On the definition of the domain growth rate constant on a two dimensional substrate

In chemical vapor deposition (CVD) methods, the domain grows by attachment of diffusing surface bound species on the substrate to an island of solid domain. We formulate the process of single domain growth under two-dimensional diffusion by taking into account the movement of the domain boundary. We first discuss two types of definition of the domain area growth rate constant; the one defined through the domain size divided by the time duration of CVD growth and the other defined through the area divided by time. Then, we show that the domain size is proportional to time for the reaction limited growth and the domain area is proportional to time for the diffusion limited growth. We also show that the domain area growth rate changes from the reaction limited growth to the diffusion limited growth as the domain size increases beyond a characteristic size.