Elements of Ellipsometry
1. Introduction
An ellipsometer is an instrument for measuring the change in polarization which occurs when light is incident on an interface or sequence of interfaces between media of different refractive index. Light with its electric vector parallel to the surface (s or Transverse Electric) is reflected with a change in amplitude and phase which is different from that for light with its electric vector in the plane of incidence (p or Transverse Magnetic). Incident light with both s and p components will be elliptically polarized after reflection (except in special cases), and this fact gives the instrument its name. A null ellipsometer has a polarizing prism (called the analyzer) in the reflected beam, and this prism is rotated to minimize the light reaching the detector. If the reflected light is linearly polarized, no light reaches the detector when the analyzer is crossed with it, and the instrument is 'at null'. For the reflected light to be linearly polarized, the incident light must have an appropriate elliptical polarization. This elliptical polarization is produced by two optical components inserted into the incident beam. The incident light passes first through a rotatable polarizing prism (called the polarizer), and then through a quarter-wave plate with its axes fixed at 45 degrees to the plane of incidence. After passing through the wave plate, the incident light is elliptically polarized with axes at 45 degrees to the plane of incidence. The ellipticity of the incident light is determined by the angle between the axes of the polarizer and the wave plate. For a null at the detector, the polarizer is rotated to find the incident ellipticity that results in linear polarization after reflection. The optics of the instrument will be discussed in detail in Section 7.
Reflection and refraction are governed by the electromagnetic nature of light, in particular by the requirement that the tangential components of E and H be continuous across boundaries between media. At normal incidence, however, light waves obey the same laws of reflection as waves on a string and waves in quantum mechanics. The same boundary conditions apply at interfaces, and the same matrices can be used to deal with sequences of interfaces. The layout of the following sections takes advantage of this fact. Concepts are introduced in their simplest forms, then are brought together to deal with the reflection of polarized light from film-covered surfaces.