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 , 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
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

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 Polarizationy
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 Polarizationy
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° and Eox = 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 q B 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 BtcosqtBr 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 qtBr qr q B Er E qr q
Ercosqr
Ecosq
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. External Reflection, n2/n1 = 1.5
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 , 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 , 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 ,
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 ,
p. 237

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

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