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

STM and RHEED study of the Si(001)-c(8x8) surface

The Si(001) surface deoxidized by short annealing at T~925C in the ultrahigh vacuum molecular beam epitaxy chamber has been in situ investigated by high resolution scanning tunnelling microscopy (STM) and reflected high energy electron diffraction (RHEED). RHEED patterns corresponding to (2x1) and (4x4) structures were observed during sample treatment. The (4x4) reconstruction arose at T<600C after annealing. The reconstruction was observed to be reversible: the (4x4) structure turned into the (2x1) one at T>600C, the (4x4) structure appeared again at recurring cooling. The c(8x8) reconstruction was revealed by STM at room temperature on the same samples. A fraction of the surface area covered by the c(8x8) structure decreased as the sample cooling rate was reduced. The (2x1) structure was observed on the surface free of the c(8x8) one. The c(8x8) structure has been evidenced to manifest itself as the (4x4) one in the RHEED patterns. A model of the c(8x8) structure formation has been built on the basis of the STM data. Origin of the high-order structure on the Si(001) surface and its connection with the epinucleation phenomenon are discussed.Comment: 26 pages, 12 figure

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