Elastic relaxation of truncated pyramidal quantum dots and quantum wires in a half space: An analytical calculation

We give a fully analytical solution for the elastic displacement and strain fields of arbitrarily shaped truncated pyramidal quantum dots (QDs) and trapezoidal quantum wires buried in a half space, assuming linear isotropic elasticity. The half-space geometry pertains in particular to QD semiconductor structures both during and after growth. The calculations are illustrated by examples showing quantitatively that with respect to the case of the infinite matrix and depending on the depth of the QD under the free surface the strain relaxation afforded by this surface may significantly affect the magnitude and the distribution of the various strain components inside the QD as well as in the matrix.