A mathematical modelling of dislocations reduction in InxGa1−xN/GaN heteroepitaxy using step-graded interlayers

In this work, a mathematical approach has been developed to calculate dislocations reduction in step-graded InGaN heteroepitaxy. The generation of different types of misfit dislocations (MDs) in expected slips and their reduction with increasing interlayer have been calculated. The significant improvements of MDs confirm the prohibition of their generation with increasing the interlayer up to 4 where 8% In composition difference used for each step-graded interlayers. The system of differential equations for threading dislocations (TDs) according to all possible burger vectors have been developed considering annihilation, fusion reaction as well as TDs blocking by MDs and solved them numerically. The results show the decreasing nature of TDs with the average densities of 8.68×10¹⁰, 7.4×10¹⁰ and 1.32×10¹⁰ cm^-2 for edge, screw and mixed character respectively at the top surface of the epilayer. The results have good agreement with the published experimental values.