From ultrananocrystalline diamond to single crystal diamond growth in hot filament and microwave plasma-enhanced CVD reactors: a unified model for growth rates and grain sizes

CVD Diamond can now be deposited either in the form of single crystal homoepitaxial layers, or as polycrystalline films with crystal sizes ranging from mm, mu m or nm, and with a variety of growth rates up to 100s of mu m h(-1) depending upon deposition conditions. We previously developed a model which provides a coherent and unified picture that accounts for the observed growth rate, morphology, and crystal sizes, of all of these types of diamond. The model is based on competition between H atoms, CH(3) radicals and other C, radical species reacting with dangling bonds on the diamond surface. The approach leads to formulas for the diamond growth rate G via mono and biradical dimer sites and for the average crystallite size < d >, that use as parameters, the substrate temperature and the concentrations of H and CH, (0 <= x <= 3) near the growing diamond surface. We recently added a correction factor to the equation for < d > and we now test the predictions of this new equation for diamond crystallite sizes ranging from 10 nm (ultrananocrystalline diamond) to several mm (for single crystal diamond). We find that our model predicts the growth rates of all the forms of diamond to within a factor of 2, and predicts crystal sizes for the growth from CH(3) that are consistent with those seen experimentally. We deduce that growth of diamond is a sliding scale, with different types of diamond arising from a smoothly changing ratio of atomic H to hydrocarbon radical concentrations [H]:Sigma CH(x)] at the growing surface. The different growth conditions, gas mixtures, temperatures and pressures reported in the literature for diamond growth, simply serve to fix the value of this ratio, and with it, the resulting film morphology and growth rate. In general, for conditions of high [H] at the surface, diamond growth is predominantly from CH(3) addition to monoradical sites, leading to large crystals (or even single crystal growth). With decreasing [H]/[CH(3)], a competing growth channel emerges whereby CH(3) adds to biradical sites and the average crystallite size is reduced simultaneously to mu m or even nm for very low [H]/[CH(3)] ratio. In a third growth channel involving atomic C adding to either mono or biradical sites, the spare 'dangling bond' can promote renucleation events and increase possibilities for cross-linking, leading to even smaller nm-sized crystallites. This channel can be dominant in high temperature reactors (e.g., MW plasma-enhanced CVD in 1%CH(4)/(0-2%)H(2)/Ar mixtures) where high hydrogen dissociation degree shifts the population distribution in CH(x) group in favor of C atoms.