Quadratic Zeeman effect of shallow donors in silicon

Abstract

The Zeeman behavior of shallow donors in silicon has been investigated within the framework of the effective-mass theory. A numerical approach has been used to calculate the wave functions on a discrete radial mesh by the Lanzcos method. The Zeeman Hamiltonian has been evaluated in a limited basis set of zero-field wave functions resulting in an accurate description of the lowest excited states up to fields of about 6 T. In order to describe the Zeeman behavior of the higher excited states, magnetic-field-dependent wave functions have been calculated and used as a basis for the residual coupling terms in the Zeeman Hamiltonian. The results of our calculations are compared with experimental data on magnesium- and phosphorus-doped silicon.