  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. The results are
consistent with the measured domain growth rates of graphene on Cu substrate.
