Mechanical properties, strength physics and plasticity

Elastic fields and physical properties of surface quantum dots

N. A. Bert^a, A. L. Kolesnikova^b, I. K. Korolev^b, A. E. Romanov^a, A. B. Freidin^b, V. V. Chaldyshev^a, E. C. Aifantis<sup>c

a</sup> Ioffe Institute, St. Petersburg
^b Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, St. Petersburg
^c Aristotle University of Thessaloniki, Thessaloniki, Greece

Abstract: Elastic fields in a system consisting of a surface coherent axisymmetric quantum dot-island on a massive substrate have been theoretically studied using the finite element method. An analysis of the influence of the quantum dot shape (form factor) and relative size (aspect ratio) $\delta$ on the accompanying elastic fields has revealed two critical quantum dot dimensions, $\delta_{c1}$ and $\delta_{c2}$. For $\delta>\delta_{c1}$, the fields are independent of the quantum dot shape and aspect ratio. At $\delta\ge\delta_{c2}$, the quantum dot top remains almost undistorted. Variation of the stress tensor component $\sigma_{zz}$ ($z$ is the quantum dot axis of symmetry) reveals a region of tensile stresses, which is located in the substrate under the quantum dot at a particular distance from the interface. Using an approximate analytical formula for the radial component of displacements, model electron microscopy images have been calculated for quantum dot islands with $\delta>\delta_{c1}$ in the InSb/InAs system. The possibility of stress relaxation occurring in the system via the formation of a prismatic interstitial dislocation loop has been considered.

Received: 10.03.2011
Accepted: 17.03.2011

 English version: Physics of the Solid State, 2011, 53:10, 2091–2102

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