Electron spin resonance experiments were performed on Si-doped wurtzite and
zinc-blende GaN and Si-doped wurtzite AlxGa1-xN alloys with x = 0.15, 0.32
, 0.52, 0.75, and 1. For zinc-blende GaN, an isotropic g factor of 1.9475 i
s found. The g tensors of the silicon effective mass donor in wurtzite GaN
and AlxGa1-xN alloys are determined experimentally, and for x<0.38 are iden
tical within experimental error to tensors observed in unintentionally n-ty
pe-doped material. With increasing Al content, the g values increase and th
e g-tensor anisotropy is reduced. The g values are calculated within a five
-band k . p model in the cubic approximation. To account for the isotropic
g factor of wurtzite AlN, a nonvanishing spin-orbit coupling of the higher
<Gamma>(5) conduction bands of the order of 50 meV is necessary. To describ
e the anisotropy at lower Al content, a full seven-band k. p model for the
wurtzite crystal structure is investigated. The model shows that the anisot
ropy in this material system is also due to coupling to higher conduction b
ands rather than to valence bands. Additional estimates for the momentum ma
trix elements and the interband mixing coefficients are discussed.