Elastic Energy Relaxation in Buried Quantum Dots
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Elastic Energy Relaxation in Buried Quantum Dots Vladimir V. Chaldyshev1, Anna L. Kolesnikova2, and Alexei E. Romanov1 1 Ioffe Institute, St. Petersburg, Russian Federation 2 Institute of Problems of Mechanical Engineering, St. Petersburg, Russian Federation ABSTRACT We theoretically analyze three models, which correspond to three different ways of the elastic energy relaxation in buried quantum dots. The first model considers formation of a pair of prismatic dislocation loops. One of them lies on dot/matrix interface, whereas the other is a satellite and locates in the adjacent matrix. The second model also includes the satellite loop and differs from the first one by non-local reduction of the dot plastic distortion. The origin of the satellite loop is the materials conservation requirement. The third model considers the case when this requirement is violated and only the misfit dislocation loop is formed. We determine the critical radii of the dots and loops, as well as the dependence of the satellite loop size on the dot size. The model calculation are compared to the relevant experimental data. INTRODUCTION Elastic distortions play an important role in the material systems with buried quantum dots. These distortions often govern the dot self-organization and ordering processes, electronic and atomic structure, optical and electronic properties. Relaxation of the elastic energy is usually undesirable due to crucial impact on the material crystallinity and corresponding device performance. Elastic strains in structures with quantum dots (QD) are caused by crystal lattice mismatch between the materials of QD and surrounding matrix. The energy associated with these elastic strains and corresponding mechanical stresses scales with the volume of the QD if the coherency state at the interface is maintained. Stress relaxation leads to the strain energy release due to generation of dislocation at the QD. These dislocations can be either misfit dislocations (MDs) nucleated at QD/matrix interface [1,2] or satellite dislocations (SD) placed in a vicinity of the QD [3,4]. In this paper we analyze three schemes of the strain energy release, involving MD and SD formation in heterosystems with QDs (also referred to as nanoinclusions). ELASTIC FIELDS AND ENERGY OF A NANOINCLUSION In our analysis, unrelaxed QD can be considered as a spheroid nanoinclusion coherently embedded in a matrix. It is therefore assumed that no defects (i.e. dislocations) are located at (or near) QD/matrix interface. For the simplest case of cubic materials, the crystal lattice mismatch a QD − a mat ( a QD between QD and matrix can be characterized by a single misfit parameter ε m = a QD and a mat are lattice parameters of QD and matrix materials, correspondently). Knowledge on the inclusion shape, misfit parameter and elastic constants for both QD and matrix materials is enough to find elastic fields and energy associated with a nanoinclusion.
For the most general case of lattice mismatch between QD and matrix, the technique of self- (“ei
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