Diffusion coefficient of the order parameter in the early stages of the time evolution of InGaN phase separation

Abstract

We have carried out a study involving a model for the diffusion mechanism of group III atoms in an InGaN alloy semiconductor that uses a cell dynamical system (CDS) approach. In this CDS analysis, we focused on gathering information concerning the In-rich region with a dot-like structure that is formed at an early stage in the time evolution of phase separation of this alloy. A similar dot-like structure is known to appear in the active layer of InGaN-based multiquantum well laser diodes. Thus, we can determine the diffusion coefficient of group III atoms in InGaN by comparing the dot-like structures observed by cross-sectional transmission electron microscopy with those obtained by the CDS numerical approach. In order to perform this comparison quantitatively such that we could use it to calculate the diffusion coefficient, we derived a relationship between the rule of mapping used in CDS, and the discretization of the Cahn–Hilliard–Cook equation, which describes the dynamics of phase separation with a conserved order parameter. The value obtained for the diffusion coefficient is 4×10−16 cm2/s at a growth temperature of 800 °C. From this result, we can conclude that the diffusion of group III atoms arises from atomistic migration on the surface of an InGaN active layer during growth, instead of diffusion within the solid phase.