A method based on the Green’s function technique for calculating strain in quantum dot (QD) structures has been developed. An analytical formula in the form of a Fourier series has been obtained for the strain tensor for arrays of QDs of arbitrary shape taking into account the anisotropy of elastic properties. Strain distributions using the anisotropic model for semiconductor QDs are compared to results of a simplified model in which the elastic properties are assumed to be isotropic. It is demonstrated that, in contrast to quantum wells, both anisotropic and isotropic models give similar results if the symmetry of the QD shape is less than or equal to the cubic symmetry of the crystal. The strain distribution for QDs in the shape of a sphere, cube, pyramid, hemisphere, truncated pyramid, and flat cylinder are calculated and analyzed. It is shown that the strain distributions in the major part of the QD structure are very similar for different shapes and that the characteristic value of the hydrostatic strain component depends only weakly on the QD shape. Application of the method can considerably simplify electronic structure calculations based on the envelope function method and plane wave expansion techniques.
A simple method is presented for calculating the stress and strain distributions arising from an initially uniformly strained quantum dot of arbitrary shape buried in an infinite isotropic medium. The method involves the evaluation of a surface integral over the boundary of the quantum dot and is therefore considerably more straightforward to implement than alternative stress evaluation techniques. The technique is ideally suited to calculating strain distributions within disordered arrays of pyramidal quantum dots prepared by Stranski–Krastanow growth. The strain distribution for a cuboidal quantum dot is presented and compared to that of a rectangular quantum wire.
Strain and quantum confinement energies in ntype modulationdoped latticemismatched InAsP quantumwell wires
Strain analysis of a quantum-wire system produced by cleaved edge overgrowth using grazing incidence x-ray diffraction Appl. Phys. Lett. 83, 872 (2003); 10.1063/1.1597962In-plane strain distribution in free-standing GaAs/InGaAs/GaAs single quantum well surface nanostructures on GaAs[001] J. Appl. Phys. 85, 1524 (1999); 10.1063/1.369282Threshold current of quantum-disk and quantum-wire gain-coupled distributed feedback lasers Analytic expressions are derived for the strain field due to a lattice-mismatched quantum wire buried in an infinite medium whose cross-section is composed of any combination of line elements and circular arcs. Expressions for the strain field for rectangular, triangular and circular quantum wires are found confirming published results. For the rectangular wire, useful limiting relations are obtained for the stress components close to the edge of the wire. Good agreement is demonstrated with measurements of lattice spacing reported by Chen et al. ͓Appl. Phys. Lett. 65, 2202 ͑1994͔͒ for an In 0.2 Ga 0.8 As/GaAs rectangular wire if the indium concentration is assumed to be 24%. The strain field of a single AlGaAs/GaAs crescent-shaped wire, with and without lateral wells, is presented. The lateral wells introduce only minor modifications to the strain distribution when compared to a wire of the same thickness but without lateral wells. For a crescent-shaped quantum-wire stack, it is found that the strain field of each wire is almost independent of other wires in the stack when the wire separation is five times the thickness or more.
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