  Nucleation and its mechanism of diamond on titanium substrates under very low
pressure was studied using hot-filament chemical vapor deposition. Very high
nucleation rates and densities (10^8-10^{10} cm^{-2}) were obtained under 1
torr, which were 1-3 orders of magnitude higher than the counterpart (10^7
cm^{-2}) under conventionally low pressure (tens of torr). The effects of
substrate temperature and methane concentration under very low pressure were
also investigated, revealing that, overly high substrate temperature leads to a
relatively low nucleation density, and that higher CH_4 concentration gives
rise to a higher density and a higher rate. The nucleation mechanism is
discussed in detail. While a large amount of atomic hydrogen creates nucleating
sites, sufficient supersaturation of carbon and/or hydrocarbon species on/near
the substrate surface is the key factor for nucleation, in competition against
the rapid formation of carbide. Very low pressure leads to long mean free path
and other benefiting effects, and hence, is critical for rapid, high-density
nucleation. Effects of substrate temperature and CH_4 concentration are also
important. This further implies that C_2H_x (x<6) and CH_4 also contribute to
nucleation, but CH_{1-3} dominates under very low pressure. The
very-low-pressure method seems to be the only candidate to make diamond
deposition on titanium films applicable. It also sheds light on how to increase
the diamond growth rate.
