Ellipsometry

1. 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

2. 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

3. Linear Polarization 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) • Any polarization state can be represented as a sum of two linearly polarized, orthogonal light waves y complex amplitude Ēy Ē Ē z Ēx x

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

5. 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

6. 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

7. 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

8. 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

9. 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°andEox = Eoy  right circular polarization Ērcp = Eo [ îcos(kz-wt) -ĵsin(kz-wt)] y w v z x

10. 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

11. 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 = ?

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

13. Boundary Conditions TE polarized light (s-polarized) Bt qt Et Btcosqt qt n2 n1 Br B q qr qr q Bcosq Brcosqr E Er Boundary conditions : Bcosq – Brcosqr = Btcosqt E + Er = Et

14. Boundary Conditions TM polarized light (p-polarized) Etcosqt y Bt x qt qt Et z n2 n1 Br qr q B Er E qr q Ecosq Ercosqr Boundary conditions : B + Br = Bt Ecosq- Ercosqr = Etcosqt

15. 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

16. 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

17. 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

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

19. 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

20. 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)

21. 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

22. 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

23. 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

24. 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

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

26. 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

27. 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

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

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