Dislocation contrast in cathodoluminescence and electron-beam induced current maps on GaN(0001)

TL;DR

This paper provides a theoretical analysis of contrast mechanisms at threading dislocations in GaN(0001) using cathodoluminescence and electron-beam induced current maps, incorporating exciton diffusion and recombination effects.

Contribution

It introduces a rigorous analytical solution for exciton diffusion and recombination near dislocations, enabling quantitative interpretation of experimental contrast.

Findings

Determined exciton diffusion length in GaN.

Quantified recombination strength of threading dislocations.

Validated the model with experimental data.

Abstract

We theoretically analyze the contrast observed at the outcrop of a threading dislocation at the GaN(0001) surface in cathodoluminescence and electron-beam induced current maps. We consider exciton diffusion and recombination including finite recombination velocities both at the planar surface and at the dislocation. Formulating the reciprocity theorem for this general case enables us to provide a rigorous analytical solution of this diffusion-recombination problem. The results of the calculations are applied to an experimental example to determine both the exciton diffusion length and the recombination strength of threading dislocations in a free-standing GaN layer with a dislocation density of $6\times10^{5}$~cm$^{-2}$.