Introduction to Ellipsometer
4. Drude's Equations

Ellipsometry was first used by Drude to measurement very thin film in 1889. Drude's equation is a counterpart of Fresnel's equation for the film structure. It is the basic of the ellipsometry.

Drude's equations can be derived from Fresnel's equation with combination of the interference between the layers. The reflected light is a superposition of beams , and , where the subscript 01 means light enter medium 1 from medium 0 and b is the phase delay the beam experiences during propagating from the top surface of the film to the bottom surface of the film. The subscripts s and p are ignored here for both components, following this rule. From last section we know that and . These lead us to the Drude's equations:

For a stack of multiple layers, the Drude's equations can be used recursively from the bottom to the top layer. Frensel's reflection and transmission amplitude coefficient of each surface are first calculated; an effective coefficient of the bottom film is calculated by substituting the amplitude coefficient into Drude's equations; then by using this effective coefficient as an amplitude coefficient, an effective coefficient of next-to-the-bottom layer is calculated by the Drude's equations, until the top layer is reached.

For transparent films, will be periodic as the thickness of film increases, causing the periodicity of vector (Y,D) as functions of film thickness. This non-uniqueness is a main limitation of ellipsometer.

Reflection and Fresnel's Equation Ellipsometers and Software