Excitations in amorphous pyramidally bonded solids. I. Electrons

The electronic and phonon state densities of amorphous pyramidally bonded solids are calculated. These solids are shown to exhibit a unique isomorphism between the electronic and vibrational state densities. This atypical correspondence between the state densities suggests that a study of the electronic states can be used to understand the vibrational states. Arsenic, which epitomizes pyramidally bonded solids, is chosen as a prototype. Our results reproduce the trends founds in the x-ray photoemission data (XPS) for rhombohedral and amorphous As. The effects of bond-angle variations and topological disorder upon the $s$- and $p$ -like regions of the XPS spectra are investigated. A prescription is given by which the behavior of the $p$-like electrons in pyramidally bonded solids can be understood in terms of the behavior of the $s$-like electrons.