  The chemical vapor deposition of polycrystalline diamond (PCD) films is
typically done on substrates seeded with diamond nanoparticles. Specular laser
reflectance and a continuous film model have been used to monitor the thickness
of these films during their deposition. However, most seeds are isolated during
the early stages of the deposition, which questions the utility of applying
such a continuous film model for monitoring deposition before film formation.
In this work, we present a model based on the Rayleigh theory of scattering for
laser reflectance at substrates with growing nanodiamonds to capture the early
stages of PCD deposition. The reflectance behavior predicted by our model
differs from that of a continuous film, which is well-described by the
continuous film model. This difference enlarges as the seed density used in our
model decreases. We verify this trend experimentally by depositing diamond
under identical conditions on substrates with various seed densities. A
relation derived from our model is used to fit reflectance data from which seed
densities are obtained that are proportional to those found with electron
microscopy. We also show that relying on the continuous film model for
describing the early stages of deposition can result in falsely deducing the
existence of incubation, and that the continuous film model can be used safely
beyond the early stages of deposition. Based on these findings, we delineate a
robust method for obtaining growth rates and incubation periods from
reflectance measurements. This work may also advance the general understanding
of nanoparticle growth and formation.
