Elastic relaxation in transmission electron microscopy of strained-layer superlattices

We demonstrate that thin, cross-sectioned transmission electron microscopy samples from strained-layer superlattices undergo elastic relaxation such that the local lattice parameter modulation amplitude can be reduced by a large fraction. Relaxation is dependent on the ratio of the superlattice wavelength to the local sample thickness and is demonstrated experimentally for molecular beam expitaxially grown Ge_xSi_1-x superlattices both by selected-area diffraction and high-resolution electron microscopy. The results can be qualitatively explained by a simple linear elasticity theory model. Reports of anomalies in the elastic properties of semiconductor superlattices from electron microscopy can be resolved. Evidence is also presented for expected lattice plane bending due to relaxation which can cause strong diffraction contrast. This thin-sample]] artefact" allows unexpectedly weak strain fields to be imaged and permits probing of local elastic properties of individual layers within a superlattice. Similar relaxation effects occur for more general, nonperiodic, elastically strained thin samples, such as the important case of single interfaces.