Possibility of finding reliable solid-state tight-binding parameters for the Si-N bond through quantum-chemistry calculations

Tight-binding parameters are obtained through a fit to the molecular levels and electronic populations of ${\mathrm{NH}}_3$, ${\mathrm{SiH}}_4$, Si(${\mathrm{NH}}_2$ ${)}_4$, and N(${\mathrm{SiH}}_3$ ${)}_3$ molecules. The resulting rms deviation of the adjusted molecular levels is only 0.31 eV, proving the goodness of the approach. The electronic structure of stoichiometric silicon nitride is calculated within a Bethe-lattice approach for our tight-binding parametrized Hamiltonian. Our results are discussed and compared with similar calculations using tight-binding parameter sets of several authors. Since our result is as good as or better than previously published electronic structures of a-${\mathrm{Si}}_{3/7}$ ${\mathrm{N}}_{4/7}$, we proceed to further solid-state applications using an effective-medium approximation for the description of the electronic structure of silicon nitride alloys: (i) isolated N impurity in amorphous silicon in two different atomic configurations [planar (three bonds) and tetrahedral (four bonds)], (ii) the evolution of valence- and conduction-band edges of a-${\mathrm{Si}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{N}}_{\mathrm{x}}$ as N content increases, (iii) the position of the Si dangling-bond defect level for the whole range of silicon nitride compositions (the N dangling bond does not introduce any defect level into the semiconducting gap), (iv) the electronic structure around Si-Si homopolar bonds embedded in stoichiometric silicon nitride, and (v) the electronic structure of isolated Si-H and N-H bonds and their behavior as a function of the [N]/[Si] ratio. At the end of the whole process, we reach the conclusion that although our tight-binding parametrization of the Si-N bond cannot be the final one, a large step towards internal consistency is given by our quantum-chemistry approach. We conclude by suggesting some careful experimental analysis that would eventually confirm the existence of the predicted state produced at $E_v$(a-Si)+0.55 eV by isolated N impurities in threefold coordination.