On strain state and pseudo-moiré TEM contrast of InSb quantum dots coherently grown on InAs surface

Abstract

In this article, we report on the theoretical analysis of transmission electron microscopy (TEM) images of surface InSb quantum dots (QDs) coherently grown on InAs substrate. Afinite element method (FEM) is used to calculate elastic fields and total displacements in a QD and an adjusted region of the substrate. The effects of QD form factor and QD aspect ratio d on displacements and TEM images are analyzed. A quasilinear dependence of radial displacements on radial coordinate for spherical, elliptical, and truncated spherical QDs is demonstrated. It has been found that the displacement field does not depend on the shape and aspect ratio for QDs with δ>δ c1, and the upper part of a QD remains practically undistorted for QDs with δ≥δ c2. For InSb/InAs heterosystem these critical values are δ c1≈0.13 and δ c2≈0.33. The total displacements are used for computation of TEM diffraction contrast associated with QDs. To achieve this the Howie-Whelan dynamic approach is utilized. Calculated TEM images of heavily strained QDs demonstrate the picture of pseudo-moiré with a strong dependence of moiré-like fringe distance Δ on aspect ratio δ. This dependence gives the possibility to determine the aspect ratio and height of QDs from the results of TEM experiments. © 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.