Electronic structures of ${\mathrm{Si}}_2$${\mathrm{N}}_2$O and ${\mathrm{Ge}}_2$${\mathrm{N}}_2$O crystals

We present the results of calculations of electronic band structures, density of states (DOS), and partial density of states of orthorhombic crystals of ${\mathrm{Si}}_2$ ${\mathrm{N}}_2$O and ${\mathrm{Ge}}_2$ ${\mathrm{N}}_2$O. The first-principles orthogonalized-linear-combination-of-atomic-orbitals method is used with the basis function including the Si or $\mathrm{Ge}d$ orbitals. The crystal potential is constructed from a simple superposition of atomic potentials. An indirect band gap of 5.97 eV for ${\mathrm{Si}}_2$ ${\mathrm{N}}_2$O and a direct gap of 3.78 eV at $\Gamma$ for ${\mathrm{Ge}}_2$ ${\mathrm{N}}_2$O are found. It is further recognized that (1) the valence-band DOS of ${\mathrm{Si}}_2$ ${\mathrm{N}}_2$O can be approximately regarded as a superposition of that of $\alpha -\mathrm{S}\mathrm{i}{\mathrm{O}}_2$ and $\beta -{\mathrm{Si}}_3{\mathrm{N}}_4$ crystals with an exception at the top of the valence-band edge which is derived from the oxygen lone-pair orbitals. (2) The effective charges on Si and Ge atoms are 1.99 and 1.50 electrons, respectively, indicating that ${\mathrm{Si}}_2$ ${\mathrm{N}}_2$O is more covalent than ${\mathrm{Ge}}_2$ ${\mathrm{N}}_2$O. These and other results are discussed in connection with local atomic structures and with available experimental information.