Symmetry of the phosphorus donor in diamond from first principles

Abstract

Phosphorus is the only donor in diamond which can be used technologically. Several ab initio theoretical models have been published on substitutional phosphorus, and most of them have predicted that it should have tetrahedral or trigonal symmetry. Recent ab initio calculations suggested that $C_{2v}$, $C_{3v}$, and $D_{2d}$ conformations reduce the total energy. Electron-paramagnetic-resonance experiments performed on phosphorus-doped diamond revealed a phosphorus-related center with tetragonal symmetry, although the signal is only observed below 20 K. We present a detailed ab initio study to show that the phosphorus substitutional atom has tetragonal symmetry at low temperatures. A study of the vibrational modes allows us to investigate the Jahn-Teller origin of the tetragonal distortion and to predict the solubility of phosphorus when grown by chemical vapor deposition with phosphine in the gas phase.