Characterization of non-uniform InGaN alloys: spatial localization of carriers and optical properties

Statistical indium fluctuations in InGaN alloys have been demonstrated to induce spatial localization of carriers. This phenomenon has a strong influence on the behavior of InGaN based light emitting diodes and it is further exacerbated by the presence of compositional non-uniformities. In the present work, we theoretically characterize non-uniform InGaN alloys, taking into account the impact of indium clustering on the electronic and optical properties of the material. The assumption of a non-uniform indium distribution within the bulk structure results in a reduction of the band gap energy and a broadening of the absorption edge with respect to the uniform random alloy configuration, in agreement with the experimental results found in literature. Moreover, we find that it is crucial to consider the presence of compositional non-uniformity in order to derive a theoretical description that is consistent with the outcomes of the experimental studies, especially when the indium content exceeds 10%. Such an effect suggests that a growing indium concentration yields an increment in the amount of indium clustering. Finally, we use the Getis-Ord statistics in order to derive the characteristic localization length of the carriers. This is an original application of this method, usually employed in geospatial analysis.