Interface structure and strain state of InAs nano-clusters embedded in silicon

We present a quantitative transmission electron microscopy (TEM) study about the interface structure and strain state of buried InAs nano-clusters in Si(001) grown by molecular beam epitaxy. The nano-clusters show a typical polyhedral shape of 4-12 nm in diameter with {1 1 1} and {0 0 1} interface planes. Moiré fringe analysis based on dark-field images and high-resolution (HR) TEM reveals that the nano-clusters are almost fully relaxed via the creation of misfit dislocation loops that are restricted only in the InAs/Si interface region, whereas the Si matrix is defect-free. Nevertheless, depending on the individual shape of the nano-clusters, a small amount of anisotropic residual strain in the nano-clusters is identified via strain mapping by geometric phase analysis. The scenario of mismatch stress relaxation by the formation of dislocation loops is discussed with a theoretical model based on continuum elasticity which qualitatively explains the experimental results.