk.

PVD Physical Vapor

Deposition,

or sputtering.Thin

film deposition

technique

that

allows control offilm

composition and microstructure.IC Integrated Circuit. An

electronicdevice

manufacturedin

a sequence of unit steps at a semiconductor## fabrication

facility

ACRONYMS

viiiDOF Depth

ofFocus. Range

offocus

positions with acceptableimage fidelity.

NA

Numerical Aperture

of alens.

EMA

Effective Media Approximation.

A

model oflight-matter

interaction that

allows

for

estimation ofthe

composite material optical properties.XPS

X-ray

photoelectron spectroscopy.An

analysistechnique that

allowsto

Symbols

n refractive

index.

k

extinctioncoefficient,

or## imaginary

part ofthe

complex refractiveindex

h

complex refractiveindex:

h

=_{n}

+

_{\k}

e complex

dielectric

constant: e = ft'2A

wavelength oflight.

E

electricfield

vectorB Magnetic field

vectorD

electricdisplacement

vectorE'

local

electricfield

vectorp

dipole

moment vector.P

averagedipole

moment per unit volume vector.N

concentration,

or number of atoms per unit volume.a

polarizability,

p

=_{qE'.}

k\

resolutionfactor

k2

Depth

ofFocus factor

^

ellipsometric magnitude: representsthe

magnitude ofthe

ratio of complexreflection coefficients

for

two

different

polarization states.SYMBOLS

xA

ellipsometric phasedifference:

phasedifference between

the

two

waves with## different

polarizationp

ratio of complex reflection coefficientsin

an ellipsometric measurement.rj_

Amplitude

reflection coefficientin

TE

caser||

Amplitude

reflection coefficientin TM

caseR

Intensity

reflection coefficientin TE

caseR\\

Intensity

reflection coefficientin TM

caseA$ Phase Shift

Elements

and

Compounds

AI2O3

aluminaMo Molybdenum

MoN Molybdenum Nitride

MoO Molybdenum Oxide

CrOx

Chromium

Oxide

CrN Chromium Nitride

Cr Chrome

Nb Niobium

NbN

Niobium

Nitride

Nb205

Niobium

Oxide

Zr

Zirconium

ZrN

## Zirconium

Nitride

Ti

Titanium

TiN

Titanium

Nitride

Ti02

Titanium

Oxide

Ta

Tantalum

TaN

Tantalum

Nitride

ELEMENTS AND COMPOUNDS

xuTa205

Tantalum

Oxide

Si02

Silicon Oxide

Chapter

1

Introduction

1.1

Evaluating Microlithography

Process

The

performance of opticallithography

andits

limitations

canbe best

quantifiedconsidering the

mainfigures

of merit:## Critical dimension

(CD),

andDepth

ofFocus

(DOF).

CD

=k^

(1.1)

DOF

=k2J^

(1.2)

Here,

CD

representsthe

minimumfeature

that

canbe

patterned with a particular opticallithography

system.As

canbe

seen,

CD is dependent

onthree

parametersof

the system,

resolutionfactor

(hi),

wavelength(A),

andNumerical Aperture

(NA)

[1].

The

resolutionfactor

representsthe

"quality" ofthe

imaging

system andis higher

than

0.5 for

a conventional coherent setup.This is

atheoretical

limitation,

impossible to

achievein

practice.It

canbe

approachedby lowering

the

lens

aberrations and## enhancing the

contrast ofboth

the

aerialimage

andphotoresist.

The

othertwo parameters, the

actinic wavelengthA

andthe

imaging

tool

NA

are muchharder

to change,

leading

to very

slow rate ofchange,

as shownin

Figure

1.1.

Lowering

the

theoretical

limit

onk\

is

the

most cost efficientway

ofimproving

resolution.

Some

ofthe

techniques

that

extendthe

limit

to

## 0.25 include

off-axisCHAPTER

1.

INTRODUCTION

bO

a Qj

>

'c

10

0.1

0.436

Progress

ofthe

resolutionfactor

Resolution

Wavelength

Sub-wavelength

Above

wavelength0.11

1980

1985

1990

1995

Year

2000

2005

Figure

1.1:

Progress

oflithography

systems'

CHAPTER

1.

INTRODUCTION

1.1.1

Attenuated

Phase Shift Mask

In

this

approach,

the typical

binary

absorberis

replaced with aphase-shifting

attenuator

layer. This

creates a"negative"

electric

## field

in

place ofnofield,

thus

enhancing

contrast ofthe

image,

seeFigure

1.2

[1].

Conventional

Binary

Mask Attenuated Phase Shift MaskFigure

1.2:

An illustration

ofthe working

principle ofAPSM. Note

the

widerdynamic

range(or

higher modulation)

in the

image

onthe right, resulting

in

higher image

contrast.The

materialcommonly

usedin

the

conventionalbinary

masksis

a gradedcomposite of

Cr, CrN,

andCrOx.

It

provides an## Optical

Density

(OD)

of3

orhigher

atthickness

values around1

kA.

This

material cannotbe

usedin

the

APSM

casedue

to

its high

absorption characteristics.The

requirementsfor

asuccessful

APSM

material arelisted below:

Phase

shift of n(typical

thickness

of approx.1

kA)

Thickness

non-uniformity

better

than

0.5%.

Transmission

ofbetween

6%

and20%

(tunable)

Etch

process compatible with semiconductorfabrication

requirements,

capable of

low defect levels

## Deposition

process capable oflow defect levels

CHAPTER

1.

INTRODUCTION

As

the

transmission

ofthe

APSM layer has

to

be

adjustedaccording to the

layout

requirements,

no single-component materialis

acceptable.The

successfulAPSM

materialhas

to

be

comprisedoftwo

or morecomponents,

whose ratiowilldetermine

the

final

transmission

at it phase shift.While

bulk

materialdata is

readily

available[4],

the thin

film

opticalprop

erties

## may be significantly different.

Sputtered

film data is

_{available}

_{at}

A

=193

nm[5,

6],

but

there

is

no availabledata

atA

=157

_{nm.}

The

_{ensure}

that

no possible

winning

combinationis

missed,

asurvey

ofthe

optical propertiesin

the

Vacuum

Ultra Violet

(VUV)

spectral regionhas

to

be

undertaken.After

the

material optical properties are

collected, the

candidatesfor APSM films have

to

be

identified. The

composite## films

arethen

to

be deposited

and analysed.If

all ofthese

steps aresuccessful,

the

candidate materialsfor APSM layer for

the

157

nm node canbe

consideredidentified.

1.2

Dielectric

constant

modeling

The

complexdielectric

constant(e)

of a materialis

defined

as[7]:

D

=_{eE}=

E

+ 4vrP

(1.3)

Here,

electricdisplacement

vector(D)

is

sometimes referredto

asthe

electricfield inside

the

dielectric.

In

the

case of ahomogeneous isotropic

mediumthe

solution can

be found

## exactly

in

two

steps.First,

the

electrostatic problemis

solved

to

obtainlocal

electricfield

(E'),

anddipole

moment(p).

Then,

these two

quantities are averaged

to

obtaintheir

macroscopiccounterparts,

electricfield

(E)

and average

dipole

moment per unit volume(P).

The

relationship

between

the

local

electricfield

andthe

total

dielectric

mo mentis

givenby

the

Clausius-Mossotti

expression[7,

8].

E' =

E+-^P

(1.4)

## Considering

e>p

= aE'or

P

=Np

= NaE'(1.5)

where a

is

polarizability

ofthe

particle andN is

the concentration,

or particlecount per unit

volume,

andcombining

with equation(1.3),

we obtainthe

Lorentz-Lorenz

equation-1

4i

,=

Na

1.6

+2

3

CHAPTER

l.

INTRODUCTION

1.2.1

Lorentz

Oscillator

The

Lorentz

Oscillator

model offersthe

simplest picture of atom-fieldinterac

tions.

It is purely

classical,

however,

this

_{model}

is

_{an elegant}

tool

for

visualizing

and

## approximating

the

frequency-dependent

dielectric

constant.nofield

E'

Figure

1.3:

Representation

offield-induced

dipole

moment.In

this

modelthe

atomis

representedby

a mass(nucleus)

connectedto

asmaller mass

(electron)

by

a spring.The

electronis

setinto

motionby

the

im

pinging

electricwave,

andis

kept in

the vicinity

ofthe

nucleusby

the spring

returnforce. Lorentz did

not suggestthe

existence of a physicalspring connecting the

electron and

## the nucleus, rather,

it is

a generalizedforce

that

canbe

adequately

described

by

Hooke's

Law,

i.e.

F(r)

=kt,

where ris

the

displacement

from

equilibrium,

and kis

the returning

force

constant.This

system canbe described

by

the

Abraham-Lorentz

equation[7]

mr

+

71*+

Kr=eE'(t)

;i.7)

where e

is

the

charge onthe electron,

mis

the

mass ofthe

electron.The

equationis

quite commonin

mathematicalphysics,

andLorentz

wasaware of

this.

It

wasthus easily

solved.The

only

term

that

can notbe

explained## classically

is

the

damping

coefficient 7.The

main sources ofdamping

are atomiccollisions,

and spontaneous emission.The

specificform

of equation(1.7)

consideredby

Lorentz

wasthe

case represented

by

E'(t)

= E'0e-',UJt(1.8)

where

E'n

is

a real-_{valued vector.}

The

impinging

electromagnetic wavethus

has

frequency

u> andlocal

amplitudeE'0-The

non-dampening

solutionin this

caseis

representedby

(1.9)

CHAPTER

1.

INTRODUCTION

where

And

thus,

considering

that

771

we obtain

e2E'

P

=Ap

=Ner

=N

e *

,

(Lll]

771

(cJq

UJ)

1^7

A^

=A

(

26'

(1-12)

m

(oJq

w^)

1W7

## Now. comparing

with equation(1.6)

it

follows:

3

"1

_{,T}e2

,

1

n=N^~2^

:(1-13)

47r

+

2

m(ul-uj2)

-itu7

For

agas,

canbe

considered closeto

1,

therefore

+ 2

rs3

andthe commonly

known form

ofthe

Lorentz dispersion

relationship

canbe

obtained:47rAe2

~1

+

r^

2^

L14

m

[u)q

uiz)

io;7

So far it has been

assumedthat

the

systemhas

only

one resonancefrequency. In

general, there

willbe

many

suchfrequencies. In

this

case-Na =

S

=V

-2

f*

(1.15)

3

+

2

3

*-

m(uj2-uj2)

-iw7fc

v ;where

Nfk

is

the

number of electrons## corresponding to the

resonancefrequency

uk.1.2.2

Free

electron plasmaThe Drude free-electron

plasma model canbe

obtainedfrom

equation(1.13)

by

setting the restoring

force

to

zero(uj0

=0).

In

this case, the

plasmafrequency

2 _

4-nNe2

^ ^e

meantime

between

collisions r =_{are}

introduced.

The

V m 7

expression

is

then

reducedto

_

1

1

4?rAe21

oj2(1.16)

CHAPTER

1.

INTRODUCTION

Or,

in

the

case of rs1

,2

^

(1.17)

w2+ i

_{r}

This

modelhas

provento

be

of usein

representing

conductivematerials,

wherethe

majority

contributionto

## field-matter

interaction

is

due

to the

free

electrons.In

this case, the

bound

electrons are consideredinsignificant.

For

real-worldapplications,

allterms

shouldbe

considered,

andthe

Drude

modelbecomes just

one of

the terms

in

summation equation(1.15)

withuj0

=0.

1.2.3

Cauchy

approximation

The

approximateformula

developed

by

Baron

Augustin-Louis

Cauchy[9],

is

ap

plicable

to

a wide range ofmaterials.It

canbe

obtainedfrom

the

equation(1.15)

by

## assuming

that the

dielectric

constantis

closeto

one(as

is for

many gases),

andthat

no absorptionis

presentin the

material.Despite

these assumptions,

the

formula

has

provento

provide accuratedispersion

relationship

for

many

di

electric materials.

With

slightmodifications,

it

canbe

extendedto

coverDeep

Ultra Violet

(DUV)

and evenVUV

spectral regionsfor

certain materials.It

is,

therefore,

ofgreatinterest for

this

study.To

obtainthe

## Cauchy

formula,

the

Lorentz dispersion

relationship

has

to

be

re-_{written}

in the

form

(assuming

=_{-R}

(e)

= n2~

1

_{and}

7^

=0):

A2A2

n2-l =

4TvNa

=Y,Pky

3^,(1-18)

l, k

where

Using

the

identity

A2-A2 'A2-A2

and

applying the

Taylor

expansion seriesPk

=N^-^h

irmc2(1.19)

V

1 +

A

(1-20)

B

C

2

1

=A+

+

+

A2 A4

/_{\}2 n>_{\}4

CHAPTER

1.

INTRODUCTION

where

PkK

^

=E,A&

b

=y.^.

c

=Y.

B--sr^Pk^k

~Z_>

c2 fc B' =X^2,

it /,H

^' =5"P*T-.

(!-22)

^-A

fcIn

the

absorption-free

region,

wherethe

value ofrefractiveindex

(n)

differs little

from

## unity,

n2-1 may be

replacedby

2(n

-1).

Moreover,

the terms

B',

C,

. .usually do

not exhibit appreciableinfluence.

Therefore,

if only terms

no smallerthan

O

(p-)

areretained, the

equation(1.21)

canbe

reducedto

Cauchy

:s formula:

where

n =

1 +

Ai

(-)

<-f

-1

;i.23)

(1.24)

1.3

Effective Medium

Models

1.3.1

Wiener

Bounds

Let

us considerthe

bounds

onthe

dielectric

constant of aheterogeneous

material,

consisting

oftwo

(or

more) homogeneous

## components[10, 11. 12].

Boundary

perpendicularto

field

In

the

simplified case of periodicassembly

oflayers

oftwo

disparate

materials,

components

1

and2.

Let

t\,

andt2

be

the thickness

of eachlayer;

whilei,

and2

arethe corresponding

dielectric

constant of each component.Consider

a plane monochromatic waveincident

onthe

structurein

Figure 1.4

with

the

electricfield

vector perpendicularto the

planes.If

the

characteristicdimensions

ofthe

structure(t\,

andt2)

are small comparedto the

wavelength oflight

A,

the

field

## inside

the

layers

canbe

considered uniform.The

normal component of

the

electricdisplacement

vectorD

mustbe

continuous atthe

materialsboundaries.

Therefore

(1.25)

D

D

Ei

=-E2

=CHAPTER

1.

INTRODUCTION

l

i

tt

',

2

2

02

tl

CHAPTER

l.

INTRODUCTION

10

and

the

mean electricfield

averaged over volumeis

h^

+

t2^E

= _bilii

(1.26)

h+h

The

effectivedielectric

constant of mediain

this

caseis

-1

e

^-

+

-^ El 2or

1*

=

W

+

W

(1-28)

where

h

=t4t

> andi'2

=T^tr

=

l

~h

(L29)

Cl

-+-t2

t\

-t-12

This

caseis

representedby

the

curvedline

in

Figure

1.5.

Boundary

Parallel

to

field

In

the

case withthe

electricfield

vector parallel## to the

layer boundaries in

Fig

ure

1.4

onthe

preceding

pagethe

electricfield

itself

is

continuous atthe

boundary.

Thus

D!

=E!.

D2

=E2

(1.30)

and

the

mean value ofD is

UEei

+

t2Ee,2

D

=j

1

2_

2^^

h

+

h

with

the

effective mediadielectric

constantD

1i

+

22

11

E

h

+

12

This

caseis

representedby

the

straightline in

Figure 1.5

CHAPTER

1.

INTRODUCTION

11

Example

ofWiener

bounds

Figure

1.5:

An

example ofthe

Wiener bounds for

two

materials.The

two

materials are represented

by

the

## dots labeled

i

and 2.The

two

lines

representthe

possible mixed materials

for

the

two

limiting

cases.The

area_{il(1;}

2) bound

by

n and

_l

represents all ofthe

possible materialsthat

canbe

obtainedby

mixing

2-CHAPTER

1.

INTRODUCTION

12

Intermediate

casesWhile

the

valuesy,

andj_

above represent a small portion ofreal-lifescenarios,

they

werefound

to

bind

the

effectivedielectric

constant of anarbitrary

mixtureof

the two

materials.In

other words,for

any

possible physical structuralform

of

## mixing

the two

materials withdielectric

constants :. and2,

the

resulting

dielectric

constantEeff

has

to

lie

withinthe

regionQ(ei,

e2) defined

by

the

expressions ||. and

X

((1-32)

and(1.28),

respectively).Any

combination ofthe

two materials,

withany

fractional

weighting

/i,

withany

structure ofthe

composite material,

has

to

have its dielectric

constante//

in

the

regiondefined

by

the

## Wiener bounds.

A

more strictrestriction,

considering

some microstructureinformation is

exploredbelow

1.3.2

Effective Media Approaches

Let

us consider a case oftwo

(or

more)

materialsintermixed

on a molecularscale.

Applying

the

Lorentz-Lorenz

_{equation}

(1.6)

on page4

independently

to

both

materials we obtainl

~1

4%

at

2

~

l

4lv

at n no\

I7T2

= YN^7TT2

= T7^2(L33)

Combining

the

above with equation(1.6)

andNa

=N1ai

+

N2a2

(1.34)

we obtain

/i^

+

/2^

(1-35)

+

2

j +

2

2 + 2

where

Ai

o^

-K?n2

(1'36)

is

the

volume materialfraction.

The

expression(1.35)

is

the

basis

ofallEMA

models,

whichdiffer

in

defining

CHAPTER

1.

## INTRODUCTION

13

Bruggeman

modelIn

the

Bruggeman

Model

[13]

the

self-consistent assumptionis

made.The dielec

tric

constant ofthe

mediumin

whichthe

particles are suspendedis

taken to

be

the

same asthe

complexdielectric

constant(e)

ofthe

composite medium.With

that

assumption,

we obtain:A-TF

+

^-TF

+

/3^7L+

--- =### 0

(1.37)

i +

A

2 +

Kt

3 +

A

Here,

multipletypes

of particles are embeddedin

the

same medium.The

valueof

K

2

representsthe

assumption of spherical microstructure(this

assumptionwas used

to

obtain equation(1.6)).

In

principle,

the

Bruggem.an

theory

shouldbe

validfor

all values of/

asit

## treats the

componentsin the

mixture on an equalbasis.

However,

when one component's ratiois

muchhigher

than the

other's,the

retarding

nature ofthe

induced

polarization mustbe

taken

into

account.Maxwell Garnett Model

This

approach makesthe

assumptionthat

one or more materials(2,

or3)

aresuspended

in the

host

medium ofanother material(1)

[14].

l"

f2^-

+

h^-(1-38)

+

2i

2 +

2i

3 +

2i

where

fi, f2,

and/3

arefractional

weights ofthe

constituents, with/1+/2+/3

=1-As is

implied in

its

derivation,

this

formula is

asymmetrical with respectto

the

choice of

the

host.

The

## accuracy

ofthis

approachis

best

when one materialis

present

in

overwhelming

amount.Therefore,

this

approachis

limited

to

smallvolume

fractions

f2

andfs-The Effective Media Approximation

modelThe

combination ofboth

approaches,

the

EM

A

theory

developed

by

Aspnes[8]

can explain

both Maxwell Garnett

andBruggeman

cases.The

effectivedielectric

function in

the

EM

A

theory

## is defined

as12 + (/ll +

/22)

_{n}_..

=

= _{77} r \

(1.39)

+

(/i2

+

/2i)

where

=

(1~9)h".

CHAPTER

1.

INTRODUCTION

14

Here,

q

is

ascreening

parameter(or

the

depolarization

factor)

withthe

rangeExample

ofthe

EMA

modelF

Figure

1.6:

An

example ofthe

variationin

optical propertiesaccording to the

EMA

model.The

ema

kne

representsq varying

from 0

to

1,

while/j

=0.7.

0-1.

The

actual value ofthe

depolarization

factor

(q)

is

determined

by

the

specificgeometrical configuration of

the

particles.## Namely,

the

Wiener bounds

are givenby

q

=0,

andq

=I,

_{while}

the

two-dimensional

macroscopically isotropic

caseis

represented

by

q

=1/2,

_{and}

the

three-dimensional

_{case of perfect}

mixing is

givenby

q

=1/3.

An

_{example}

_{of}

the

_{change}

in

optical properties withvarying

q

is

given

in Figure

1.6.

1.4

Presnel

equations

CHAPTER

1.

INTRODUCTION

15

based

on ellipsometric measurements.The

reflectance coefficientsfor both

polarization

states canbe

modeledusing

the

materialdata,

thin

film

model ofthe

physical structure and

the

## Fresnel

equations.The

materialdata

(n

and extinction

coefficient(A:))

canbe

thus

determined

if the

physical structure usedin

the

model

is

correct.k><

yEr .

B\

Figure

1.7:

Diagram

of electricfield

notation usedfor TM-polarization

set ofFresnel

equations.In

general,

when a wave reaches a materialboundary,

part ofthe

waveis

reflected and part

is

transmitted,

withthe

total

energy

preserved.The

coefficientfor

reflection ofthe

"transverse

electricfield"'

wave(see

## Figure

1.7)

is

denoted

r,

while

the

coefficientsfor

the

reflection ofthe

"transverse

magneticfield"

wave

is

denoted

r\\.Power

(or

intensity)

coefficients aredefined

asthe

square ofthe

o i [2

corresponding

amplitudecoefficients, i.e.

R

=\r\

, andi?y

=

ry

.In

the

case ofnon-magnetic materialsthe

reflection coefficients are:r

Er

Et

n\

cos9-n2

coset

h\

cos9

+

n2

COS0,

n2

cose-fix

COSot

hi

cos9t

+

h2

cos9

Using

Snell's law

h\

sin9

=h2

_{sin}

9t

the

equations canbe

simplifiedto:

sin(#

-9t)

r

r\\ =

sm(8

+

9t)

tan(9

-9t)

sin9t

cos9t

sin9

cos9

tan(9

+

9t)

sin9

cos9

+

sin9t

cos6t

(1.41)

(1.42)

(1.43)

(1.44)

CHAPTER

1.

INTRODUCTION

16

Figure

1.8:

Notation

usedin

the

calculation ofthe

modeled## transmission.

In

the

case of normalincidence,

the

magnitudes ofr

andr\\

areequal,

andare reduced

to

-r =

r\\

/?

Rn

n2

-nx

h2

+

hi

n2

-n-i

h2

+

hi

(1.46)

(1.47)

1.5

Phase

Shift

and

Transmission

Direct

measurement of phase shift at157

nmis

notcurrently possible, there

fore,

the

measured n andk

values were usedto

modelthe

phase shift andthe

transmission

ofthe

proposedAPSM

materials.The

transmission

loss

due

to

absorptionin

the

phase shiftfilm is

Tabs

=_{e}A kd

(1.48)

where

d is

the

physicalthickness

ofthe

film.

## Considering

the

relativetransmission

with respect

to the

clear areas onthe mask,

(1

-R12)

(1

-R23)

T

ret eA kd

1-Ri3

Here,

the

reflectance coefficients are calculatedusing

Fresnel

equations(1.47)

(1.49)

Rn

ni

n2

hi

+h2

(ni

-n2f

+

(fci

-k2f

CHAPTER

1.

INTRODUCTION

17

The

phase shiftis

calculatedsimilarly,

withthe

phase shiftin

the

APSM film

when compared

to the

phase shiftin

air givenby

2tt

A$

=(n2

-n3)d

+

A$12

+

A$23

-A$13

(1.51)

A

The interfacial

phaseterm

is

givenby

A$12

=arg

h-)

(1.52)

1.6

Modeling

of

Composite APSM

materials

In

additionto

EMA

## modeling

described

in

Section

1.3

some moredetailed

analysishad

to

be

performedbefore

the

composite materials couldbe deposited.

Utilizing

the

modelsin

Section

1.3,

the

atomicfraction

ofthe

absorber material canbe

determined. The fractional

volume occupiedby

each material canbe

calculatedv=f~

(1.53)

P

where v

is

the

volumefraction,

/

is

the

atomicfraction,

A is

the

atomicweight,

and

p

is

the

density

ofthe

materialin

consideration.The

volumefraction

canthus

be

calculatedby

normalizing the

## total

volume:, <Jirei

vi

+

v2

=1

_{=>}

vi

=-(1.54)

Vl,rel + ^2,reZ

Vl

=f A r.

(L55)

1 _i_

h AzPi

v '

After

the

thickness

ratios ofthe

two

materialshave been

calculated,

deposition

tool

power ratios needto

be

modeled.This is done

using the

proceduredescribed

in Section

2.1.5.

The

total

deposition

time

is

adjustedusing

equation(2.1)

to

achieve it phase shift.

The

procedurefor

modeling the

phase shift## based

onChapter

2

Experimental

2.1

Thin

film deposition

Optical

requirementsfor

the

materials understudy

dictate

the thickness

ofthe

materials

in

question.These

considerations, along

withmanufacturing

compatibility,

lead

to

Physical Vapor Deposition

(PVD)

asthe

processtechnique.

This

technique

allowsto

deposit

very

thin

films

with## highly

controlled and customizable physical properties.

The

setup

ofthe

sputter(PVD)

chamber atRIT

allowedfor

a physical mixture oftwo

materialsto

be deposited. Two distinct

methods ofintermixing

the

materials are possibleAtomic level

mixing,

ordeposition

oflayers

of averagethickness

onthe

order of

1

A

orless

Superlattice

type structure,

ordeposition

ofdiscrete layers

withthickness

on

the

order of1/10

ofthe

wavelength of## interest

For

this research, the

two-target

approach,

orthe

atomiclevel mixing

was utilized.2.1.1

Capacitatively

Coupled

Glow discharge

plasma

The

plasma usedin

sputtering

is

typically

characterized as "nonthermal" plasma[16,

17,

18].

This describes

the

condition of matterin

whichthe

electrons arevery

energetic while

the

bulk

ofthe

molecules are near ambienttemperature.

To

createthis condition, the ionized

matterhas

to

be

presentin

gasform,

atthe

pressure## between 1

mTorr and50

mTorrA

negative electrodeis introduced into

the

CHAPTER

2.

EXPERIMENTAL

19

vicinity

ofthe gas,

accelerating

the

existing

gasions

towards

it.

These ions bom

bard

the

cathode,

discharging

secondary

electrons,

which arerapidly

acceleratedaway

from

the

cathode.These

high

energy

electronsionize

the

gas molecules on## impact,

the

ions

bombard

the

cathode andthe

processis

thus

sustained.The

ionization

process produces a photon, whichis

responsiblefor

the

"Glow'' part of

the

processdescription.

2.1.2

Sputtering

To

utilizethis

processto

producethin

films,

atarget

made ofthe

materialto

be

sputteredis

placed onthe

cathode.Argon is

used asthe

plasma gas.The

advantageous properties of

Ar

gas arethat

it is

inert,

andreadily

availablein

Ultra High

## Purity

form.

The

atomic weight ofAr

allowsthe

ions

to

accelerateto

high

enoughvelocity to

dislodge

globules of materialfrom

the target.

The

globules ejected

from

the target

land

onthe

substratelocated in

the vicinity,

andform

afilm. Typical deposition

rates canvary

from

aslow

as0.5

A/s

to

afew

1000

A/s,

depending

onthe

power## density

appliedto

the

target

andthe target

to

substratedistance.

Ar

^Target

-substrate

1

CHAPTER

2.

EXPERIMENTAL

20

The

limitations

ofthe

sputtering

process areThe

lowest

process pressureis

approximately 1

mTorrIf

the

pressure

is

lowered

below

this value, the

meanfree

path ofthe

electronsejected

from

the

cathodebecomes larger

than

the

## dimen

sionsof

the

chamber andthe

ionization

rateis

nothigh

enoughto

sustain

the

plasma.This

meansthat

the

deposition

takes

placein

low-grade

vacuum,

instead

ofhigh,

or ultra-high vacuum.The

potential

for

contaminationis

greater comparedto

ultra-high vacuum

techniques.

The

substrateis

exposedto

plasma.This

canhave

far-reaching

negative effects

in terms

of plasmadamage,

charge## accumulation,

etcHowever,

becauase

no charge sensitivedevices

arebeing

madethis

case,the

effects of surface plasmatreatment

onthe

films

in

questionis

negligible.2.1.3

Reactive

sputtering using RF

power sourceIf

the

sputtering

gas containsany

reactive species(such

as oxygen ornitrogen)

the

material composition of

the

film

may

differ

from

the

composition ofthe

target.

These

reactive species can combine withthe

target

materialto

produce oxidesand nitrides of

the

original material.The

reaction## typically

takes

place atloca

tions

withhigh

energy

availability.Those locations include

the target

andthe

substrate.

Depending

onthe relationship

between

the sputtering

rate andthe

reaction

rate,

the

oxidelayer

canform

in

both locations. If

the

reactiontakes

placeon

the substrate,

it is

possibleto

obtain under-stoichiometricfilms,

## if the

sourcematerial arrival rate exceeds

the

reaction rate.If

the

reaction occursmostly

atthe

target,

adifferent

problem presentsitself.

The

oxides and nitrides of variousmaterials are

typically

electricalinsulators,

preventing the

chargefrom reaching

the

surface ofthe

target.

In

this

case,

asions

bombard

the

target,

it

accumulatespositive charge until

the

electric## field is high

enoughto

preventany

moreions

from

reaching the

target.

In

such a case(or

if

the

target

itself

is

made of aninsulating

material), the

cathode

is

attachedto

anRF

power supply.Unlike

withDC-mode

powersupply,

the

RF

powersupply

providesboth

positive and negative voltages.During

the

negative part of

the

duty

cycle,

the

ions

are attractedto

the

target

andsputtering

commences.

## During

the

positivepart ofthe

duty

cycle, the

electronsare attractedto the target

(with

much greatermobility)

and neutralizethe

ions

collected atCHAPTER

2.

EXPERIMENTAL

21

negative charge at

the

surface, resulting

in

DC-bias. This

value canbe

measuredand

is

typically

usedto

analyzethe

state of plasmain

PVD

chambers.2.1.4

Single

target

mode

vs.Dual target

mode

Deposition

ofcomposite## films

canbe

carried outin

two

distinct fashions

withthe

RIT

PE2400

chambertarget setup

(see

Figure

2.2).

Metal Si

CHAPTER

2.

EXPERIMENTAL

22

One

target

is

turned

on at atime

-Discreet films

of each material aredeposited.

-Mostly

laminar-type

structure,

withboundaries

parallelto

the

electricfield

-Maximum

film

thickness

ofA/

10 is

usedTotal

of4

film

## pairs,

withbetween

12

and60

table

revolutions

perfilm

Both

targets

are on atthe

sametime

Materials

are mixed onthe

atomic scale

-less

than

2

A

of materialis

deposited

per pass under eachtarget

Approx.

350

table

revolutions are requiredto

produce anAPSM film

2.1.5

Deposition

ofComposite

Materials

After

the

theoretical

modeling

had been

performed,

the

desired film

optical parameters are

## known.

In

the

process ofmodeling, the

desired

film

thickness

and ratio of constituents are generated.The

required power ratio was calculatedusing

the

equation(2.1).

dCOmP

=(ri-Pi

+

_{r2-P2)t}

(2.1)

Here

dcomp

is

the

compositefilm

thickness in

A,

r1;

andr2

arethe

deposition

ratesof

the two

materialsI

in

mi^ .

w

j

, andt

is

the

deposition

time.

Considering

that

the

total

deposition

power wasdetermined

by

tool

capabilities:Ptotai

Pi

+

P2,

the

equation(2.1)

canbe

solvedfor

the

respective power## levels

Pi,

andP2. These

power

levels

then

had

to

be

setfor

the two targets

anddelivered

simultaneously.In

aPVD

processthe

power cannotbe

measureddirectly

at eachtarget,

only

at

the

power supply.In

orderto

estimatethe

powerdelivered

to

each ofthe two

targets the

bias

voltage was used as anindicator.

In

a singletarget

chamberthe

power andbias

voltagehave

adefinitive

relationship, i.e.

a certain voltagelevel

corresponds## to only

one powerlevel

and vice versa(see

Figure 2.3).

While

this may

notbe

perfectly

accuratein

the

case of a multipletarget chamber, the

approach of

relating

powerto

bias

voltagedeviates

minutely

from

the truth.

In

CHAPTER

2.

EXPERIMENTAL

23

Power Calibration

ro

CD 2000

1800

1600

1400

1200

1000

800

200 400

o Nb Si

600 800

Power

(W)

1000 1200 1400

Figure

2.3:

The data

usedfor

power calibrationin the

composite mode of sputtering.

Note

the

## different

power rangefor Si

andNb

targets.

This

correspondsCHAPTER

2.

EXPERIMENTAL

24

corresponding

process conditions.In

this experiment,

a certainknown

amount of poweris

delivered

to

a singletarget,

andthe

bias

voltageis

recorded.With

this

data

collectedfor both

targets,

it is

then

possibleto

deduce

the

amount ofpowerdelivered

to

each ofthe

multipletargets

in

the

co-deposition process.During

the

processdevelopment

for

the

composite## films,

severaldry

runs were performedin

orderto

arrive atthe

correct power split value.The

power splitterand

the total

powerlevel

were adjusted untilthe

desired

voltage was achieved oneach of

the two targets

usedfor deposition.

The

power splittersetting

andthe

power

level

were recorded and usedin the

subsequentiteration

ofthe process,

if

necessary.

2.2

Thin

film

characterization

2.2.1

Profilometry

The

simplest method ofdetermining

## the thickness

of athin

film is

via profilometry.

In

this

technique,

a stylus scans acrossthe sample,

following

the

surface profile.Deviations

in the

vertical position ofthe

stylus are measured and reported

to the

user.If

the

scanned sample contains astep, the

step'sheight

canbe

measured(see

Figure 2.4

onthe

following

page).The

profilometer's resolutionin

the

vertical(or

height)

dimension is limited

by

the sensing

electronics and vibrationisolation

ofthe

setup.It is

## typically

on

the

order of afew Angstrom

orless.

The

mostchallenging

part ofusing the

profilometry technique

for

film

thickness

measurements provedto

be generating

of

the

consistentstep

in

the

film.

2.2.2

Spectrophotometry

One

ofthe

mostbasic

optical properties of athin

film

criticalto this study

is

its

transmittance.

The

transmission

of an object canbe

measureddirectly

## using

a spectrophotometer.In

a spectrophotometersetup,

the

intensity

of abeam

that

has

passedthrough

an objectis

comparedto the

intensity

of abeam

passing

through

empty space,

andthe

ratio ofthe two

valuesis

taken to

be

the

transmission

ofthe

film. For

this work, two

measurementapparatus'

were used:

aPerkin-

Elmer Lambda UV11

spectrophotometerwith available range of190

nmto

900

nm,

andthe

VASE

tool

## in transmission

measurement mode.Both

tools

CHAPTER

2.

EXPERIMENTAL

25

Stylus

Wafer

Figure 2.4: A

schematic representation of a profilometer scan.Transmission

ofTaSiOx

film

onQuartz

100 200 300 400 500

wavelength

(nm)

600 700 800

CHAPTER

2.

EXPERIMENTAL

26

2.2.3

Ellipsometry

The

ellipsometry

approachdoes

notrely

on measurements ofintensity

ofreflectedor

transmitted

light,

but

rather onits

polarizationstate[19].

The

two

parametersmeasured

during

an ellipsometric run are\F/

andA,

defined

as^

=tan*eiA

(2.2)

where

p

representsthe

ratio of complex reflection coefficientsfor

## the two

different

polarization states s and

p

(see

Section

1.4

on page14).

These

parameters are measured at multipleincidence

angles(typically 3)

and over alarge

spectral region(typically

140

nmto

800

nm).Thus,

a set of6

vector measurements

is

obtained(3

angles x2

parameters across wide spectralrange).

These

parameters arethen

modeledusing

the

assumedknowledge

offilms

optical constants and

film

thickness.

Typically,

only

one set of optical constantsis

unknown(the

film in

question),

and one ortwo thickness

valuesfor

the

film

stack are unknown.

Thus,

by

## using

the

equationsin

section1.4 the 2

unknownvector quantities

(n

andk)

arefitted

to the

6

measured vector parameters(vp

andA

x3

angles).The Mean

Square Error

(MSE)

is

used asthe quality

offit

indicator.

1

NMSE

=y

N

^

aexper _ \ model aA+

*

exper*

model(2.3)

where \I> and

A

representthe

measured and modeled ellipsometric parameters(see

equation(2.2)),

and aAand

a*

are

the

standarddeviations

ofthe

measuredvalues.

The

values of n andk

are modeledusing the

common material modelsde

Chapter

3

Results

The

results ofthis

work are## twofold:

adatabase

of material optical propertiesin

the

VUV

spectralregion,

as well as ademonstration

of compositefilm

withproperties suitable

for APSM

use.3.1

Materials

Database

Table 3.1

includes

all ofthe

materialsthat

were measuredin the survey

portion ofthis

thesis.

Both

n,

k.

and(where

=(n

+

ik)2)

are given.Standard deposition

conditions wereused.In

the

cases whenacceptablefilm

quality

was notachieved,the

process wasoptimized.The

film

thickness

was measured## using

astep

createdwith photoresist on a separate sample.

A

physical profilometertechnique

was usedto

measurethe thickness.

This deposition

rate was usedto

estimate ofthe

material

fraction

ratioin the

subsequent co-deposition experiments.For

eachone ofthe

materialsin

Table

3.1

a set of ellipsometric measurementswas obtained.

These

data,

ellipsometric magnitude(ty)

and ellipsometric phasedifference

(A)

werethen

fitted

to

athin

film

stack model with variablen,

k,

andfilm

thickness

using the

Fresnel

equations(1.42).

An

example ofthe

modelfit

canbe

seen## in Figures

3.1

and3.2.

The

results ofthe

fit

weretaken

to

be

the

measured optical constants

(see

Figure 3.3).

Fitted

thickness

was comparedto

the

thickness

measured with a profilometer as aconsistency

check.A

summary

ofthe

optical properties atA

=157

_{nm}

is

_{shown}

in

Figure

3.5.

The

two

lines

represent all ofthe

possible materialsthat

wouldhave

a certainCHAPTER

3.

RESULTS

28

Table

3.1:

A

list

of materialssurveyed,

material constants are measured atA

=157

nm.Materials deposited

## using

reactivesputtering

are marked with"-r"

while

non-reactively deposited

films

are marked with"-n" .

Material

nk

()

3(e)

Al203-r

2.091

0.106

4.361

0.443

Al203-n

2.053

0.207

4.172

0.850

CrOx

1.431

0.832

1.356

2.381

CrN

1.120

0.781

0.644

1.749

Nb

0.918

0.758

0.268

1.392

NbN

1.706

1.022

1.866

3.487

Nb205

1.808

1.035

2.198

3.743

Ta

1.113

1.371

-0.6413.052

TaN

1.538

0.983

1.399

3.024

Ta205

1.569

1.516

0.164

4.757

Mo

0.719

1.492

-1.7092.145

MoN

1.212

1.516

-0.8193.675

MoO

1.164

1.367

-0.5143.182

Zr

1.440

0.818

1.404

2.356

ZrN

1.844

1.512

1.114

5.576

Ti

1.057

1.081

-0.0512.285

TiN

1.472

1.458

0.041

4.292

CHAPTER

3.

RESULTS

29

*

vsA for Cr(X

35

30

25

20

15

10

5

### 0

Model

Exper

65

Exper 70

Exper

75

100

200

300

400

500

600

700

800

900

A

(nm)

Figure 3.1:

An

example plot ofthe

experimental and modeled^

valuesfor CrOx.

The

final fitted

thickness

was1071

A.

A

vsA

for

CrOx

200

i i i i i 1 1180

## -Model

160

f V *Exper 65

140

-jC \ o

Exper

70

*120

r \ *Exper 75

-100

-80

-60

-40

\20

%\.### 0

1 1 1 1 1 i

100

200

300

400

500

600

700

800

900

A

(nm)

CHAPTER

3.

RESULTS

30

T3

ro

2.5

2.0

1.5

1.0

0.5

0.0

Optical

constantsfor

CrOx

-| i i i i r

j i i i i

L-100

200

300

400

500

600

700

800

900

A

(nm)

Figure

3.3:

An

example plot ofthe

optical properties ofCrOx

obtained afterfitting

ofthe

data-Optical

constantsfor

CrOx

5

i 1 1 1 1 1 1 r_

4

CJ

&

-a

3

c rooj

?

1

-3()

j l l l_

o

100

200

300

400

500

600

700

800

900

A

(nm)

CHAPTER

3.

RESULTS

31

at

157

nm-2

1 I 1

T 207c Zr.N

=_{67c}

- Ta,(>-

-Id

T.O,

TiX \[>,0,

MoO

TaX,

-NbNTi OO,

/

^

"

Cr.N Zr/ ^^

-\l,

/

^^Al,0,-n _ -l l SiO, AljOrr 1

-2

()

Figure 3.5: A

summary

plot ofthe

imaginary

vs.the

real part ofthe

## dielectric

constant at

157

nmfor

all materials measured.transmission

at it phase shift.These lines

canbe described

by

combining

equations

(1.49)

and(1.51)

k

In

(l-Hi2)(l-fl23)

(i--Ri3)r

2

(tt

-A$12

-A$23

+

A$13)

\n

D

(3.1)

where

T is

the

desired

transmission,

andthe

material notationis

givenin

Fig

ure

1.8

on page16.

As

is

evidentfrom Figure

3.5,

no material's optical propertiesfall

in the