On the formation of multiple quantum dots inside elongated pits on semiconductor films deposited epitaxially on pit-patterned substrates

We report numerical simulation results that provide a comprehensive explanation to recent experimental observations of multiple quantum dot formation inside pits on surfaces of thin films grown epitaxially on nanofabricated substrates with ordered patterns of pits that are elongated and have unequal pit wall inclinations. Our self-consistent dynamical simulations are based on a properly parameterized surface morphological evolution model for biaxially stressed epitaxial thin films and are supported by a nonlinear surface morphological stability theory. Consistently with the experimental observations, we find that quantum dots form inside pits on the film surface if the pits are sufficiently large, with sufficiently steep pit wall slopes, and that the number of quantum dots forming inside each one of these pits increases with increasing length of the long side of elongated pits with different wall inclinations along the two principal pit directions. We also demonstrate that we can precisely control how many quantum dots will form inside each one of the pits by properly tailoring geometrical parameters of the pits on the substrate, such as the pit opening dimensions and pit wall slopes. (paper)