Statistical Analysis of the Spatial Distribution of InAl Droplet-Etched Nanoholes in In0.52Al0.48As Layers

By analyzing atomic force microscopy images, we studied the spatial distribution of nanoholes etched by InAl droplets in In0.52Al0.48As surfaces, employing molecular beam epitaxy. We identified two temperature regimes, which exhibit significantly different droplet aggregation behavior. The droplet density shows an exponential decrease with increasing temperature in the low-temperature regime (300–390 °C), which is characterized by an activation energy of 0.34 eV, whereas for the high-temperature regime (435–505 °C), the exponential decrease persists but with a much larger activation energy of 2.20 eV. The increased activation energy is accompanied by a strong elongation of the denuded zone around the nanoholes in the distribution of the nearest neighbors along the [011] direction, whereas the distribution is almost isotropic in the low-temperature regime. In both temperature regimes, we observe a narrowing of the capture-zone size distribution with increasing temperature; however, the distribution broadens with the transition to the high-temperature regime before narrowing again with further increasing temperature. By employing nucleation theory, we find that the critical nucleus size does not appear to be significantly different between the two temperature regimes. However, Ostwald ripening is probably relevant, so nucleation theory does not describe our experiments completely. We propose a change in the surface reconstruction, with a more anisotropic arrangement in the high-temperature regime as the underlying reason for the significantly different behavior in the two regimes.