Localization by an external magnetic field of electrons on the ions of hydrogen-like donors in non-degenerate semiconductors

Abstract

In the quasi-classical approximation of quantum mechanics a model for the localization of conduction electrons on the ions of hydrogen-like donors in an external magnetic field was developed. The thermal ionization energy of donors in lightly doped and moderately compensated crystals of gallium arsenide and indium antimonide of n-type was calculated depending on the induction of the external magnetic field. In contrast to the known theoretical works (which use variational methods for solving the Schrödinger equation), a simple analytical expression is proposed for the ionization energy of the donor in the magnetic field, which quantitatively agrees with the known experimental data. It is shown that the magnitude of the magnetic field induced by the orbital motion of the electron around the ion core of the donor is negligible compared to the external field and does not contribute to the ionization energy of donors.