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 Ill-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 …