Electronic states and bonding configurations in hydrogenated amorphous silicon

A series of realistic structural models have been constructed for hydrogenated amorphous silicon ($a-\mathrm{Si}:\mathrm{H}$) with the hydrogen atoms appearing as SiH, Si${\mathrm{H}}_2$, Si${\mathrm{H}}_3$, ${\left(\mathrm{S}\mathrm{i}{\mathrm{H}}_2\right)}_2$, SiHHSi (a broken Si-Si bond with two H atoms inserted), SiHSi (bridge form), an interstitial atom, and an atom at the center of a six-member ring (ring-center model) in an otherwise continuous-random-tetrahedral network of amorphous silicon. The electronic energies for each structural model (with one H-bonding configuration) are calculated by using the first-principles method of linear combinations of atomic orbitals in which all the multicenter integrals in the Hamiltonian matrix elements are evaluated exactly. In the cases of the SiH, Si${\mathrm{H}}_2$, Si${\mathrm{H}}_3$, SiHHSi, and ${\left(\mathrm{S}\mathrm{i}{\mathrm{H}}_2\right)}_2$ configurations, the calculated local densities of states of the valence band for the H atoms agree well with photoemission experiment, but a distinct discrepancy is found for the SiHSi bridge model and the ring-center model. The SiHHSi and ${\left(\mathrm{S}\mathrm{i}{\mathrm{H}}_2\right)}_2$ models give gap states near the conduction-band edge, the occurrence of which is attributed to the interhydride interaction. The SiHHSi model is in good agreement with several sets of experiments and provides a simple mechanism for incorporating H atoms in amorphous Si to fairly high concentrations.