The classical orbits of an electron with anisotropic mass interacting with a Coulomb center in the presence of a magnetic field are investigated. It is shown that the shape and duration of the closed orbits depend on the magnetic-field direction. Reasonable agreement with available experimental results for donor-doped silicon samples in a magnetic field is found, when the energy value of the conduction electron is appropriately chosen.

Phosphorous donors in silicon have an electronic structure that mimics the hydrogen atom, albeit on a larger length, smaller energy and smaller magnetic field scale. While the hydrogen atom is spherically symmetric, an applied magnetic field imposes cylindrical symmetry, and the solid-state analogue involves, in addition, the symmetry of the Si crystal. For one magnetic field direction, all six conduction-band valleys of Si:P become equivalent. New experimental data to high laboratory fields (30 T), supported by new calculations, demonstrate that this high symmetry field orientation allows the most direct comparison with free hydrogen.

No abstract

A finite-difference scheme is used to calculate bound electronic states of an electron in a hydrogen atom subject to a magnetic field. The numerical results are in good agreement with exact results, in the absence of the magnetic field, and with a two-parameters variational calculation, when the magnetic field is applied.