Three-dimensional strain field calculations in multiple InN/AlN wurtzite quantum dots

A detailed calculation of the three-dimensional elastic strain field and Gibbs free energy in and around InN/AlN wurtzite quantum dots is presented. The strain tensor is calculated by minimizing the Helmholtz free energy on a three-dimensional grid. The boundary conditions for a free surface are rigorously implemented to enable the strain field and Gibbs free energy at the surface to be modeled realistically. This has implications for the growth of additional layers of dots above a seed layer and can serve as an arbiter for determining possible nucleation sites. Results are presented for a single dot as well as coupled dots. The Gibbs free energy is seen to exhibit strong minima directly above a layer of seed dots, facilitating vertical ordering. Under certain conditions, satellite minima can also occur. Using the calculated strain field, the piezoelectric polarization field is also calculated. Because of the strong lattice mismatch, the strain field is quite large, particularly near the base and apex of the dots. This, in turn, leads to piezoelectric charges with magnitudes as high as 10(14) cm(-2) in regions of high strain. (C) 2001 American Institute of Physics.