Two new structures for epitaxy of diamond and c-BN on a Si(001) substr
ate, in a parallel orientation and with 3:2 registry, are proposed and
also compared with a structure proposed earlier for a 45-degrees rota
ted orientation of a diamond overlayer. All the models largely elimina
te dangling bonds in the interface, and several variations are conside
red with and without additional atoms of hydrogen or oxygen incorporat
ed into the structure. The atomic geometry of each model is optimized
by minimization of the total energy of periodically repeated atomic cl
usters, calculated by fully self-consistent semi-empirical quantum che
mical methods. It is found that the 45-degrees rotated structure is pa
rticularly favourable for very thin diamond layers, but for thicker la
yers the single bridge 3:2 model that works best for c-BN is also pref
erred by diamond. The differences in the two materials are interpreted
in terms of the way that the parallel model exploits the differences
in both the size and atomic valencies of the constituent atoms in c-BN
.