Ellipsometry Measures the amplitude and phase of reflected light Provides : Film thickness (monolayer capability) Optical constants of thin films (real and imaginary parts) Composition Microstructure (surface roughness, crystallinity) From Herman et al, Fig. 10.22, p. 248

Linear Polarization E-field and B-field are confined to a plane Projection of E-field amplitude onto x-y plane produces a vector y z B Ē x Ē Magnetic field Electric field

Linear Polarization Any polarization state can be represented as a sum of two linearly polarized, orthogonal light waves Ēx = î Eoxei(kz – wt + fx) Ēy = ĵ Eoyei(kz – wt + fy) Ē = Ēx + Ēy = [ î Eoxeifx + ĵ Eoyeify ] ei(kz-wt) = Ēoei(kz-wt) y complex amplitude Ēy Ē Ē z Ēx x

Linear Polarization Ē = [ î Eoxeifx + ĵ Eoyeify ] ei(kz - wt) Ēx and Ēy are in phase  fx = fy y Ē z Ēy Ēx x

Ē = [ î Eoxeifx + ĵ Eoyeify ] ei(kz - wt) What if Ēx and Ēy are not in phase  fx ≠ fy ? fy ≠ fx y Ēy z x Ēx

Elliptical Polarization Ē = [ î Eoxeifx + ĵ Eoyeify ] ei(kz - wt) If Ēx and Ēy are not in phase  Resultant Ē traces out an ellipse  Elliptically polarized light y Resultant Ē w z x v

Elliptical Polarization y fy > fx  left elliptical polarization Polarization vector rotates ccw when looking toward the source w z x v fx > fy  right elliptical polarization Polarization vector rotates cw when looking toward the source y w z v x

Elliptical Polarization y Left elliptical polarization Polarization vector rotates ccw when looking toward the source w x Right elliptical polarization Polarization vector rotates cw when looking toward the source y w x

Circular Polarization fy - fx = 90° and Eox = Eoy  left circular polarization Ēlcp = Eo [ îcos(kz-wt) + ĵsin(kz-wt)] y w z x v fx - fy = 90° and Eox = Eoy  right circular polarization Ērcp = Eo [ îcos(kz-wt) - ĵsin(kz-wt)] y w v z x

Circular Polarization Left circular polarization Polarization vector rotates ccw when looking toward the source y w x Right circular polarization Polarization vector rotates cw when looking toward the source y w x

Polarization by Reflection Light polarization changes upon reflection or transmission at a surface surface normal qi qr Er = ? E n1 dielectric interface n2 qt Et = ?

s and p-polarized light TE polarized light (s-polarized) Bt Et qt n2 n1 Br qr q B Er E TM polarized light (p-polarized) Bt Et qt n2 n1 Br qr q B Er E

Boundary Conditions TE polarized light (s-polarized) Bt qt Et Btcosqt Br B q qr qr q Bcosq Brcosqr E Er Boundary conditions : Bcosq – Brcosqr = Btcosqt E + Er = Et

Boundary Conditions TM polarized light (p-polarized) Etcosqt y Bt x qt Br qr q B Er E qr q Ercosqr Ecosq Boundary conditions : B + Br = Bt Ecosq - Ercosqr = Etcosqt

Fresnel Equations n = n2/n1 Reflection Coefficients: TE: r = Er / E = cosq - √ n2 – sin2q cosq + √ n2 – sin2q TM: r = Er / E = n2cosq - √ n2 – sin2q n2cosq + √ n2 – sin2q Transmission Coefficients: TE: t = Et / E = 2cosq cosq + √ n2 – sin2q TM: t = Et / E = 2ncosq n2cosq + √ n2 – sin2q

Reflectance and Transmittance Reflectance, R = Ir / I = (Er/E)2 = r2 Transmittance, T = It / I = (n2/n1)(cosqt/cosqi) t2 accounts for different rates of energy propagation accounts for different cross-sectional areas of incident and transmitted beams

( ) Reflectance and Transmittance External Reflection, n2/n1 = 1.5 4% R + T = 1 (conservation of energy) At normal incidence (and small angles), R = ( ) 2 n1 - n2 n1 + n2

External Reflection, n2/n1 = 1.5 Phase Shifts External Reflection, n2/n1 = 1.5 qp

Ellipsometry Amplitude and phase of light are changed on reflection from a surface The polarization state of reflected light depends on n1, n2, and q through the Fresnel equations From Herman et al, Fig. 10.22, p. 248

Ellipsometry Ellipsometric parameters r = Rp / Rs = taneiD Rp = Ep (reflected) / Ep (incident) Rs = Es(reflected) / Es(incident) Ellipsometry measures  & D  = tan-1(r) D = differential phase change = Dp - Ds The Fresnel equations relate  & D to the film thickness and optical constants Ellipsometry is surface-sensitive due to ability to measure polarization extremely accurately (extinction ratios > 105 with polarizing prisms)

PRSA Ellipsometry Configuration is polarizer-retarder-sample-analyzer (PRSA) The polarizer and retarder are adjusted to produce elliptically polarized light until the reflected light is linearly polarized as detected using the analyzer (null at the photodetector) retarder (QWP) photodetector laser I = 0 polarizer analyzer n1 n2

Ellipsometry Penetration depth of light in semiconductors ~ mm’s But ellipsometry has monolayer resolution. How? Large dynamic range in intensity measurement (> 105 extinction ratio with polarizing prisms) Use incident angle close to Brewster’s angle

VASE Ellipsometry Vary q and l to determine the optical constants of multilayer thin films laser retarder photodetector l polarizer q q analyzer multilayer film

Rotating Analyzer Ellipsometry PRSA is too slow for real-time monitoring during deposition In situ measurements achieved using rotating analyzer ellipsometry I linear t circular elliptical 2p/w laser photodetector w polarizer q q analyzer multilayer film

In Situ Ellipsometry From Herman et al, Fig. 10.23, p. 249

Other Techniques RAS : Reflectance Anisotropy Spectroscopy = Normal Incidence Ellipsometry (NIE) = Perpendicular Incidence Ellipsometry (PIE) SPA : Surface Photoabsorption = p-polarized reflectance spectroscopy (PRS) SE : Spectroscopic Ellipsometry From Herman et al, Fig. 10.13, p. 237

In Situ Ellipsometry SPA commonly employed for film growth studies SPA commonly performed near qB to maximize surface sensitivity From Herman et al, Fig. 10.13, p. 237

RAS From Herman et al, Fig. 10.18, p. 244

RAS From Herman et al, Fig. 10.19, p. 245