Phonon Spectra of Tetrahedrally Bonded Solids

Abstract
A theorem is presented which establishes an isomorphism between the eigenvalues of Keating's model Hamiltonian for the vibrations of tetrahedrally bonded solids, in the limit in which bond-bending forces are zero, and those of a simple "one-band" Hamiltonian which has been found useful in understanding features of the electronic density of states of amorphous semiconductors. We explain the similarity of the phonon spectra of amorphous and crystalline group-IV semiconductors, demonstrated in various recent experiments.