The Zeeman behavior of shallow donors in silicon has been investigated
within the framework of the effective-mass theory. A numerical approa
ch 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 ac
curate description of the lowest excited states up to fields of about
6 T. In order to describe the Zeeman behavior of the higher excited st
ates, magnetic-field-dependent wave functions have been calculated and
used as a basis for the residual coupling terms in the Zeeman Hamilto
nian. The results of our calculations are compared with experimental d
ata on magnesium- and phosphorus-doped silicon.