Ellipsometry Equations for Film-Covered Surfaces

Derivation of Ellipsometry Equations for Film-Covered Surfaces 

Derivation of the reflection coefficient expressions and the ellipsometry equations for film-covered surfaces employing matrix operations will be shown here. The treatment is similar to Heavens and Hayfield and White. This matrix method is less cumbersome, especially when multiple films are involved, compared to another frequently used method of deriving the reflection coefficients, in which amplitudes of individual beams resulting from multiple reflections and transmissions at the interfaces are summed. 

we want to find the matrix relations between the amplitudes across the two boundaries at 2 = 0 and z = t. For waves 

The situation at the second boundary at z = t is identical except that subscripts 1 and 2 are now replaced by 2 and 3, respectively  

Since the amplitudes E - remain constant within each medium, Eq. (A-14) also holds for the amplitudes  

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Al. Derivation of Ellipsometry Equations for Film-Covered Surfaces... 

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