Impact of the dislocation density on the transient photoluminescence intensity in GaN semiconductor

The time-resolved photoluminescence in a layer of GaN with an embedded array of threading dislocations is studied. An instantaneous spatially uniform source of excitons is considered. The transport and recombination of excitons is governed by a 3D transient drift-diffusion-recombination equation with mixed Dirichlet and Robin boundary conditions on the plane surface and the cylindrical boundaries of the dislocations. We develop a stochastic simulation algorithm which solves this problem by tracking exciton trajectories. The drift of the excitions is affected by the piezoelectric fields around the dislocations. The parameters of the piezoelectric field, the exciton's diffusion length and its mean life time are taken from the experimental study published recently in our triple article in Physical Review Applied of 2022. The main finding in the present paper concerns the relation between the photoluminescence intensity and the dislocation density. It is shown that from a transient photoluminescence curve it is possible to extract the dislocation density with high resolution.