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

CMOS-compatible dense arrays of Ge quantum dots on the Si(001) surface: hut cluster nucleation, atomic structure and array life cycle during UHV MBE growth

We report a direct observation of Ge hut nucleation on Si(001) during UHV molecular beam epitaxy at 360°C. Nuclei of pyramids and wedges were observed on the wetting layer (WL) (M × N) patches starting from the coverage of 5.1 Å and found to have different structures. Atomic models of nuclei of both hut species have been built as well as models of the growing clusters. The growth of huts of each species has been demonstrated to follow generic scenarios. The formation of the second atomic layer of a wedge results in rearrangement of its first layer. Its ridge structure does not repeat the nucleus. A pyramid grows without phase transitions. A structure of its vertex copies the nucleus. Transitions between hut species turned out to be impossible. The wedges contain point defects in the upper corners of the triangular faces and have preferential growth directions along the ridges. The derived structure of the {105} facet follows the paired dimer model. Further growth of hut arrays results in domination of wedges, and the density of pyramids exponentially drops. The second generation of huts arises at coverages >10 Å; new huts occupy the whole WL at coverages ~14 Å. Nanocrystalline Ge 2D layer begins forming at coverages >14 Å

КРЕМНИЕВЫЕ ПРИБОРНЫЕ СТРУКТУРЫ С ЭФФЕКТИВНОЙ ИЗЛУЧАТЕЛЬНОЙ РЕКОМБИНАЦИЕЙ НА ДИСЛОКАЦИЯХ Мудрый А.В.1, Живулько В.Д.1, Мофиднахаи Ф.1, Ивлев Г.Д.2, Якушев М.

The efficient electroluminescence in the region of band-to-band (1,1 eV) and dislocationrelated (D1 – 0,8 eV) transitions has been detected from Si p-n structures at room and liquid nitrogen temperatures. It was found that dislocation-related luminescence in Si single crystals is considerably stronger than the intrinsic band-to-band emission in the wide temperature range of 4,2–300 K. The temperature dependent measurement of the D1 photoluminescence intensity shows that two energy levels placed below the conduction (0,04 eV) and above valence (0,32 eV) bands are responsible for this radiative recombination on dislocations.В кремниевых p-n структурах обнаружена эффективная электролюминесценция в области переходов зона–зона (1,1 эВ) и переходов, обусловленных дислокациями (D1–0,8 эВ), при комнатной температуре и температуре жидкого азота. Установлено, что люминесценция, обусловленная дислокациями в монокристаллах Si, значительно сильнее, чем собственное межзонное излучение в интервале температур 4,2–300 К. Измерение температурной зависимости интенсивности полосы фотолюминесценции D1 показало, что за излучательную рекомбинацию на дислокациях ответственны два энергетических уровня, расположенных ниже зоны проводимости (≈ 0,04 эВ) и выше валентной зоны (≈ 0,32 эВ)

Miniband-related 1.4–1.8 μm luminescence of Ge/Si quantum dot superlattices

The luminescence properties of highly strained, Sb-doped Ge/Si multi-layer heterostructures with incorporated Ge quantum dots (QDs) are studied. Calculations of the electronic band structure and luminescence measurements prove the existence of an electron miniband within the columns of the QDs. Miniband formation results in a conversion of the indirect to a quasi-direct excitons takes place. The optical transitions between electron states within the miniband and hole states within QDs are responsible for an intense luminescence in the 1.4–1.8 µm range, which is maintained up to room temperature. At 300 K, a light emitting diode based on such Ge/Si QD superlattices demonstrates an external quantum efficiency of 0.04% at a wavelength of 1.55 µm