We have measured and analyzed the optical characteristics of a series of silicon nitride thin films prepared by plasma-enhanced chemical vapor deposition on silicon substrates for photovoltaic applications. Spectroscopic ellipsometry measurements were made by using a two-channel spectroscopic polarization modulator ellipsometer that measures N, S, and C data simultaneously. The data were fit to a model consisting of air/roughness/SiN/crystalline silicon. The roughness was modeled using the Bruggeman effective medium approximation, assuming 50% SiN, 50% voids. The optical functions of the SiN film were parameterized using a model by Jellison and Modine (Appl. Phys. Lett. 69 (1996) 371; 69 (1996) 2137). All the chi(2) are near 1, demonstrating that this model works extremely well for all SIN films. The measured dielectric functions were used to make optimized SIN anti-reflection coatings for crystalline silicon solar cells.