Impact of seed density on continuous ultrathin nanodiamond film formation: an analytical approach

An analytical mean field approach for describing the time evolution of film growth by seeding has been developed. The modeling deals with the generic case of anisotropic growth with different growth rates, respectively on -- and normal to -- the substrate plane. The finite size of the seeds is considered by including spatial correlation effects among seeds through hard-core interactions. The approach, based on probability theory, provides solution in closed form for mean film thickness as a function of substrate coverage, seed density and initial size of the seeds. For negligible values of the initial coverage of the substrate by seeds, manageable analytical expressions are attained. The model has been validated by comparison with experimental data available in the literature. This study is significant in connection to the possibility of determining optimal growth conditions for ultrathin nanocrystalline diamond (NCD) film. In fact, the knowledge of the seeding/nucleation density that allows a given minimum average thickness of continuous film is of utmost importance for the development of technologically advanced applications.