Elastic strain relaxation of GeSi nanoislands grown on pit-patterned Si(001) substrates

In this paper, we systematically investigate the elastic strain relaxation of GeSi nanoislands grown on pit-patterned Si(001) substrate using finite element method. The multi-faceted GeSi nanoislands, including domes, barns and cupolas, inside square pit are modeled based on experimental observations. The impacts of aspect ratio, pit angle and pit filling level are analyzed, based on which a fitting expression is obtained to give a complete description of the strain relaxation. The pit angles corresponding to the best strain relaxation and to the critical point for better relaxation in pit are determined at filling levels (range from 0 to 1) and aspect ratios (range from 0.2 to 0.4). It can be seen that beyond a specific aspect ratio, the relaxation keeps worse than the case of same nanoisland grown on flat substrate, regardless of the pit angle and pit filling level. Moreover, based on the strain energy balance criterion, the conditions to ensure that nanoislands grown inside pit are demonstrated as well.