Quantitative evaluation of stress-field attenuation in stacks of self-assembled Ge islands

Abstract

We show that a reduced critical thickness observed in stacked layers of self-assembled Ge hut-cluster islands can be quantitatively related to the stress field originating from buried islands. The experimental data for stacks with up to five island layers and Si spacer layers between 3 und 9 nm thick are compared with a simple model for stress-induced reduction of critical thickness. While it is not possible to fit the experimental data using the inverse cubic stress-field scaling of a spherical island, a more accurate fit may be determined by using an inverse linear dependence derived for a pyramid. The best fit was obtained using numerical results calculated for the stress from a truncated pyramid. Si intermixing in stacked layers of hut clusters is experimentally observed and included in the model.