Selection rules for angular-resolved photoionization of single P donor atom in silicon

In this work we analytically derive the expression of the dipole matrix elements for the photoionization process of a singe phosphorus donor atom embedded in silicon upon irradiation by linearly polarized optical pulses at different incidence angles relative to the bulk crystallographic axes. The derived expressions evidence a drastic dependence of the photoelectron angular distribution on the orientation of the polarization axis relative to the crystallographic axes of silicon. The narrowest angular distribution is obtained for a polarization directed along [001], [010] and [100] crystallographic axes.