Understanding the elastic relaxation mechanisms of strain in Ge islands on pit-patterned Si(001) substrates

Substrate pre-patterning is a new and effective route for growing ordered arrays of heteroepitaxial nanoislands. Here, by exploiting elasticity theory solved by using finite element methods, we show why islands growing inside pits are better relaxed with respect to the flat-substrate case. Pit pre-patterning is demonstrated to be more important than previously realized, allowing for further degrees of freedom in controlling not only positioning but also shape, strain, and coherence of the growing islands. Our results offer a solid interpretation for the recent experimental results obtained by the group of Professor Guenther Bauer.