A Model for the Critical Height for Dislocation Annihilation and Recombination in GaN Columns Deposited by Patterned Growth

In order to reduce vertical leakage in III-nitride detectors, we have grown a patterned array of hexagonal GaN columns on masked heteroepitaxial GaN template layers using a-plane sapphire substrates. In addition to eliminating cracking, we have found that for GaN columns tens of microns in diameter and several microns high, the dislocation density is also significantly reduced. We have developed a simple closed-form analytical model for predicting the critical column height for the onset of the reduction in the dislocation density. Among the predictions of this model is that the critical column height for the onset of dislocation density reduction is proportional to the product of column width and the grain size of the GaN film.