Surface Plasmon Polariton

7/23/2019 Surface Plasmon Polariton

http://slidepdf.com/reader/full/surface-plasmon-polariton 1/31

Surface plasmon-polariton study of the optical dielectric

function of titanium nitride

A. P. HIBBINS and J. R. SAMBLES

Thin Film Photonics Group, Department of Physics,

University of Exeter, Exeter EX4 4QL, Enlan!

and

C. R. LAWRENCE

Defence Evaluation an! "esearch #ency, Farn$orouh GU%4 &LX,

Enlan!'

Abstract

This work presents the first detaied st!d" of the opti#a diee#tri#

f!n#tion of opti#a" thi#k TiNx fi$s !sin% %ratin%&#o!pin% of

radiation to s!rfa#e pas$on&poaritons. An%e&dependent

refe#ti'ities are o(tained in the wa'een%th ran%e )**+,-) n$ and

(" #o$parison with %ratin% $odein% theor" we deter$ine (oth

the i$a%inar" and rea parts of the diee#tri# f!n#tion. This

$ethod pro'ides an aternati'e to traditiona #hara#terisation

te#hni/!es 0e'' 1ra$ers+1roni% ana"sis2 that $a" re/!ire

additiona infor$ation a(o!t fi$ thi#kness or the sa$pe3s opti#a

properties in other parts of the ee#tro$a%neti# spe#tr!$. We

4



ha'e fitted the deter$ined diee#tri# f!n#tion to a $ode (ased on

a #o$(ination of inter(and a(sorptions and free&ee#tron response

e'a!atin% (oth the pas$a ener%" and rea5ation ti$e.

1. Introduction

Titani!$ nitride 0TiNx2 (eon%s to a %ro!p of transition $eta

#o$po!nds that are of #onsidera(e interest (e#a!se the" ha'e a

'ariet" of properties whi#h end the$se'es to $an" potentia

appi#ations. 6or e5a$pe TiNx has (e#o$e wide" !sed as a wear&

resistant #oatin% on toos (e#a!se of its $e#hani#a resistan#e ow

fri#tion #oeffi#ient and hi%h $etin% point 748. Its hi%h #he$i#a

sta(iit" and ow resisti'it" aso $ake it a %ood #andidate as a

diff!sion (arrier in se$i#ond!#tor $etai9ation s"ste$s 7:;8.

TiNx is aso fas#inatin% in that it appears %od in #oo!r owin% to

the dispa#e$ent of the pas$a ed%e into the 'isi(e ran%e (" the

onset of inter(and transitions 7<)8. Hen#e it is often !sed as a

s#rat#h&resistant aternati'e to %od on de#orati'e =eweer". Its

hi%h >r!de&ike refe#tan#e in the infra&red and hi%h a(sorpti'it" in

the 'isi(e and near infra&red ha'e en#o!ra%ed its !se as a

see#ti'e a(sor(er and heat $irror. ?nfort!nate" the pas$a ed%e

is o#ated at too hi%h an ener%" to $ake it an effi#ient soar

a(sor(er in its stoi#hio$etri# for$ 7<@-8. Howe'er it is we

known that the pas$a ener%" and the opti#a and ee#tri#a

properties of TiNx fi$s are stron%" dependent on the deposition

#onditions fi$ thi#kness and titani!$&nitro%en ratio 7@&4:8. This

:



present st!d" is #on#erned with e5porin% these interestin% opti#a

#hara#teristi#s in the 'isi(e part of the spe#tr!$ !sin% the opti#a

e5#itation of s!rfa#e pas$ons.

To o!r knowed%e the first $!ti&wa'een%th st!d" of the opti#a

#onstants of TiNx was #arried o!t (" Bh$ et al' 7,8 in 4-:. The"

#a#!ated the opti#a dispersion and a(sorption para$eters of

Ti0CN2 soid so!tions (" $eans of eipso$etri# $eas!re$ents

(etween ener%ies of *.@ and ).) e. Their res!ts i!strate the

>r!de&ike response of TiN*.< at ow ener%ies and its dist!r(an#e ("

the onset of inter(and transitions as the photon ener%" is

in#reased. S#he%e et al' 7)8 #hara#terised TiNx sa$pes !sin%

1ra$ers&1roni% ana"sis 74;8 of refe#ti'it" $eas!re$ents #arried

o!t (etween *.; and 4: e. Sa$pes were prepared (" #he$i#a 'apo!r deposition 0C>2 on to heated #r"stas of TiNx. 1arsson et

al' 7<8 and Ri'or" et al' 7@8 (oth o(tained the diee#tri# f!n#tion of

opa/!e 0thi#kness ! D 4** n$2 stoi#hio$etri# TiNx sa$pes

prepared (" rea#ti'e sp!tterin% on to f!sed&sii#a and %ass

s!(strates respe#ti'e". 1ra$ers&1roni% ana"sis was a%ain !sed to

deter$ine the opti#a per$itti'ities (etween *.*: and @.: e

01arsson2 and *.) and @ e 0Ri'or"2. S9#9"r(owski et al' 74*8 and

akonen et al' 74:8 deter$ined the opti#a #onstants of sp!ttered

TiNx fi$s in the 'isi(e and near infrared spe#tra re%ions fro$

$eas!re$ents of trans$ission refe#tan#e and fi$ thi#kness 0d

;4 n$2. Pas#!a et al' 7448 deposited opa/!e TiNx fi$s (" pas$a&

;



assisted #he$i#a 'apo!r deposition 0PAC>2 and deter$ined its

diee#tri# f!n#tion (" $eans of spe#tros#opi# eipso$etr" in the

?+'isi(e ran%e.

The !se of %ratin%&#o!ped s!rfa#e pas$on&poaritons 0SPP2 74<8

in the st!d" of the profie and per$itti'it" of $eta s!rfa#es

pro'ides an aternati'e $ethod to the te#hni/!es des#ri(ed a(o'e.

The SPP #o$prises of a s!rfa#e #har%e densit" os#iation and

asso#iated ee#tro$a%neti# fieds propa%atin% aon% a

$etaFdiee#tri# interfa#e. Gwin% to the re'ersa of the nor$a

#o$ponent of the ee#tri# fied at the s!rfa#e the SPP is 'er"

stron%" o#aised in the pane and so is e5tre$e" sensiti'e to the

diee#tri# properties of the $edia either side of the interfa#e.

Howe'er on a fat s!rfa#e the wa'e 'e#tor of the SPP is %reaterthan the $a5i$!$ photon wa'e 'e#tor a'aia(e in the ad=a#ent

diee#tri# and therefore it #an neither (e dire#t" #o!ped to nor

#an it radiate. The enhan#ed wa'e 'e#tor re/!ired to #o!pe into

the $ode $a" (e pro'ided (" either in#reasin% the wa'e 'e#tor of

the in#ident radiation (" !sin% a hi%h inde5 pris$ 74)4@8 or a

#orr!%ated interfa#e. The atter is !s!a" in the for$ of an opti#a

diffra#tion %ratin% where the in&pane wa'e 'e#tor enhan#e$ent is

in $!tipes of the %ratin% wa'e 'e#tor ( 74-8. B" 'ar"in% the

$a%nit!de of the in#ident wa'e 'e#tor in the pane of the %ratin%

wa'e 'e#tor 'a!es are fo!nd at whi#h in#ident radiation $a"

<



#o!pe resonant" to the SPP $ode. E5peri$enta" the e5#itation

of a SPP is o(ser'ed as a dip in the an%e&dependent refe#ti'it".

Pre'io!s" the %ratin%&#o!ped SPP $ethod has s!##essf!" (een

!sed to #hara#terise $etas in#!din% #opper 74,8 and si'er 748

and Stein$er+Neth et al' 7:*8 ha'e reported the e5#itation of

SPPs on a thin TiNx fi$ sp!ttered onto a sin!soida" $od!ated

s!(strate. The" re#orded an%e&dependent refe#ti'ities at fo!r

in#ident wa'een%ths in the 'isi(e re%i$e and #o$pared the$ with

those predi#ted fro$ a rather si$pisti# treat$ent of the

intera#tion of radiation with the s!rfa#e. This aowed the$ to

esti$ate the diee#tri# f!n#tion of TiNx at these wa'een%ths. The

%ratin%&#o!ped SPP $ethod presents $an" ad'anta%es o'er the

other te#hni/!es des#ri(ed pre'io!s". 6or e5a$pe it does notre/!ire trans$itti'it" data or the deter$ination of fi$ thi#kness

hen#e per$ittin% the !se of opti#a" opa/!e $etai# fi$s. It #an

aso (e !sed to #a#!ate the per$itti'it" of a $ateria o'er a

i$ited wa'een%th ran%e witho!t the knowed%e of its opti#a

response esewhere in the ee#tro$a%neti# spe#tr!$ & there is no

1ra$ers&1roni% (ased interpretation.

This present st!d" !ses %ratin%&#o!pin% of radiation to SPPs on a

TiNx s!rfa#e to o(tain the dispersion reation of the TiNx fi$.

a!es of ε are deter$ined at 'isi(e wa'een%ths (" #o$parison of

the in&pane refe#tan#e fro$ the #orr!%ated TiNx&air interfa#e as a

)



f!n#tion of the an%e of in#iden#e to the predi#tions fro$ a

ri%oro!s %ratin% theor" $ode whi#h !ses the differentia

for$ais$ of Chande9on et al' 7:48. B" 'ar"in% the %ratin%

para$eters !sed to %enerate a theoreti#a refe#ti'it" tra#e it is

possi(e to o(tain a %ood /!ait" fit to the e5peri$enta data and

hen#e deter$ine the shape 7::8 and opti#a per$itti'it" 74,48 of

the TiNx s!rfa#e.

2. Experimental

The #orr!%ated s!rfa#e !sed in this work was prepared in sii#a ("

standard interfero%raphi# te#hni/!es 7:;8. The $ethod of

preparation in'o'es the e5pos!re of spin&#oated photoresist on a

sii#a dis# to the interferen#e pattern prod!#ed (" first spittin%

and then re#o$(inin% an ar%on&ion aser (ea$. After e5pos!re the

photoresist is #he$i#a" de'eoped and the res!tin% profie

transferred into the sii#a (" fast ato$ et#hin%. This prod!#es a

ro(!st and ar%e area diffra#tion %ratin% with a we&defined pit#h

0in this #ase λ =B;* n$2 and a !nifor$ s!rfa#e profie that is

so$ewhat distorted fro$ a p!re sin!soid. S!(se/!ent deposition

of an opti#a" thi#k ( )! ≈ @** n$ a"er of titani!$ nitride prod!#es

a $etai#&air interfa#e that $a" s!pport SPPs.

@



The TiNx fi$ was deposited (" TEER Coatin%s Ltd 01idder$inster

?12 !sin% the #osed fied !n(aan#ed $a%netron sp!tter ion

patin% s"ste$ 7:<8. The s!(strate is ion&#eaned (efore deposition

whi#h ens!res a hi%h de%ree of adheren#e to the sii#a s!rfa#e.

Initia sp!tterin% is fro$ a p!re titani!$ tar%et whi#h is poisoned

(" (eedin% nitro%en into the #oatin% #ha$(er. In order to atte$pt

to #ontro the titani!$Fnitro%en ratio of the sp!ttered sa$pe the

intensit" of )*4 n$ radiation e$itted fro$ the tar%et is $onitored.

6ro$ past e5perien#e it is tho!%ht that appro5i$ate"

stoi#hio$etri# TiNx $a" (e deposited on the s!(strate when the

intensit" of radiation fas to @*K of the ori%ina 'a!e. The #oatin%

press!re in the #ha$(er (a#k fied with Ar %as was < 4* ;×

− Torr

and the s!(strate (ias 'ota%e and te$perat!re were ;* and

appro5i$ate" 4)* °C respe#ti'e".

Pre'io!s workers for e5a$pe 7448 ha'e shown the rea part of the

diee#tri# f!n#tion of TiNx to (e ne%ati'e and therefore a(e to

s!pport interfa#e $odes at wa'een%ths in e5#ess of appro5i$ate"

)** n$. The wa'e 'e#tor of the in#ident radiation in the diee#tri#

is n (! * 0where ( c* *

:= =ω π λ and n! =4***;. is the refra#ti'e

inde5 of air2 and we $a" on" #o!pe to the SPP when the in&pane

#o$ponent of this has (een s!ita(" enhan#ed. This $e#hanis$ is

pro'ided (" the %ratin%3s periodi#it" whi#h $a" in#rease or

de#rease the in&pane #o$ponent of n (! * (" inte%er $!tipes of

-



the %ratin% wa'e 'e#tor ( 0( = :π λ % 2. This %i'es rise to

diffra#ted orders whi#h no on%er propa%ate in the diee#tri# when

their in&pane wa'e 'e#tor is in#reased s!#h that it (e#o$es

%reater than that of the in#ident radiation. It is the enhan#ed wa'e

'e#tor of these e'anes#ent fieds that aows in#ident radiation to

#o!pe to the SPP a##ordin% to the #ondition

( )( n ( x )(*PP !

= ±* sin θ

(1).

Here ) is an inte%er (*PP is the wa'e 'e#tor of the SPP and

n (! * sinθ is the pro=e#tion of the wa'e 'e#tor of the in#ident

radiation parae to ( 0aon% the x&a5is2. If the an%e (etween

the pane of in#iden#e and the %ratin% 'e#tor 0#aed the a9i$!tha

an%e ϕ 2 is e/!a to 9ero then a the diffra#ted (ea$s ie in the

pane of $eas!re$ent and e/!ation 4 red!#es to a s#aar e/!ation.

The SPP resonan#es were $onitored (" re#ordin% the spe#!ar"

refe#ted intensit" fro$ the TiNx+air interfa#e as a f!n#tion of the

an%e of in#iden#e 0fi%!re 42. Mono#hro$ati# p&poarised0trans'erse $a%neti#2 radiation of wa'een%th ran%in% fro$ )** to

,-) n$ in :) n$ steps was in#ident in a pane parae to the

%ratin% wa'e 'e#tor ( )ϕ = °* . The nor$aised e5peri$enta an%e&

dependent refe#ti'it" data was fitted (" a east&s/!ares pro#ed!re

!sin% a s#atterin% $atri5 7:)8 te#hni/!e (ased on the differentia

for$ais$ of Chande9on et al' 7:48. This theor" in'o'es

,



transfor$in% the $athe$ati#s into a new fra$e in whi#h the

(o!ndar" #onditions at the #orr!%ated s!rfa#e are $ore readi"

so'ed & effe#ti'e" fattenin% the s!rfa#e. This re/!ires that the

in#ident fied is represented as a 6o!rier e5pansion. The s!rfa#e

itsef is aso des#ri(ed (" a 6o!rier series

( ) ( ) ( ) # x a ( x a ( x a )( x ) 0 2 #os #os #os= + + + +4 :

:

(2).

B" fittin% the refe#ti'it" data to the $odein% theor" it is possi(eto para$eterise the %ratin% profie and #hara#terise the diee#tri#

f!n#tion of the $etai# $ateria.

In order to pro'ide an a##!rate des#ription of the #o$pe5

diee#tri# f!n#tion of TiNx it is first ne#essar" to (e #onfident of

the s!rfa#e profie. In the 'isi(e re%i$e it is we do#!$ented 7for

e5a$pe 48 that the rea part of the diee#tri# f!n#tion of si'er is

$ore ne%ati'e and the i$a%inar" part $!#h s$aer than the

#orrespondin% 'a!es for TiNx. Hen#e the s!rfa#e pas$on

resonan#es on a si'erFair interfa#e are far (etter defined

#onse/!ent" %i'in% $ore sensiti'it" to the %ratin% profie.

Therefore in order to o(tain a %ood first appro5i$ation to the

profie of the TiNx&#oated s!rfa#e we ther$a" e'aporate an

opti#a" thi#k a"er of si'er on top of the TiNx. The pit#h of the

%ratin% was #hosen so that when ϕ = °* in#ident i%ht of

wa'een%th λ * )B*= n$ wi e5#ite first se#ond and third order



SPP resonan#es 0 ) 4:;2 whi#h $a" (e o(ser'ed as resonant

feat!res in an an%e of in#iden#e s#an. B" fittin% the opti#a data

fro$ the si'er s!rfa#e to the predi#ted opti#a response !sin% the

theor" des#ri(ed a(o'e we are a(e to pro'ide a %ood esti$ate of

the three 6o!rier a$pit!des of the #orr!%ated s!rfa#e that pro'ide

the dire#t #o!pin% $e#hanis$ for the three SPP resonan#es. This

tr!n#ated 6o!rier series #an then (e !sed in the fittin% of data

o(tained fro$ the TiNx&#oated s!rfa#e o'er the whoe spe#tra

re%i$e. S!(se/!ent" after f!rther fittin% aowin% a the s!rfa#e

para$eters to 'ar" we o(tain a new profie for the TiNx s!rfa#e ("

a'era%in% the 6o!rier #o$ponents o'er a wa'een%ths. This new

a'era%e profie is then hed #onstant at a wa'een%ths and the

data fina" refitted in order to o(tain the #o$pe5 diee#tri#

#onstant at ea#h of the wa'een%ths st!died.

3. esults

6i%!re : shows two sets of t"pi#a refe#ti'it" data at in#ident

wa'een%ths of @)* n$ and ,** n$. The soid ines are the

theoreti#a fits whi#h are in 'er" %ood a%ree$ent with the data

0#ir#es2. The opti#a properties of TiNx are often ikened to those

of %od (!t the off&resonan#e refe#ti'it" of ess than )*K is #ear"

ess than the ~*K to (e e5pe#ted fro$ %od 7:@8. In addition the

resonan#es the$se'es are (road and shaow. This indi#ates that

4*



TiNx #o$pared to %od has an in#reased ε i and pro(a(" a ess

ne%ati'e ε r .

As indi#ated a(o'e the profie of the %ratin% is initia" esti$ated

fro$ the opti#a #hara#terisation of the si'er s!rfa#e and then

i$pro'ed (" fittin% to the TiNx data. The pit#h as defined (" the

an%!ar positions of the pse!do&#riti#a ed%es in the e5peri$enta

refe#ti'it" data was #a#!ated to (e λ = ±B;*4 *). . n$ with the

per$itti'it" of the diee#tri# 0air2 set as ε ! !n= =: 4***@. . The

'a!es of the #o$pe5 diee#tri# #onstants of the TiNx fo!nd fro$

the fina fits to the refe#ti'it" data are isted in ta(e 4

( )ε ε ε TiN = +r ii . The errors in these 'a!es are do$inated (" an

!n#ertaint" in the 6o!rier #oeffi#ients of the %ratin% profie. This is

attri(!ted to the ow sensiti'it" of the (road and shaow resonan#e

feat!res to the 'ario!s 6o!rier #oeffi#ients. There is aso a

'ariation in the !n#ertaint" o'er the wa'een%th ran%e d!e to a

#han%e in the n!$(er of SPP resonan#es o(ser'a(e at different

wa'een%ths in the an%e of in#iden#e s#ans. In addition there is

an in#rease in the !n#ertaint" when two refe#ti'it" $ini$a

o'erap and aso as the #o!pin% stren%th to the resonan#es

de#rease as we approa#h the i$it ε r = *. The res!ts presented in

this work aon% with those of 1arsson et al' 7<8 Ri'or" et al' 7@8

44



S9#9"r(owski et al' 74*8 Pas#!a et al' 7448 akonen et al' 74:8

and Stein$er&Neth et al' 7:*8 are i!strated in fi%!re ;.

!. "iscussion

It is we known that the opti#a properties of TiNx fi$s are

stron%" dependent on the deposition #onditions fi$ thi#kness and

the titani!$Fnitro%en ratio. Therefore the 'ariation in the 'a!es

ofε r and

ε i as i!strated in fi%!re ; is not s!rprisin%. The

works of 1arsson et al' 7<8 and Ri'or" et al' 7@8 (oth #onsider

opa/!e sa$pes 0! >4** n$2 of si$iar stoi#hio$etries 0 2x=4

and !se identi#a #hara#terisation te#hni/!es in order to o(tain the

opti#a #onstants. As a res!t the diee#tri# f!n#tion of their

respe#ti'e sa$pes #o$pare fa'o!ra(". S9#9"r(owski et al' 74*8

and akonen et al' 74:8 ha'e (oth sp!ttered $!#h thinner fi$s 0

! <;4 n$2 and atho!%h their 'a!es of ε r are #o$para(e to

those of other workers their 'a!es of ε i are #onsidera(" hi%her

d!e to in#reased ee#tron s#atterin%. The thin fi$s o(tained ("

PAC> and in'esti%ated o'er 'isi(e wa'een%ths (" Pas#!a et al'

7448 show the $ost ano$ao!s res!ts. It is not #ear wh" their

res!ts %i'e 'a!es for (oth parts of the #o$pe5 diee#tri# f!n#tion

whi#h are s$aer in $a%nit!de than other st!dies. Stein$er&

Neth et al' 7:*8 !sed a %ratin%&#o!ped SPP te#hni/!e to

#hara#terise the opti#a properties of their $a%netron&sp!ttered

fi$ at fo!r wa'een%ths. The" appear to ha'e (een the first to

4:



re#ord SPP e5#itation on TiNx. Their fi$s were of #o$para(e

thi#kness to those of S9#9"r(owski et al' 74*8 and akonen et al'

74:8 0! =)* n$2 howe'er the" do not show the asso#iated

in#rease in ε i . Howe'er it sho!d (e noted that their data fittin%

te#hni/!e is (ased on a pert!(ati'e approa#h to 6resne e/!ations

and the" ass!$e shaow 0depthFpit#h *.*-2 p!re" sin!soida

%ratin%s. In 'iew of the fa#t that their %ratin% is prod!#ed ("

interfero%raphi# e5pos!re foowed (" ion&et#hin% then the profie

is ike" to (e distorted si%nifi#ant" fro$ the ass!$ed shape. This

res!ts in poor /!ait" fits and the errors asso#iated with their

ded!#ed 'a!es of ε r and ε i wi (e ar%e.

In this work we present a #o$prehensi'e st!d" of the SPP on TiNx

!sin% a ri%oro!s $ode of the opti#a response of $etai# %ratin%s

to fit the e5peri$enta refe#ti'it" data fro$ an opti#a" thi#k

0! ≈@** n$2 sp!ttered fi$. The %ratin% profie is a##!rate"

$odeed as a distorted sin!soida s!rfa#e (" representin% it as a

tr!n#ated 6o!rier series and !sin% the theoreti#a $ode des#ri(ed

pre'io!s". 6ro$ this we prod!#e fits that show e5#eent

a%ree$ent with the e5peri$enta refe#ti'ities 0fi%!re :2. The

e5peri$enta" deter$ined diee#tri# f!n#tion 0fi%!re ;2 i!strates

that ε r is si%ht" s$aer in $a%nit!de than ded!#ed (" other

workers for si$iar fi$s 7<@8 howe'er ε i shows %ood a%ree$ent

with these other st!dies.

4;



If the diee#tri# f!n#tion of TiNx is do$inated (" a free&ee#tron

(eha'io!r at the wa'een%ths st!died in this work we wo!d

e5pe#t o!r data to #onfor$ to the >r!de $ode i'e'

( )ε ω ε ω τ

ω τ r

p= −

+*

: :

: :4

(3)

( ) ( )ε ω

ω τ

ω ω τ i

p=

+

:

: :4

(!)

where τ is the rea5ation ti$e ω p is the pas$a fre/!en#" and ε * is

resid!a diee#tri# #onstant 0#on'entiona" ass!$ed to (e !nit"2.

Therefore we sho!d (e a(e to pot ε r a%ainst λ : and ε i a%ainst

λ ; and e5pe#t inear reationships. Pottin% o!r data in this wa"

%i'es the #!r'es of fi%!re < 0a2 and 0(2 respe#ti'e". 6i%!re < 0a2

shows a hi%h de%ree of inearit" the y &inter#ept indi#atin% a

resid!a diee#tri# #onstant of appro5i$ate" ;. This #an (e

attri(!ted to a positi'e #ontri(!tion to ε r fro$ the o##!rren#e of

inter(and transitions as predi#ted (" a n!$(er of pre'io!s workers

7<&,8. The inear fit toε i is ess #on'in#in% and hen#e aso

s!%%ests that the opti#a response of TiNx is not p!re" >r!de&ike

in nat!re. In addition pre'io!s workers ha'e i!strated that the

point at whi#h ε r = * is sit!ated at a $!#h ower ener%" than the

4<



predi#ted pas$a resonan#e. The #rossin% of the ε r = * a5is is

asso#iated with a s#reened pas$on $ode whi#h has (een shifted

to ower ener%ies (" the onset of inter(and transitions at photon

ener%ies a(o'e :.) e 7<8. Conse/!ent" an" treat$ent of the

#o$pe5 diee#tri# #onstant #ose to this re%ion $!st in'o'e

spittin% it into two parts one part #orrespondin% to intra(and

e5#itations des#ri(ed (" the >r!de $ode and an inter(and part

#orrespondin% to resonant a(sorptions (ased on a Lorent9

os#iator $ode i.e.

( ) ( ) ( )ε ω ε ω ε ω r r

D

r

+ = +

(#)

and

( ) ( ) ( )ε ω ε ω ε ω

i i

D

i

+

= +

($).

We fit o!r data to a $ode that ass!$es on" one resonant

inter(and transition. This is a reasona(e ass!$ption to $ake

sin#e we e5pe#t peaks in ( )ε ω i #orrespondin% to stron% inter(and

transitions at appro5i$ate" ;.- e and ).: e 7<@:-8 (!t ha'e

on" deter$ined the diee#tri# f!n#tion at ener%ies !p to :.) e.

Hen#e we wi on" e5perien#e the effe#ts of the win% of the ower

ener%" resonan#e. The two parts of the #o$pe5 diee#tri# f!n#tion

are therefore

4)



( )( )

( )ε ω ε

ω τ

ω τ

τ ω ω ω

τ ω ω ω

r

p p= −

+ +

−

− +*

: :

: :

: :*: :

:*: : : :4

(%)

and

( )( ) ( )

ε ω

ω τ

ω ω τ

ω ωτ

τ ω ω ω

i

p p=

++

− +

:

: :

:

:*: : : :4

(&).

B" rearran%in% e/!ations - and , and p!ttin% ε * 4= we ei$inate

ω p s!#h that

( )

( )

( )

( ) ( )

ε ω

ε ω

ωτ

ω ω τ

ω ω τ τ ω ω ω

r

i

−=

+

+ + − +

−

4 4

44

*

: : :

: : : :

*

: : : :

(').

6ro$ this it is possi(e to o(tain the #onstants ω * ;B= . eC and

τ =44. eC (" fittin% the f!n#tiona for$ of e/!ation to

e5peri$enta" deri'ed data 0fi%!re )2. The fit to the e5peri$enta

data i!strated in fi%!re ) is rather poor (!t it is i$portant to note

that refe#ti'it" $eas!re$ents were #arried o!t o'er a 'er" i$ited

fre/!en#" ran%e. Howe'er the %enera !pward trend in the

e5peri$enta data is apparent in the $ode and the 'a!e of ω *

#o$pares fa'o!ra(" with the ener%" of the first peak in ( )ε ω i

deter$ined (" pre'io!s workers 0;., ± *.4 e 7<@:-82. We $a"

then fit to ω p (" !sin% e/!ations - and , 0fi%!re @ a and (2. A

4@



#o$parison of o!r 'a!es of ω p and τ to those of pre'io!s workers

is shown in ta(e :.

Gn e5a$ination of ta(e : it is apparent that there is a ar%e

spread of 'a!es of (oth ω p and τ dependent on the deposition

#onditions and stoi#hio$etr" of the sa$pe. The pas$a fre/!en#"

and rea5ation ti$e #a#!ated in the present st!d" are a$on% the

owest o(ser'ed indi#atin% a sa$pe of red!#ed $etai# nat!re

whi#h #an at east in part (e attri(!ted to a ar%e nitro%enFtitani!$

ratio 0x2. Indeed this is #onfir$ed (" ee#tron ener%" dispersi'e

spe#tros#op" $eas!re$ents whi#h indi#ate that x is we in e5#ess

of !nit".

#. onclusions

In this paper for the first ti$e we ha'e deter$ined the diee#tri#

f!n#tion of TiNx thro!%ho!t the 'isi(e re%i$e !sin% a %ratin%&

#o!ped SPP resonan#e te#hni/!e. This te#hni/!e presents a

n!$(er of ad'anta%es o'er $ore #on'entiona #hara#terisation

$ethods. 6or e5a$pe we need on" take refe#ti'it" data at the

indi'id!a wa'een%ths at whi#h we wish to #a#!ate the diee#tri#

f!n#tion and we re/!ire no $eas!re$ent of the fi$ thi#kness. We

ha'e i!strated that we are a(e to o(tain e5#eent a%ree$ent

(etween the differentia for$ais$ of Chande9on and e5peri$enta

4-



refe#ti'ities and the res!tin% diee#tri# f!n#tion #o$pares

fa'o!ra(" with that deter$ined (" pre'io!s workers. B" $akin%

the ass!$ption that TiNx is on" free&ee#tron ike in its opti#a

response we ha'e shown that the >r!de $ode aone is too

si$pisti#. Instead we ha'e fitted the e5peri$enta" deter$ined

diee#tri# f!n#tion to a >r!de&Lorent9 $ode that ass!$es a sin%e

resonant inter(and transition in order to o(tain the pas$a

fre/!en#" and rea5ation ti$e. A #o$parison of #onstants

deter$ined fro$ this work and pre'io!s st!dies shows a ar%e

spread of res!ts i!stratin% the dependen#e on the stoi#hio$etr"

and deposition #onditions of the sa$pe.

Acno*le+ements

The a!thors wo!d ike to a#knowed%e the finan#ia s!pport of the

>efen#e E'a!ation and Resear#h A%en#" 6arn(oro!%h and wish

to thank Jeffer" Jones 0Earth Reso!r#es Centre ?ni'ersit" of

E5eter2 for his #ontri(!tion to the E>S st!d".

eferences

748 M?N W. >. HG6MANN >. and H ARTIO 1. 4,@ Thin *ol! Films

'$ -.

7:8 1 ANAMGRI S. 4,@ Thin *oli! Films, 13$ 4).

4,



7;8 O AONGN O. C?RRIE J. 6. BREBNER J. L. and > ARWELL T. 4@ '

#ppl' Phys', %' -@4:.

7<8 1 ARLSSGN B. S?N>OREN J.&E and JGHANSSGN B.&G 4,: Thin *oli!

Films', &% 4,4.

7)8 SCHLEOEL A. W ACHTER P. NIC1L J. J. and LINOO H. 4-- ' Phys'

-, 1, <,,.

7@8 R IGR J. BEHAOHEL J. M. BERTHIER S. and L A6AIT J. 4,4 Thin

*oli! Films, %& 4@4.

7-8 6RANQGIS J. C. CHASSAINO O. ORAIER P. PIERRISNAR> R. and

BGNNGT A. M. 4,) Thin *oli! Films, 12% :*).

7,8 BHM O. and OGRET1I H. 4-: ' Less.-ommon /etals 2%

;44.

78 1 ?RT S. R. and OGR>GN R. O. 4,@ Thin *oli! Films, 1!,

:--.

74*8 SCRBGWS1I GN J. R OELS S. 1 ASTNER A. >IETRICH A. and

H ARTIO 1. 4,, 0a(uum.Techni(, 3% 4<.

7448 P ASC?AL E. PGLG M. C. ESTEE J. and BERTRAN E. 44

*urface *cience, 2#1-2#2 :**.

74:8 AL1GNEN E. R IBBINO C.&O. and S?N>OREN J.&E. 4,@ Proc'

*P+E, $#2 :;).

74;8 WGGTEN 6. 4-: 1ptical Properties of *oli!s 0New ork

A#ade$i# Press2 #hapter @.

74<8 R AETHER H. 4,,, *urface Plasmons on *mooth an! "ouh

*urfaces an! on Gratins 0Berin Sprin%er2.

74)8 1 RETSCHMANN E. and R AETHER H. 4@, 2' )aturf' 23a :4;).

4



74@8 GTTG A. 4@, 2' Phys' 21$ ;,.

74-8 TENO .&. and STERN E. A. 4@- Phys' "ev' Lett' 1' )44.

74,8 N ASH >. J. and S AMBLES J. R. 4) ' /o!' 1pt' !2 4@;.

748 N ASH >. J. and S AMBLES J. R. 4@ ' /o!' 1pt' !3 ,4.

7:*8 STEINMLLER &NETHL >. 1 GACS R. OGRNI1 E. and R >HAMMER P.

4< Thin *oli! Films, 23% :--.

7:48 CHAN>EGN J. >?P?IS M. T. CGRNET O. and M ASTRE >. 4,: '

1pt' *oc' #m' %2 ,;.

7::8 WGG> E. L. S AMBLES J. R. CGTTER N. P. and 1 ITSGN S. C. 4)

' /o!' 1pt !2 4;<;.

7:;8 H?TLE M. C. 4,: Diffraction Gratins 0London A#ade$i#

Press2.

7:<8 MGNAOHAN >. P. TEER >. O. L AINO 1. C. E6EGOL? I. and A RNELL

R. >. 4; *urf' an! -oatins Technol' #' :4.

7:)8 CGTTER N. P. 1. PRIEST T. W. and S AMBLES J. R. 4) ' 1pt'

*oc' #m' 12 4*-.

7:@8 W ATTS R. A. S AMBLES J. R. and H ARRIS J. B. 4- 1ptics

-ommun' 13# 4,.

7:-8 1 ARLSSGN B. SHIMSHGC1 R. P. SERAPHIN B. G. and H AOARTH J.

C. 4,; *ol' Enery /ater', % <*4.

able aptions

:*



able 1. The opti#a diee#tri# f!n#tion of titani!$ nitride

e5peri$enta" deter$ined in this work to%ether with esti$ated

errors.

able 2. A #o$parison of the 'a!es of ω p and τ of TiNx

e5peri$enta" deter$ined in this work aon% with the 'a!es

o(tained (" a n!$(er of pre'io!s workers. The nitro%enFtitani!$

ratio 0x2 and deposition $ethod is aso isted for #o$parison.

:4



/i+ure aptions

/i+ure 1. S#he$ati# representation of the e5peri$enta set !p

!sed to re#ord an%e dependent refe#ti'it" data fro$ a diffra#tion

%ratin%. In order for the si%na dete#tor to tra#k the spe#!ar"

refe#ted (ea$ the si%na dete#tor rotates at twi#e the rate of the

%ratin% $o!nted on the ta(e.

/i+ure 2. The e5peri$enta an%e&dependent refe#ti'ities 0 one

point in fi'e potted for #arit"2 #o$pared with the theoreti#a"&

$odeed refe#ti'ities 0

2 #reated fro$ a sin%e set of para$eters

des#ri(in% the %ratin% profie. (a) and (b) show R pp refe#ti'it"

$eas!re$ents 0i.e. p&poarised 0TM2 radiation was in#ident and

dete#ted2 at in#ident wa'een%ths of @)* n$ and ,** n$

respe#ti'e". The 'a!es of the diee#tri# #onstants at these

wa'een%ths that were o(tained (" fittin% the $ode to the

e5peri$enta data are shown in ta(e 4.

/i+ure 3. A #o$parison of the 'a!es of the diee#tri# f!n#tion of

TiNx deter$ined in this work 02 with the res!ts of 1arsson et al'

7<8 0 2 Ri'or" et al' 7@8 02 S9#9"r(owski et al' 74*8 0& & &2 Pas#!a

et al' 7448 0 2 akonen et al' 74:8 0 2 and Stein$er&Neth et al'

7:*8 0U2.

::



/i+ure !. A pot of (a)ε r a%ainst λ *: and (b) ε i a%ainst λ *

; for

the data presented in this work. A hi%h de%ree of inearit"

s!%%ests that the TiNx sa$pe is free&ee#tron ike. Howe'er the y &

inter#ept of 0a2 is %reater than ε *

4= attri(!ta(e to a positi'e

#ontri(!tion toε r fro$ the o##!rren#e of inter(and transitions.

The errors i!strated in the 'a!es of the diee#tri# #onstants are

do$inated (" an !n#ertaint" in the %ratin% profie.

/i+ure #. B" ass!$in% a one&resonan#e >r!de&Lorent9 $ode we

o(tain a f!n#tion reatin% the two parts of the #o$pe5 diee#tri#

f!n#tion dependent on" on ωω * and τ 0e/!ation 2. a!es of

this f!n#tion #a#!ated !sin% the e5peri$enta" deter$ined

diee#tri# #onstants and !n#ertainties 0error (ars2 are #o$pared

with the fitted theoreti#a f!n#tion 0soid ine2. We are th!s a(e to

deter$ine the 'a!es of ω * and τ .

/i+ure $. The (a) rea part (b) i$a%inar" part and the

asso#iated !n#ertainties in the diee#tri# f!n#tion of TiNx

deter$ined in the present work. We ha'e $odeed the

e5peri$enta data 0error (ars2 !sin% e/!ations - and , in order to

o(tain the pas$a fre/!en#"ω p . The res!tin% fit is shown as a

soid ine.

:;



,

(nm)

r

r

i

i ,

(nm)

r

r

i

i

)** &*.:* ±

*.*):.<4 ±

*.4)-** &;.), ±

*.4*).;@ ±

*.4*):) &*.@< ±

*.4*;.4: ±

*.:)-:) &<.:; ±

*.4*).-< ±

*.:*))* &4.*- ±

*.4*;.;- ±

*.4*-)* &<.,< ±

*.4*@.*- ±

*.:*)-) &4.<; ±

*.4*;.- ±

*.4*--) &).4 ±

*.*)@.:< ±

*.:*@** &4.4 ±

*.4*<.4- ±

*.4*,** &)., ±

*.*)@.@< ±

*.:*@:) &:.;) ±

*.*)<.;* ±

*.;*,:) &@.*; ±

*.4*@.@ ±

*.:)@;:.

,&:.@4 ±

*.*)<.;@ ±

*.;*,)* &@.@- ±

*.4*-.@* ±

*.:)@)* &:.,, ±

*.:)<.-) ±

*.;*,-) &-.)4 ±

*.:*,.4) ±

*.;*@-) &;.*: ±

*.4)).4, ±

*.4*

:<



Sample

0reference

(preparation

method)

x ωp

(e)

(e)

4arlsson

0! (")4 @.: *.;*

Schle+el

0# (")& @.+-.* *.@+*.,

i5ory 0$

(reacti5e

sputterin+)

≈4 ,.- 4.;

67hm

0& (solidsolution)

*.< ,. 4.::

4urt8

0'

(")

& ).@:+@.:) *.;+4.:-

S8c8yrbo*si

01, (reacti5e

sputterin+)

4.4@ -.) 4.4

alonen

012 (reacti5e

sputterin+)

& -.*+-.4 *.<+*.@

9resent "ata

(reacti5e

sputterin+)

D4 )., 4.4

:)



:@



10 15 20 25 30

0.25

0.30

0.35

0.40

(a)

Rpp

angle of incidence, /degrees

:-



1.4 1.6 1.8 2.0 2.2 2.4

-15

-10

-5

0

(a)

ε r

Ener%"FeC

1.4 1.6 1.8 2.0 2.2 2.40

5

10

15 (b)

Ener%"FeC

ε i

:,



0.1 0.2 0.3 0.4 0.5 0.6 0.70

2

4

6

8

ε i

λ*

;Fµ$

;

0.2 0.3 0.4 0.5 0.6 0.7 0.8

-8

-6

-4

-2

0

(a)

(b)

ε r L;.4)&4.<* 5 4*4;.λ*:

ε r

λ*

:Fµ$

:

:



2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8-1.4

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

ω

4Fτ L 4.- 5 4*4)

H9

ω* L ).B 5 4*

4)

H9

0 ε

r &

4 2 F ε

i

F4*4)

H9

;*



2.2 2.6 3.0 3.4 3.8

-8

-6

-4

-2

0

(a)

F4*4)

H9

ε r

ω

2.2 2.6 3.0 3.4 3.80

2

4

6

8

(b)

F4*4)

H9

ε i

ω

Documents

Surface Plasmon Polariton