A single crystalline silicon carbide layer can be grown on a single crystalline sapphire substrate. Subsequently, a graphene layer can be formed by conversion of a surface layer of the single crystalline silicon layer during an anneal at an elevated temperature in an ultrahigh vacuum environment. Alternately, a graphene layer can be deposited on an exposed surface of the single crystalline silicon carbide layer. A graphene layer can also be formed directly on a surface of a sapphire substrate or directly on a surface of a silicon carbide substrate. Still alternately, a graphene layer can be formed on a silicon carbide layer on a semiconductor substrate. The commercial availability of sapphire substrates and semiconductor substrates with a diameter of six inches or more allows formation of a graphene layer on a commercially scalable substrate for low cost manufacturing of devices employing a graphene layer.