A substrate for fabricating semiconductor devices based on Group III semiconductors and the method for making the same. A substrate according to the present invention includes a base substrate, a first buffer layer, and a first single crystal layer. The first buffer layer includes a Group III material deposited on the base substrate at a temperature below that at which the Group III material crystallizes. The Group III material is crystallized by heating the buffer layer to a temperature above that at which the Group III material crystallizes to form a single crystal after the Group III material has been deposited. The first single crystal layer includes a Group III-V semiconducting material deposited on the first buffer layer at a temperature above that at which the Group III semiconducting material crystallizes. In one embodiment of the present invention, a second buffer layer and a second single crystal layer are deposited on the first single crystal layer. The second buffer layer includes a Group III material deposited on the first single crystal layer at a temperature below that at which the Group III material crystallizes. The Group III material is then crystallized by heating the buffer layer to a temperature above that at which the Group III material crystallizes to form a single crystal. The second single crystal layer includes a Group III-V semiconducting material deposited on the second buffer layer at a temperature above that at which the Group III semiconducting material crystallizes.