Investigations of the electron band structures of InN and related alloys are presented. Theoretical method for calculation of electron band structures based on interactions between atomic orbitals belonging to nearest neighboring atoms is developed. The method is based on the Hartree-Fock model of electron interactions together with the corresponding Kohn-Sham corrections. The one-electron Schrödinger equation describing the interaction between neighboring orbitals is derived. It requires determination of the electron correlation energies. The energy terms, which are solutions of this equation, have further application for the calculation of the LCAO electron band structure of the corresponding compound alloy. The method is applied for the calculations of electron band structures of the following alloys: InN, InGaN, InAlN, InP, InAs, InSb, GaN, AlN and non-stoichiometric InN (with In atoms substitutional on the N site and N atoms substitutional on the In site). The calculated LCAO electron band structures of the semiconductors InN, InGaN, InAlN and non-stoichiometric InN are used for explanation of their optical properties. It is discovered existence of tunnel optical absorptions in InGaN, in InAlN and in non-stoichiometric InN. This phenomenon is investigated in details and it determines optical absorption edge in these structures to vary in interval 0.2 – 1.62 eV. It is found existence of energy pockets in the conduction band and in the valence band respectively due to the defects of these structures and it is discovered excitons of the structure formed by electrons and holes occupying corresponding pockets. The properties of these excitons are investigated in details. It is found that the annihilations between electrons and holes belonging to these excitons determine that PL spectra of these alloys to have maxima in range 0.18 – 0.82 eV. The theoretical results are compared with experimental data.

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