Structural disorder and electronic properties of amorphous silicon

We have performed a first-principles calculation of the electronic energies for amorphous Si using the method of orthogonalized linear combinations of atomic orbitals. The basis functions are the $3s$, $3p$ Bloch sums for each atom in the large quasi-unit-cell orthogonalized to all $1s$, $2s$, $2p$ Bloch sums. All the multicenter integrals and Hamiltonian matrix elements are computed exactly by the Gaussian technique with no empirical parametrization. Applied to a recently constructed periodic random-network structural model, the method yields a band gap of 0.67 eV. An alternative scheme is to employ as basis functions orthogonalized $3s$, $3p$ orbitals centered at sites within a cluster to obtain energy levels and to configurationally average the results over several clusters. This scheme is applied to make similar analyses for the nonperiodic networks of Polk and Boudreaux (as refined by Steinhardt, Alben, and Weaire) and of Connell and Temkin; the calculated band gaps are 2.19 and 1.24 eV, respectively. The general profiles of the density of states for different nets show relatively little variation, but the band gap depends quite sensitively on the details of the structural disorder.