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Strain profiles and radii of semiconductor rolled-up tubes made by a single material



Single-material rolled-up microtubes provide an opportunity to study the processes of strain relaxation and defect formation near the interface of strained-layer semiconductor heterostructures. We study theoretically tubes formed by a single strained Si layer grown beyond the critical thickness on a Ge substrate. The residual strain accumulated in the Si layer causes the layer to roll after it is released from the substrate by etching. Computer simulations are carried out using Keating's valence force field method, with uniform and non-uniform residual (initial) strain profiles and different strained layer widths. We show that the radius of the tubes is affected by a combination of these two factors and thus by the total elastic deformation present before rolling, a larger total deformation resulting in a smaller tube radius. However, uniform and non-uniform residual strain profiles can be easily distinguished by analyzing the final profiles of the azimuthal and the radial strain components.