Multiscale Kinetic Monte Carlo Simulation of Self-Organized Growth of GaN/AlN Quantum Dots

A three-dimensional kinetic Monte Carlo methodology is developed to study the strained epitaxial growth of wurtzite GaN/AlN quantum dots. It describes the kinetics of effective GaN adatoms on an hexagonal lattice. The elastic strain energy is evaluated by a purposely devised procedure: first, we take advantage of the fact that the deformation in a lattice-mismatched heterostructure is equivalent to that obtained by assuming that one of the regions of the system is subjected to a properly chosen uniform stress (Eshelby inclusion concept), and then the strain is obtained by applying the Green's function method. The standard Monte Carlo method has been modified to implement a multiscale algorithm that allows the isolated adatoms to perform long diffusion jumps. With these state-of-the art modifications, it is possible to perform efficiently simulations over large areas and long elapsed times. We have taylored the model to the conditions of molecular beam epitaxy under N-rich conditions. The corresponding simulations reproduce the different stages of the Stranski-Krastanov transition, showing quantitative agreement with the experimental findings concerning the critical deposition, and island size and density. The influence of growth parameters, such as the relative fluxes of Ga and N and the substrate temperature, is also studied and found to be consistent with the experimental observations. In addition, the growth of stacked layers of quantum dots is also simulated and the conditions for their vertical alignment and homogenization are illustrated. In summary, the developed methodology allows one to reproduce the main features of the self-organized quantum dot growth and to understand the microscopic mechanisms at play.