Mechanical modeling of GaN pillars coalescence for growth parameter optimization

Abstract This work focuses on optimizing various growth parameters related to a novel pendeo-epitaxy manufacturing approach aimed at producing high quality gallium nitride (GaN) for optoelectronic applications. The proposed approach consists of growing GaN pyramids on top of GaN/AlN/Si(111)/SiO 2 etched nanopillars on silicon-on-insulator substrates. It is expected that the excess of energy on the vertical edge of the GaN pyramids will allow the pillars to rotate so that the GaN on the top can align crystallographically. This should result in the formation of well-oriented GaN layer with low dislocation density. Finite element simulations using Abaqus software are performed to determine the optimal pillar parameters (e.g. radius ( r ), length, center-to-center distance between two pillars (pitch)) that would reduce the required rotation energy for it to be lower than the available energy, thus making the rotation of the pillars energetically feasible. The results showed that the pitch and the length of the pillars have the least effect on the required rotation energy while the latter is proportional to the square of the rotation angle. These numerical results allowed the development and validation of a simplified analytical model that accounts for the mechanics of the nanopillar in both tilt and twist case. The analytical formulation demonstrated that the most critical parameter is the radius as the required rotation energy is proportional to r 4 . Finally, this work allowed us to predict the optimal strategy for designing samples to enable the growth of high quality GaN layers suitable for micro light-emitting diodes.