Higher Donor Excited States for Prolate-Spheroid Conduction Bands: A Reevaluation of Silicon and Germanium

An extension of the Kohn-Luttinger method for the energy levels of the effective-mass Hamiltonian H=(Pₓ²2m_⊥+Py²2m_⊥+Pz²2m_∥)-e²Kr is made via the Rayleigh-Ritz approach. The method is capable of indefinite extension provided one is prepared to deal with large matrices. The first nine S-like energy levels and the first eighteen P-like energy levels are presented here as a function of the mass ratio γ=m_⊥m_∥ for 0<γ≤1. The experimental results for the P-like excited states of silicon and germanium can be fitted to within experimental error if one takes the low-temperature static dielectric constant of silicon to be 11.40±{}0.05, and that of germanium to be 15.36±{}0.05. The situation concerning donor levels in GaP is discussed briefly.