Strain in ultrathin SiGeSn layers in a silicon matrix

Strain in SiGeSn alloy layers with thicknesses of $d = 1.5$ and $2.0$ nm grown in a Si matrix by molecular-beam epitaxy is investigated using the geometric-phase analysis of high-resolution electron microscopy images. The layer thickness is comparable to the spatial resolution of the method ($\Delta\sim 1$ nm), which leads to a considerable distortion of the strain distribution profile and an error in determining the strain value. A correction to the measured strain making it closer to the true value is obtained by comparing the shapes of the observed and real strain distributions in the investigated layers. The correction is determined by the $\Delta/d$ ratio. The found strain values are in good agreement with the calculations for pseudomorphic layers in the model of a rigid substrate.