Electronic structure of SiN$_x$

The electronic structure of amorphous silicon nitride SiN x enriched with silicon as a function of its chemical composition has been calculated in the tight-binding approximation without fitting parameters. A new method of parametrization of the matrix elements of the tight-binding Hamiltonian has been proposed with allowance for the variation of the localization region of the valence electrons of the isolated atom in the process of its incorporation into a solid. It has been shown that allowance for these variations makes it possible to calculate the electronic structure using the parameters of the isolated atoms as the initial data. The latter circumstance allows the calculation on the absolute energy scale with zero corresponding to the energy of the electron in vacuum.