1. Ellipsometry with Mueller Matrix for Transparent Substrate
Dept. of Physics, Kyunghee University, Suwon
Tae Dong Kang

2. Reflection of Linearly Polarized Light
plane of incidence E
p-plane
s-plane
1. linearly polarized light ...
2. reflect off sample ...
3. elliptically polarized light !

3. Jones Vector
Non-depolarization, completely polarized light
;Ref.[1]

4. Possible reasons of depolarization
Scattering in the sample or at its surface (rough interface)
Variation in the film thickness or refractive index across the illuminated area (inhomogeneous)
Not or partially resolved interference pattern, if the layer is thick with respect to the resolution of the measurement (resolution limit)
coherent
incoherent

5. Mueller-Stokes approach

6. Reflected Light = ; degree of polarization 1 1 ;Ref. [1],[3],[8]
The definition of partially polarized light in Ref. [1] is distinguished from that in ref. [8].
; degree of polarization

7. Relationship between Jones and Mueller matrices,

8. Calculation

9. Mueller Matrix

10. ;where there is cross-polarization. [5]
->The p- and s-polarized lights can be mixed in anisotropic media. ( e.g. the sample have optical activity or an opto-magnetic material which is given light or magnetic field.) [6]

11. Stokes Vector for reflected light
Theoretical values of Stokes vector 1 1
; P=45o
Polarizer =
;degree of polarization
;Ref. [8] ,
degree of polarization

12. Reflection coefficient

13. Ref.[4]

14. ; thickness nonuniformity
Phase thickness
Stokes parameters

15. Application to a glass substrate
MSE=
MSE=
MSE : mean square error

16. Calculation of Degree of Polarization
; experimental data
Stokes parameters of experimental value of a glass substrate and the degree of polarization.
We can not find out the degree of polarization from the experimental data.

17. ; theoretical data of degree of polarization

18. Conclusion
A relationship between Jones and Mueller matrices derived for random media is applied to incoherence effects in photometric ellipsometry.
Such effects are for example depolarization after reflection from a sample with varying film thickness or from a layer which is thicker than the coherence length of the incident light.
We can apply ellipsometry to thick transparent substrates, for example as transmission ellipsometry or as ellipsometry at the back surface of the substrate.
We can find out the degree of polarization not from the experimental data but by fitting the theoretical values to the experimental values.

19. References K. Forcht et al., Thin Solid Films 302(1997) 43-50.
R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light, North-Holland, Amsterdam, 1987, p. 51.
M. Kildemo et al., Thin Solid Films (1998)
Mathias Schubert et al. J. Opt. Soc. Am. 13(1996)
김상열, 타원법, 아주대학교 출판부, p. 52.
Y. H. Yang and J. R. Abelson, J. Vac. Sci. Technol. A 13(3) (1995)
David S. Kliger et. Al., Polarized Light in Optics and Spectroscopy, Academic Press, p. 82.