Thermodynamic Self-Limiting Growth of Heteroepitaxial Islands Induced by Nonlinear Elastic Effect

We investigate nonlinear elastic effect (NLEF) on the growth of heteroepitaxial islands, a topic of both scientific and technological significance for their applications as quantum dots. We show that the NLEF induces a thermodynamic self-limiting growth mechanism that hinders the strain relaxation of coherent island beyond a maximum size, which is in contrast to indefinite strain relaxation with increasing island size in the linear elastic regime. This self-limiting growth effect shows a strong dependence on the island facet angle, which applies also to islands inside pits patterned in a substrate surface with an additional dependence on the pit inclination angle. Consequently, primary islands nucleate and grow first in the pits and then secondary islands nucleate at the rim around the pits after the primary islands reach the self-limited maximum size. Our theory sheds new lights on understanding the heteroepitaxial island growth and explains a number of past and recent experimental observations.