Random-Bethe-lattice model applied to the electronic structure of amorphous and liquid silicon

Bethe lattices of arbitrary number of nearest-neighbor atoms and geometrical configurations are defined for the standard ${\mathit{sp}}^3$ ${\mathit{s}}^{\mathrm{*}}$ tight-binding Hamiltonian that gives correctly both valence and conduction bands of crystalline Si. Averaged densities of states are obtained through a well-grounded extension of the coherent-potential approximation to random Bethe lattices with off-diagonal disorder. In that way, a unified picture of the electronic structure of Si in amorphous and liquid phases is obtained. Formation energies of dangling and floating bonds are estimated within Chadi’s tight-binding scheme.