Spectroscopic ellipsometry (SE) has been used to routinely characterize amorphous silicon nitride and diamond thin films. Since SE measurements do not yield quantities of interest directly, the SE data must first be fit to a model to obtain useful parameters such as film thickness and optical functions. The Tauc-Lorentz (TL) model for the optical functions of amorphous materials [Appl. Phys. Lett. 69, 371/373, 2137 (1996)] has been shown to be very useful in interpreting these SE results. A four-parameter model is usually sufficient to describe the optical functions of the thin film to the accuracy of the ellipsometer. One of these parameters, the band gap E-g, correlates with other mechanical and chemical properties of the film, such as the silicon-to-nitrogen ratio in silicon nitride films, and to the sp(3)-bonded carbon fraction and the hardness of amorphous carbon films.