Assessing the composition of hetero-epitaxial islands via morphological analysis: an analytical model matching GeSi/Si(001) data

A simple, but still three-dimensional, model describing the morphological stability of realistic SiGe islands on Si(001) is presented. The experimental evolution toward steeper islands with volume can be predicted for any average composition. Despite the use of elastic theory for stress relaxation under the assumption of a uniform SiGe distribution, and of a common mean surface energy of the faceted islands, the model seems to capture the essence of the energetic balance determining the morphological evolution with volume, with no fitting parameters. This is suggested by close comparison with molecular beam epitaxy data at three different temperatures (i.e. compositions). The good agreement also allows for interpreting the minor scattering of experimental data with temperature and provides a reliable tool for extracting the average Ge content from standard atomic force microscopy analysis.