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

TL;DR

This paper analyzes the growth rate constants of domains in chemical vapor deposition on a 2D substrate, distinguishing between reaction and diffusion limited growth, and how the dominant process shifts with domain size.

Contribution

It introduces a formulation for single domain growth considering boundary movement and clarifies the relationship between domain size, area, and growth regimes.

Findings

Domain size grows linearly with time in reaction limited growth.

Domain area grows linearly with time in diffusion limited growth.

Growth regime transitions from reaction to diffusion as domain size increases.

Abstract

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.