Numerical Study of InGaN Pattern Formation Caused by Phase Separation

Abstract

We performed a numerical study of the two-dimensional pattern formation of InGaN driven by a phase separation using the cell dynamical system (CDS) approach to reveal the detailed nature of a self-assembled InGaN dot-like structure showing characteristic optical properties. We calculated two-dimensional pattern formations under various conditions. First, over a wide In compositional range (0 < In < 0.6), a dot-like structure appears arising from a phase separation as well as due to the effects of strains and defects. These results are consistent with those in the case of experimentally observed structures reported earlier. Thus, we can conclude that in the present study, the pattern formation by a phase separation affects the emission mechanism of InGaN-based semiconductor light-emitting device because of a compositional fluctuation of In. Second, the calculated results suggest that the pattern formations depend on the experimental parameters, such as growth temperature, the average and local fluctuation of In composition, the lattice mismatch of InGaN and GaN, and defects.

Effect of anisotropic current of the order parameter onInxGa1−xNcompositiona

“…In previous papers, 6,7 we also found that the diffusion of the constituents has a strong effect on the evolution rate in the phase separation, that is, on the width of the In compositional fluctuation at an early stage of phase separation. Furthermore, we noticed that it is very important to enhance the diffusion in order to obtain a spatially uniform In composition.…”

“…In a numerical study of InGaN-based light-emitting devices, this CDS simulation represents the process simulation of the phase separation during the growth of the InGaN active layer. 6,7 In the second step, we consider the two factors responsible for the time evolution of : ͑i͒ phase separation induced by the driving force due to the mixing free energy and ͑ii͒ compositional uniformity induced by the driving force due to the diffusion of the constituents denoted by a phenomenological diffusion constant D. For factor ͑i͒, we introduced the map f () for the transformation as the driving force arising from the mixing free energy ⌬G, as described by the single-cell dynamics. This map f should have the features provided by the bistability of ⌬G for InGaN.…”

“…͑3͒ includes both factors ͑i͒ and ͑ii͒, and the second term represents the current of the order parameter induced by diffusion: namely, the factor ͑ii͒. In the model for isotropic current in previous works, [5][6][7] we defined ͗͗(t,n)͘͘ in Eq. ͑3͒ as follows:…”

“…We studied numerically the details of In compositional fluctuation and a spontaneous formation of a dotlike structure in the InGaN QW active layers of InGaNbased LD's and LED's. 6,7 In these previous works, we ob-tained the following outcome for each of the LD's and LED's by comparing the numerical results with experiments. First, the numerical result for InGaN with an average In composition close to the spinodal point (In 0.24 Ga 0.76 N) employed as the active layer of LD's shows that the dotlike structure formation is induced by the small spatial fluctuation in In composition at an early stage in the time evolution of phase separation.…”