Shallow acceptor resonant states in Si and Ge

The energy spectrum and the wave functions of shallow acceptors in Si and Ge are computed within the effective-mass approximation using the full cubic symmetry and including the spin-orbit split-off band ${\mathrm{\Gamma }}_7^{+}$. In addition to the usual bound states, resonant states are found and distinguished from other states which lie in the continuum; they are connected with the ${\mathrm{\Gamma }}_7^{+}$ band, but also contain ${\mathrm{\Gamma }}_8^{+}$ mixing. The oscillator strengths of the optical transitions from the ground to the odd-parity states have been calculated, and an interpretation of the experimental spectra in terms of bound and resonant states is given for Si. For the case of Ge our results predict the existence of shallow hydrogenlike resonant states associated with the ${\mathrm{\Gamma }}_7^{+}$ split-off band.