Strain distribution in quantum dot of arbitrary polyhedral shape: Analytical solution in closed form

An analytical expression of the strain distribution due to lattice mismatch is obtained in an infinite isotropic elastic medium (a matrix) with a three-dimensional polyhedron-shaped inclusion (a quantum dot). The expression was obtained utilizing the analogy between electrostatic and elastic theory problems. The main idea lies in similarity of behavior of point charge electric field and the strain field induced by point inclusion in the matrix. This opens a way to simplify the structure of the expression for the strain tensor. In the solution, the strain distribution consists of contributions related to faces and edges of the inclusion. A contribution of each face is proportional to the solid angle at which the face is seen from the point where the strain is calculated. A contribution of an edge is proportional to the electrostatic potential which would be induced by this edge if it is charged with a constant linear charge density. The solution is valid for the case of inclusion having the same elastic constants as the matrix. Our method can be applied also to the case of semi-infinite matrix with a free surface. Three particular cases of the general solution are considered--for inclusions of pyramidal, truncated pyramidal, and "hut-cluster" shape. In these cases considerable simplification was achieved in comparison with previously published solutions. A generalization of the obtained solution to the case of anisotropic media is discussed.Comment: revtex4, 12 pages, 6 figures; Ch. II rewritten, new Ch. V added, errors in Eq.(13) and Eq.(22) fixe

Phonon bottleneck in p-type Ge/Si quantum dots

We study the effect of quantum dot size on the mid-infrared photo- and dark current, photoconductive gain, and hole capture probability in ten-period p-type Ge/Si quantum dot heterostructures. The dot dimensions are varied by changing the Ge coverage and the growth temperature during molecular beam epitaxy of Ge/Si(001) system in the Stranski-Krastanov growth mode. In all samples, we observed the general tendency: with decreasing the size of the dots, the dark current and hole capture probability are reduced, while the photoconductive gain and photoresponse are enhanced. Suppression of the hole capture probability in small-sized quantum dots is attributed to a quenched electron-phonon scattering due to phonon bottleneck