Single-crystalline hexagonal GaN (&agr;-GaN) films have been grown on (0001) sapphire substrates by metalorganic chemical vapor deposition at 1040 °C. The complex dielectric functions,&egr;(E)=&egr;1(E)+i&egr;2(E),of the epitaxial films have been measured by spectroscopic ellipsometry (SE) forE⊥cin the region between 1.5 and 5.0 eV at room temperature. Previously published ultraviolet SE spectra of &agr;-GaN are examined by considering the effects of surface roughness using an analysis based on an effective medium model.Ex situatomic force microscopy is used to assess independently surface flatness. By mathematically removing the effects of surface roughness, the most reliable&egr;(E)values for &agr;-GaN are presented in the 1.25–10 eV photon–energy range. Theoretical dispersion analysis suggests that theE0structure could be characterized by a three-dimensionalM0critical point and theE1&agr;(&agr;=A,B,C)structures by two-dimensionalM1critical points. To facilitate design of various optoelectronic devices, dielectric-function-related optical constants, such as the complex refractive index, absorption coefficient, and normal-incidence reflectivity of &agr;-GaN are also presented. ©1997 American Institute of Physics.