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

The Role of Interdiffusion and Spatial Confinement in the Formation of Resonant Raman Spectra of Ge/Si(100) Heterostructures with Quantum-Dot Arrays

The phonon modes of self-assembled Ge/Si quantum dots grown by molecular-beam epitaxy in an apparatus integrated with a chamber of the scanning tunneling microscope into a single high-vacuum system are investigated using Raman spectroscopy. It is revealed that the Ge-Ge and Si-Ge vibrational modes are considerably enhanced upon excitation of excitons between the valence band $\Lambda_3$ and the conduction band $\Lambda_1$ (the E1 and E1 + $\Delta_1$ transitions). This makes it possible to observe the Raman spectrum of very small amounts of germanium, such as one layer of quantum dots with a germanium layer thickness of 10 \r{A}. The enhancement of these modes suggests a strong electron-phonon interaction of the vibrational modes with the E1 and E1 + $\Delta_1$ excitons in the quantum dot. It is demonstrated that the frequency of the Ge-Ge mode decreases by 10 cm^-1 with a decrease in the thickness of the Ge layer from 10 to 6 \r{A} due to the spatial-confinement effect. The optimum thickness of the Ge layer, for which the size dispersion of quantum dots is minimum, is determined.Comment: 14 pages, 9 figure

Spin Relaxation in Ge/Si Core-Shell Nanowire Qubits

Controlling decoherence is the most challenging task in realizing quantum information hardware. Single electron spins in gallium arsenide are a leading candidate among solid- state implementations, however strong coupling to nuclear spins in the substrate hinders this approach. To realize spin qubits in a nuclear-spin-free system, intensive studies based on group-IV semiconductor are being pursued. In this case, the challenge is primarily control of materials and interfaces, and device nanofabrication. We report important steps toward implementing spin qubits in a predominantly nuclear-spin-free system by demonstrating state preparation, pulsed gate control, and charge-sensing spin readout of confined hole spins in a one-dimensional Ge/Si nanowire. With fast gating, we measure T1 spin relaxation times in coupled quantum dots approaching 1 ms, increasing with lower magnetic field, consistent with a spin-orbit mechanism that is usually masked by hyperfine contributions

Permutative automorphisms of the Cuntz algebras: quadratic cycles, an involution and a box product

Permutative automorphisms of the Cuntz algebra O_n are in bijection with a class of permutations of n^k elements, that are called stable, and are further partitioned by rank. In this work we mainly focus on stable cycles in the quadratic case (i.e., k = 2). More precisely, in such a quadratic case we provide a characterization of the stable cycles of rank one (so proving Conjecture 12.1 in [3]), exhibit a closed formula for the number of stable r-cycles of rank one (valid for all n and r), and characterize and enumerate the stable 3-cycles of any given rank. We also show that the set of stable permutations is equipped with a natural involution that preserves the cycle-type and the rank, and that there is a map that associates to two stable permutations of n^k and m^k elements, respectively, a stable permutation of (nm)^k elements

Permutative automorphisms of the Cuntz algebras: Quadratic cycles, an involution and a box product

Permutative automorphisms of the Cuntz algebra On are in bijection with a class of permutations of nk elements, that are called stable, and are further partitioned by rank. In this work we mainly focus on stable cycles in the quadratic case (i.e., k=2). More precisely, in such a quadratic case we provide a characterization of the stable cycles of rank one (so proving Conjecture 12.1 in [3]), exhibit a closed formula for the number of stable r-cycles of rank one (valid for all n and r), and characterize and enumerate the stable 3-cycles of any given rank. We also show that the set of stable permutations is equipped with a natural involution that preserves the cycle-type and the rank, and that there is a map that associates to two stable permutations of nk and mk elements, respectively, a stable permutation of (nm)k elements

Formation of Fused Images of the Land Surface from Radar and Optical Images in Spatially Distributed On-Board Operational Monitoring Systems

This paper considers the issues of image fusion in a spatially distributed small-size on-board location system for operational monitoring. The purpose of this research is to develop a new method for the formation of fused images of the land surface based on data obtained from optical and radar devices operated from two-position spatially distributed systems of small aircraft, including unmanned aerial vehicles. The advantages of the method for integrating information from radar and optical information-measuring systems are justified. The combined approach allows removing the limitations of each separate system. The practicality of choosing the integration of information from several widely used variants of heterogeneous sources is shown. An iterative approach is used in the method for combining multi-angle location images. This approach improves the quality of synthesis and increases the accuracy of integration, as well as improves the information content and reliability of the final fused image by using the pixel clustering algorithm, which produces many partitions into clusters. The search for reference points on isolated contours is carried out on a pair of left and right images of the docked image from the selected partition. For these reference points, a functional transformation is determined. Having applied it to the original multi-angle heterogeneous images, the degree of correlation of the fused image is assessed. Both the position of the reference points of the contour and the desired functional transformation itself are refined until the quality assessment of the fusion becomes acceptable. The type of functional transformation is selected based on clustered images and then applied to the original multi-angle heterogeneous images. This process is repeated for clustered images with greater granularity in case if quality assessment of the fusion is considered to be poor. At each iteration, there is a search for pairs of points of the contour of the isolated areas. Areas are isolated with the use of two image segmentation methods. Experiments on the formation of fused images are presented. The result of the research is the proposed method for integrating information obtained from a two-position airborne small-sized radar system and an optical location system. The implemented method can improve the information content, quality, and reliability of the finally established fused image of the land surface