A stochastic simulation of the dislocation-mediated etching of porous GaN distributed Bragg reflectors

Abstract

Distributed Bragg reflectors (DBRs) can be fabricated by electrochemically etching nitride epitaxial structures consisting of alternating layers of highly n-type doped and non-intentionally doped (NID) GaN. Threading dislocations (TDs) can be electrochemically etched into transport pipelines that can carry the etchant through the NID layers to access the doped material. Experimentally this has been shown to involve a mechanism where the etching pathway may follow one TD into a doped layer and then propagate sideways through the doped layer to continue via a different TD. Across multiple layers this process creates complex pore structures that have been described as 'cascades'. Here, we build a stochastic simulation for the DBR etching process that can reproduce some key features of the observed microstructures including the cascade morphology. By comparing the simulation output to samples etched at a range of voltages, we show that we can reproduce variations in experimental chronoamperometry data with applied bias by varying the probability of etching the doped layers within the simulation. The outputs of the resulting simulations replicate the experimentally observed cascade morphology. At higher voltages, experimental data reveal a lower proportion of cascade features, a trend that is also replicated by the simulations for relevant probability values. Outputs of the simulations also correlate well with experimental chronoamperometry data for samples where - unlike in a DBR - the thicknesses of the doped layers vary through the epitaxial multilayer, suggesting that the probabilistic simulation can be applied to a range of structures to help understand the dislocation-mediated electrochemical etching process.