PHOTO-IONIZATION OF DEEP IMPURITIES IN SEMICONDUCTORS

A calculation has been made of the photo-ionization spectrum for transitions from an atomic-like ln shell of an impurity to a conduction or valence band in a semiconductor. As a specific example we consider transitions from a localized substitutional impurity to a Γ conduction band in a semiconductor of zinc-blende symmetry. The photo-excited carrier wave function is taken as u(k, r)F(k, r) where u(k, r) is the periodic part of the Bloch function and F(k, r) is the wave function of an unbound electron in a Coulomb field. The shape of the spectrum of photo-ionization from an l n configuration of a free atom is largely determined by the variation with energy of the l ± 1 component of F(k, r). On the other hand, the spectrum for an ln impurity in a semiconductor is dominated by the variation with energy of the l ± 1 component of u(k, r). In the calculation, this variation was obtained from Kane's k. p method. The calculated spectrum for chromium-doped gallium arsenide is in good agreement with experimental results near the absorption edge.