Theory of Donor States in Silicon

Kohn and Luttinger’s 1955 paper on the hydrogen-like states of a shallow donor in an indirect semiconductor with anisotropic mass produced a model that predicted the Hamiltonian, the wave functions and their energies, for both the ground state and the excited states. The paper was published just after the first spin resonance experiments on the ground state, and just before the first results for optical excitation to the excited states. The correspondence of the experimental results with Kohn's theoretical prediction is amazing, and although increases in computation power now allow exact solutions of Kohn’s Hamiltonian, they are almost the same as his approximate solutions. In this talk I shall describe two significant extensions, to include (phenomenologically) the central cell correction, and a high magnetic field. The former predict the variation among the Group V impurities in silicon and is important for emerging silicon quantum technologies, and the latter has been used to experimentally validate models of hydrogen on the surface of high magnetic field white dwarf stars.