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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.

Strained semiconductor nanostructures can be used to make single-photon sources, detectors and photovoltaic devices, and could potentially be used to create quantum logic devices. The development of such applications requires techniques capable of nanoscale structural analysis, but the microscopy methods typically used to analyse these materials are destructive. NMR techniques can provide non-invasive structural analysis, but have been restricted to strain-free semiconductor nanostructures because of the significant strain-induced quadrupole broadening of the NMR spectra. Here, we show that optically detected NMR spectroscopy can be used to analyse individual strained quantum dots. Our approach uses continuous-wave broadband radiofrequency excitation with a specially designed spectral pattern and can probe individual strained nanostructures containing only 1 × 10(5) quadrupole nuclear spins. With this technique, we are able to measure the strain distribution and chemical composition of quantum dots in the volume occupied by the single confined electron. The approach could also be used to address problems in quantum information processing such as the precise control of nuclear spins in the presence of strong quadrupole effects.

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