Optical properties of thin films

In this paper we discuss the connection between the microstructure of a heterogeneous thin film and its macroscopic dielectric response ε. Effective medium theory is developed from a solution of the Clausius-Mossotti problem from basic principles. The solution is generalized to obtain the Lorentz-Lorenz. Maxwell Garnett and Bruggeman expressions. The connection between microstructure and absolute limits to the allowed values of the dielectric response of two-phase composites is reviewed. The form of these limits for two-phase composites of known composition and two- or three-dimensional isotropy can be used to derive simple expressions for ε and also for the average fields within each phase. These results are used to analyze dielectric function spectra of semiconductor films for information about density, polycrystallinity and surface roughness. Examples illustrating the detection of unwanted overlayers and the real-time determination of nucleation growth are also given.