The new method of solid-phase epitaxy based on the substitution of atoms and on the creation of dilatation dipoles solves one of the major problems in heteroepitaxy. It provides the synthesis of low-defective unstrained epitaxial films with a large difference between the lattice parameters of the film and the substrate without using any additional buffer layers. This method has another unique feature distinguishing it from the classical techniques of SiC films’ growth—it allows the growing of SiC films of hexagonal polytypes. A new kind of phase transformation in solids owing to the chemical transformation of one substance into another will be described theoretically and revealed experimentally. This type of phase transformation, and the mechanism of a broad class of heterogeneous chemical reactions between gas and solid phases, will be illustrated by an example of the growth of SiC epitaxial layers due to the chemical interaction of CO gas with the monocrystalline silicon matrix. The discovery of this mechanism yields a new kind of template: namely, substrates with buffer transition layers for wide-gap semiconductor growth on silicon. The properties of a variety of heteroepitaxial films of wide-gap semiconductors (SiC, AlN, GaN and AlGaN) grown on a SiC/Si substrate by solid-phase epitaxy will be reported. Grown films contain no cracks and have a quality sufficient to manufacture micro- and opto-electronic devices. Also, the new abilities in the synthesis of large (150 mm diameter) low-defective SiC films on Si substrates will be demonstrated.