  The dependence of the g-factors of semiconductor donors on applied electric
and magnetic fields is of immense importance in spin based quantum computation
and in semiconductor spintronics. The donor g-factor Stark shift is sensitive
to the orientation of the electric and magnetic fields and strongly influenced
by the band-structure and spin-orbit interactions of the host. Using a
multimillion atom tight-binding framework the spin-orbit Stark parameters are
computed for donors in multi-valley semiconductors, silicon and germanium.
Comparison with limited experimental data shows good agreement for a donor in
silicon. Results for gate induced transition from 3D to 2D wave function
confinement show that the corresponding g-factor shift in Si is experimentally
observable.
