Electronic Structure of InN/GaN Quantum Dots: Multimillion-Atom Tight-Binding Simulations

The theoretical calculation of the electronic structure of any constituent materials is the first step toward the interpretation and understanding of experimental data and reliable device design. This is essentially true for nanoscale devices where both the atomistic granularity of the underlying materials and the quantum-mechanical nature of charge carriers play critical roles in determining the overall device performance. In this paper, within a fully atomistic and quantum-mechanical framework, we investigate the electronic structure of wurtzite InN quantum dots (QDs) self-assembled on GaN substrates. The main objectives are threefold: 1) to explore the nature and the role of crystal atomicity, strain field, and piezoelectric and pyroelectric potentials in determining the energy spectrum and the wave functions; 2) to address the redshift in the ground state, the symmetry lowering and the nondegeneracy in the first excited state, and the strong band mixing in the overall conduction-band electronic states, which is a group of interrelated phenomena that has been revealed in recent spectroscopic analyses; and 3) to study the size dependence of the internal fields and its impact on the electronic structure as a whole. We also demonstrate the importance of 3-D atomistic material representation and the need for using realistically extended substrate and cap layers (multimillion-atom modeling) in studying the built-in structural and electric fields in these reduced dimensional QDs. The models used in this study are as follows: 1) valence-force-field Keating model for atomistic strain relaxation; 2) 20-band nearest neighbor sp ³ d ⁵ s* tight-binding model for the calculation of single-particle energy states; and 3) microscopically determined polarization constants in conjunction with an atomistic 3-D Poisson solver for the calculation of piezo- and pyroelectric contributions.