A cascade model for the defect-driven etching of porous GaN distributed Bragg reflectors

Fabrication of porous GaN distributed Bragg reflectors (DBRs) via the selective electrochemical etching (ECE) of conductive Si-doped layers, separated by non-intentionally doped (NID) layers, provides a straightforward methodology for producing highly reflective DBRs suitable for device overgrowth and integration, which has otherwise proven difficult in the III-nitride epitaxial system via conventional alloying. Such photonic materials can be fabricated by a lithography-free defect-driven etching process, where threading dislocations intrinsic to heteroepitaxy form nanoscale channels that facilitate etchant transport through NID layers. Here, we report the first three-dimensional characterisation of porous GaN-on-Si DBRs fabricated in this methodology with different ECE voltages, using serial-section tomography in a focused ion beam scanning electron microscope (FIB-SEM). These datasets reconstruct the pore morphology as etching proliferates through the alternating Si-doped/NID layer stack. Volumetric reconstruction enabled us to enhance the established `kebab' model for defect-driven etching by proposing a `cascade' model where etchant cascades through the material via vertical etching down nanopipes and horizontal etching across pores, forming complex networks directly related to the pathways taken. This accounts for premature nanopipe termination and discontinuities in nanopipe formation, where dislocations are observed to activate and deactivate individually. Statistical analysis of individual etching behaviour, across all dislocations for each tomograph, revealed a greater tendency to form continuous structures that follow conventional kebab behaviour at higher ECE voltages. We propose that higher ECE voltages alter the probability of dislocation etching relative to doped layer etching, thereby empowering morphological optimization through improved mechanistic understanding of ECE.