A method of depositing a semiconductor material on a substrate. The method sequentially comprises (a) providing the semiconductor material in a depositable state such as a vapor for deposition on the substrate; (b) depositing the semiconductor material on the substrate while heating the substrate to a first temperature sufficient to cause the semiconductor material to form a first film layer having a first grain size; (c) continually depositing the semiconductor material on the substrate while cooling the substrate to a second temperature sufficient to cause the semiconductor material to form a second film layer deposited on the first film layer and having a second grain size smaller than the first grain size; and (d) raising the substrate temperature, while either continuing or not continuing to deposit semiconductor material to form a third film layer, to thereby anneal the film layers into a single layer having favorable efficiency characteristics in photovoltaic applications. A preferred semiconductor material is cadmium telluride deposited on a glass/tin oxide substrate already having thereon a film layer of cadmium sulfide.