Can we determine the carrier diffusion length in GaN from cathodoluminescence maps around threading dislocations?

17.04.2020

A popular method to experimentally determine the diffusion length of minority carriers or excitons in semiconductors relies on the perception that threading dislocations are line defects that act as nonradiative sinks for carriers. The zone of reduced luminescence intensity around the dislocation is thus directly related to the carrier or exciton diffusion length. Here, we show that this understanding of a diffusion-controlled intensity contrast around threading dislocations in GaN{0001} is a misconception.

First, we have derived a rigorous solution for the intensity contrast around threading dislocations in GaN{0001} considering fully three-dimensional generation, diffusion and recombination of excitons in the presence of a surface and a dislocation both possessing finite recombination strengths [1]. Our study shows that the phenomenological expression adopted in previous works does not represent a sensible approximation of this intensity profile, and in fact leads to a gross underestimation of the diffusion length.

In a subsequent work [2], we have shown that the relaxation of strain at the outcrop of edge threading dislocations in GaN{0001} gives rise to a piezoelectric field with a strength sufficient to dissociate free excitons and to spatially separate electrons and holes at distances over 100 nm from the dislocation line. The spatial separation inhibits radiative recombination of the electron-hole pairs, and edge threading dislocations hence give rise to dark spots in CL maps very similar to those observed experimentally regardless of exciton diffusion. This result raises the question to what extent the intensity contrast is actually still affected by exciton diffusion, if at all.

Hence, we have next performed Monte Carlo simulations of the exciton diffusion, drift, and recombination in the piezoelectric field at an edge threading dislocation in GaN{0001} [3]. For comparison with the theoretical predictions, we have recorded hyper-spectral CL maps around the outcrop of a threading dislocation of a free-standing GaN(0001) film. To facilitate the clear distinction of the effects of exciton drift and diffusion, these maps have been recorded for various temperatures ranging from 10 to 200 K. Our measurements show that the CL intensity profiles do not notably depend on temperature, despite the fact that the diffusion length is known to significantly decrease with increasing temperature. In contrast, the CL energy profile is observed to depend strongly on temperature. These findings are reproduced by our simulations, which reveal that the mechanism dominating the intensity contrast is the piezoelectric field around the dislocation outcrop, with exciton diffusion changing this contrast only marginally. However, the energy contrast turns out to be highly sensitive to the diffusion length, which we thus propose as a new experimental observable for the actual determination of the carrier diffusion length in GaN.