Ellipsometry Overview

Transcription

1 llpsometry Overvew ~ R Δ p ρ = ta( Ψ) e = ~ Rs ñ(λ) = (λ) + k(λ) ε = ñ 2 p-plae s-plae p-plae plae of cdece s-plae

2 llpsometry buldg-blocks Lght ad Polarzato Materals / Optcal Costats Iteracto of Lght wth Materals llpsometry Procedure Measuremet Aalyss

3 lectromagetc Plae Wave Lght From Maxwell s equatos we ca descrbe a plae wave X 2π ( z, t) = 0 s ( z vt) + ξ λ ampltude l wavelegth velocty arbtrary phase Y lectrc feld, (z,t) Magetc feld, B(z,t) Z Drecto of propagato

4 Lght Lght Frequecy of wave remas the same Velocty ad wavelegth vary dfferet materals υ = v λ c v = ergy of photo ( ev speed speed of of lght lght ) = hυ = 1 = 2 1,240 λ ( m ) Plack s Plack s costat costat

5 Itesty ad Polarzato Lght Itesty = Sze of lectrc feld. I 2 Polarzato = Shape of lectrc feld travel. Y Less Itese Dfferet Sze (Itesty) More Itese Y X Same Shape! (Polarzato) X

6 Learly Polarzed Lght Lght X ad Y propagate same drecto -felds orthogoal; waves -phase Result: learly polarzed wave the 'plae of vbrato' depeds o ampltudes of x & Y X wave1 Y wave2 Z

7 Crcularly Polarzed Lght Lght x ad Y have: equal ampltude X wave1 90 out of phase Y wave2 Z

8 llptcally Polarzed Lght Lght x ad Y have arbtrary phase ad ampltude Result s ellptcal X wave1 Y wave2 Z

9 Optcal Costats Materal Complex Refractve Idex: ñ= + k Descrbes what materal does to lght wave. Alteratvely Complex Delectrc Fucto:ε= ε 1 + ε 2 Descrbes what lght does to materal. ε 1 = volume polarzato term ε 2 = volume absorpto ε = ñ 2

10 Complex Refractve Idex Materal (λ) = Refractve Idex ñ(λ) = (λ) + k(λ) Descrbes wave velocty ad refracto. k(λ) = xtcto Coeffcet Descrbes loss of eergy.

11 Kramers-Krog Relato Materal Real ad magary parts deped o each other. ε 1 ε 2 Absorpto causes aomalous dsperso. k Frequecy (eergy)

12 Optcal Costats Materal Absorpto by dfferet mechasms: Free-carrer, lattce ad molecular vbrato, electroc trasto IR UV

13 Trasparet Rego Materal Idex decreases for loger wavelegths. Hgher dex whe close to large absorpto. Idex, SO2 S3N4 S Wavelegth m

14 Delectrc Materal lectrc feld causes oscllatg electro charge cloud. Photo I lectros move easly, atomc core too heavy to move. Dsplaced charge = lectrc Dpoles.

15 Delectrc Materal Atoms borrow eergy from electrc feld. The gve t back wth NO LOSS. DIPOL RADIATION! Oscllatg Dpole New Photo Out! - Same Frequecy - Same ergy = hν

16 Delectrc Materal Oscllatos take tme Re-emtted wave s delayed. I Phase Out of Phase Referece Wave Wave has bee slowed Idex, = (speed vod)/(speed materal)

17 Absorbg Rego Materal lectrc feld loses eergy to a process materal lectroc Trasto Lattce Vbrato Molecular Vbrato Free-carrer

18 lectroc Trasto Materal lectros eergy bads. Gap betwee valece ad coducto bad. If photo has eergy larger tha gap, electro ca excte to hgher state.

19 lectroc Trasto Materal ergy bads ca be very complcated wth dfferet acceptable trastos (drect or drect). S. Adach, Optcal propertes of crystalle ad amorphous semcoductors, Kluwer Academc Publshers, Bosto (1999).

20 lectroc Trasto Materal Absorpto for each trasto. 1.2 Imag(Delectrc Costat), ε Slco GaAs ε Idrect gap S GaAs Drect gap Photo ergy (ev) Photo ergy (ev)

21 Amorphous or Crystalle Materal lectroc trastos broadeed for amorphous materals.

22 Molecular Vbrato Materal lectrc Feld wth slow frequecy (IR) ca vbrate molecules (stretch or bed). CH2 stretch (symmetrc) CH2 stretch (asymmetrc) N-H stretch C=O stretch

23 Lattce Vbratos Materal lectrc Feld causes lattce to vbrate Logtudal (LO) or Trasverse (TO) Optcal 180 TO 2TO TO+LO k Δ degrees TO+LA Wave Number (cm -1 )

24 Free-carrers Materal Metals have more electros tha eeded for bodg (covalet bods = sharg electros). lectrc feld causes free electros to move! Wave eergy lost as heat.

25 Free-carrers Materal Absorb strogly for low frequecy electrc feld k creases toward IR Idex of refracto, k Nckel Wavelegth (m) xtcto Coeffcet, k Idex of refracto, k Alumum xtcto Coeffcet, k Wavelegth (m)

26 Optcal Costat Summary Materal Trasparet rego: dex decreases toward loger wavelegths (ormal dsperso) Absorbg rego: KK cosstecy creates aomalous dsperso Dfferet absorbg mechasms cosdered.

27 Lght at terface Iteracto Reflectos caused by dex dfferece: Normal cdece: Oblque Icdece Refracto Reflecto Ñ 1 s φ 1 = Ñ 2 s φ 2 R = ( ) 1 2 ( + ) dex, Ñ 1 velocty, c φ 1 φ 1 φ = φ r dex, Ñ 2 velocty, v φ 2

28 Plae of Icdece Iteracto lectrc feld ether parallel (p) or perpedcular (s) to plae of cdece. Plae of Icdece defed by: p p Icdet Ray s p s Sample Normal Reflected Ray s plae of cdece

29 Iteracto Polarzed Reflecto P- ad S- waves do ot mx (sotropc-case) Materal dfferetates betwee p- ad s- lght Rp Rs Reflecto Agle of Icdece ( )

30 Fresel Coeffcets Descrbe reflecto ad trasmsso at terface: Deped o agle ad polarzato drecto (p or s) t t t t p r p r θ θ θ θ cos cos cos cos = = t t t t s r s r θ θ θ θ cos cos cos cos = = t t s t s t θ θ θ cos cos cos = = t t p t p t θ θ θ cos cos cos = = Iteracto

31 Th Flm Iterferece Iteracto r tot = -2β -4β r01 + t01r12t10e + t01r12 r10t10e r 01 t 01 r 12 t 10e -2β FILM PHAS THICKNSS ~ 0 ~ 1 t 01 r 12 r 10 r 12 t 10 e -4β β = d1 2π 1 cos θ 1 λ ~ 2

32 llpsometry Measuremet Iteracto Measures chage polarzato of reflected lght. Sample s defed by reflecto of p- ad s- polarzed lght. p s out = ~ R 0 p 0 ~ R ~ R Δ p ρ = ta( ψ ) e = ~ Rs s p s p-plae s-plae plae of cdece p-plae s-plae ρ = Re( ρ) + Im(ρ ) = ta(ψ)cos( Δ) + ta(ψ)s(δ) = ta(ψ)e Δ = R p R s e (δ p δ s ) =?R p?r s

33 What ca S determe? llpsometry Measures: Propertes of Iterest: Flm Thckess Refractve Idex Ps (Ψ) Delta (Δ) Surface Roughess Iterfacal Mxg Composto Crystallty Asotropy Uformty

34 What I Stu llpsometry Measures Substrate temperature Substrate surface qualty Oxde thckess ad desorpto Iterfacal regos Growth ad etch rates Substrate ad flm optcal costats (before surface oxdato) Idex gradets Alloy composto Multple-layer thckesses