Electronic structure of piezoelectric In 0.2Ga 0.8N quantum dots in GaN calculated using a tight-binding method

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We have analyzed the electronic structure of In 0.2Ga 0.8N quantum dots (QDs) in a GaN barrier layer using a polarization-potential-dependent sp 3 tight-binding calculation. The dot shapes examined are a hexagonal prism and a hexagonal pyramid. A valence-force-field method was used for calculating the atomic positions and strain; a finite-difference method was used for calculating a piezoelectric potential. For the prismatic QD ( 86.4 A ̊ diameter and 20.8 A ̊ height), we obtained a 0.208 eV red shift of the energy gap between the ground electron and hole levels caused by the built-in piezoelectric field; i.e., the quantum-confined Stark effect. The electron state moves up toward the top and the hole state moves down toward the bottom plane of the QD. At the same time, the squared wave functions for these states exhibit atomic scale fluctuation due to the alloy disorder. For the pyramidal QD (the diameter and height unchanged), a smaller red shift of 0.100 eV is obtained due to the smaller piezoelectric field and smaller dot volume compared to the prismatic QD. The energy gap of the pyramidal QD is in better agreement with the reported photoluminescence peak energy.