Semi-classical orbits of phosphorus donors in silicon under a magnetic field

The manifestation of semi-classical orbits of an electron in the optical spectrum of a hydrogen atom in a magnetic field has been studied experimentally and theoretically in the 1980's. According to the effective-mass theory, shallow donor impurities in semiconductor materials should display a similar dynamics. In 2009, Chen et al. have found experimental evidence of this by photothermal ionisation spectroscopy of a phosphorus-doped silicon sample, with 1011 impurities per cubic centimeter, at 17 K. However, the anisotropy of the effective mass in each valley of the conduction band of silicon poses new theoretical challenges. By numerically solving the equations of motion, we have shown that the shape and duration of the main closed orbits depend on the magnetic-field direction [4]. When the field is applied along the main directions of the silicon crystal, the periods have been found in good agreement with the experimental data reported by Chen et al. [3]. Additionally, a discussion on the appropriate experimental conditions for the manifestation of the semi-classical orbits in the optical spectrum of silicon and other semiconductor materials is presented.