Electronic energy structure of amorphous silicon

Abstract

By using the method of orthogonalized linear combinations of atomic orbitals (OLCAO), a first-principles calculation of the electronic energy of amorphous silicon has been performed. The lattice model used is Henderson's quasiperiodic continuous random tetrahedral network (CRTN) with 61 atoms per unit cell. The potential function is contructed from a superposition of the atomic potentials of Si at each site with a Slatertype exchange approximation. The basis functions consist of the $3s$- and $3p$-type Bloch sums for each atom in the unit cell orthogonalized to all the $1s$, $2s$, $2p$ Bloch sums so that the latter can be deleted from the basis set. All the multicenter integrals occurring in the Hamiltonian matrix elements are evaluated exactly by means of the Gaussian technique and the summation of the multicenter integrals over the lattice is carried to convergence. The calculated density of states (DOS) of the valence band is in good agreement with the experimental data. No intrinsic gap is found in this calculation but the DOS near the Fermi level is very small. Local maxima in the DOS are found to be present both above and below the Fermi level. As an alternative scheme, we have also performed OLCAO calculations based on configurational average of clusters generated from Henderson's CRTN instead of covering the entire quasicrystal as done by using Bloch-sum functions. The undesirable surface effect in cluster calculations is circumvented by taking the Hamiltonian as that of the infinite solid. The resulting DOS are compared with that obtained from the quasicrystal calculations in order to assess the accuracy of the cluster approach.