Dislocation contrast in cathodoluminescence and electron-beam induced current maps on GaN(0 0 0 1)

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 × 10 5 cm −2 .

Determination of the Carrier Diffusion Length inGaNfrom Cathodoluminescence Maps Around Threading Dislocations: Fallacies and Opportunities

“…For example, a diffusion length of 400 nm was obtained in Ref. [17] from the room-temperature profile taken on the same sample as in the present work.…”

“…In the present work, we extend our previous theoretical framework [17] and explicitly consider, in addition to exciton diffusion, the effects of the three-dimensional strain distribution associated to an edge threading dislocation at the GaN{0001} surface, i. e., exciton drift in the strain field and exciton dissociation in the piezoelectric field induced by the changes in strain. We solve this complex three-dimensional problem by an advanced Monte Carlo scheme [25,26].…”

“…where Γ is the surface z = 0 of the half-infinite crystal, ν the outward surface normal vector, and S the surface recombination velocity. A similar boundary condition, with an analogous recombination velocity, can be written at the dislocation line represented by a thin cylinder [17]. Let us integrate Eq.…”

Recombination activity of threading dislocations in GaInP influenced by growth temperature

“…In order to deconvolve these parameters, line plots of the CL intensity at individual dislocations were extracted from the CL images and compared to a phenomenological model of CL intensity at dislocations. 13 In this model, an analytical solution is obtained for CL intensity in thin films with a point source of carriers, a dislocation with arbitrary recombination strength, and front and back surfaces with arbitrary surface recombination velocities. We adapt this solution to our quantum wells with a few assumptions.…”

“…Thus, the value of was assumed to be constant and equal to 1 nm as has been done previously. 13 Finally, the model setup to calculate CL intensity for a point source lends itself to convolution to account for a laterally diffuse source in the quantum well due to electron beamsample interactions in CL. Ordinarily, the spread due to beam-sample interaction in bulk samples is lowest at low accelerating voltage.…”