The influence of surface stress on the equilibrium shape of strained quantum dots

The equilibrium shapes of InAs quantum dots (i.e., dislocation-free, strained islands with sizes >= 10,000 atoms) grown on a GaAs (001) substrate are studied using a hybrid approach which combines density functional theory (DFT) calculations of microscopic parameters, surface energies, and surface stresses with elasticity theory for the long-range strain fields and strain relaxations. In particular we report DFT calculations of the surface stresses and analyze the influence of the strain on the surface energies of the various facets of the quantum dot. The surface stresses have been neglected in previous studies. Furthermore, the influence of edge energies on the island shapes is briefly discussed. From the knowledge of the equilibrium shape of these islands, we address the question whether experimentally observed quantum dots correspond to thermal equilibrium structures or if they are a result of the growth kinetics.Comment: 7 pages, 8 figures, submitted to Phys. Rev. B (February 2, 1998). Other related publications can be found at http://www.rz-berlin.mpg.de/th/paper.htm

A New Method of Generating Exact Inflationary Solutions

The mechanism of the initial inflation of the universe is based on gravitationally coupled scalar fields $\phi$. Various scenarios are distinguished by the choice of an {\it effective self--interaction potential} $U(\phi)$ which simulates a {\it temporarily} non--vanishing {\em cosmological term}. Using the Hubble expansion parameter $H$ as a new ``time" coordinate, we can formally derive the {\it general} Robertson--Walker metric for a {\em spatially flat} cosmos. Our new method provides a classification of allowed inflationary potentials and is broad enough to embody all known {\it exact} solutions involving one scalar field as special cases. Moreover, we present new inflationary and deflationary exact solutions and can easily predict the influence of the form of $U(\phi)$ on density perturbations.Comment: 32 pages, REVTeX, 9 postscript figures (or hardcopy) available upon request, Cologne-thp-1994-H

Effect of high magnetic fields on orientation and properties of liquid crystalline thermosets

In this report we provide the first description of the orientation of liquid crystalline thermosets (LCT`s) in field strengths of up to 18 T, as well as the first report of tensile properties for both unoriented and oriented LCT`S. The LCT we have chosen for study is the diglycidyl ether of dihydroxy-a-methylstilbene cured with the diamine, sulfanilamide. Orientation in magnetic fields leads to an increase of almost three times the modulus compared to the unoriented material. These values are much greater than can be obtained with conventional thermosets. The strain at break is also significantly affected by the chain orientation. The coefficient of thermal expansion and x-ray diffraction of oriented samples show high degrees of anisotropy, indicating significant chain alignment in the magnetic field. We are working to further understand the field dependence of orientation and properties plus the mechanisms of the alignment process

On the exciton binding energy in a quantum well

We consider a model describing the one-dimensional confinement of an exciton in a symmetrical, rectangular quantum-well structure and derive upper and lower bounds for the binding energy $E_b$ of the exciton. Based on these bounds, we study the dependence of $E_b$ on the width of the confining potential with a higher accuracy than previous reports. For an infinitely deep potential the binding energy varies as expected from $1 Ry$ at large widths to $4 Ry$ at small widths. For a finite potential, but without consideration of a mass mismatch or a dielectric mismatch, we substantiate earlier results that the binding energy approaches the value $1 Ry$ for both small and large widths, having a characteristic peak for some intermediate size of the slab. Taking the mismatch into account, this result will in general no longer be true. For the specific case of a $Ga_{1-x}Al_{x}As/GaAs/Ga_{1-x}Al_{x}As$ quantum-well structure, however, and in contrast to previous findings, the peak structure is shown to survive.Comment: 32 pages, ReVTeX, including 9 figure

Formation and stability of self-assembled coherent islands in highly mismatched heteroepitaxy

We study the energetics of island formation in Stranski-Krastanow growth within a parameter-free approach. It is shown that an optimum island size exists for a given coverage and island density if changes in the wetting layer morphology after the 3D transition are properly taken into account. Our approach reproduces well the experimental island size dependence on coverage, and indicates that the critical layer thickness depends on growth conditions. The present study provides a new explanation for the (frequently found) rather narrow size distribution of self-assembled coherent islands.Comment: 4 pages, 5 figures, In print, Phys. Rev. Lett. Other related publications can be found at http://www.fhi-berlin.mpg.de/th/paper.htm

Self-assembly of quantum dots: effect of neighbor islands on the wetting in coherent Stranski-Krastanov growth

The wetting of the homogeneously strained wetting layer by dislocation-free three-dimensional islands belonging to an array has been studied. The array has been simulated as a chain of islands in 1+1 dimensions. It is found that the wetting depends on the density of the array, the size distribution and the shape of the neighbor islands. Implications for the self-assembly of quantum dots grown in the coherent Stranski-Krastanov mode are discussed.Comment: 4 pages, 6 figures, accepted version, minor change

Equilibrium shapes and energies of coherent strained InP islands

The equilibrium shapes and energies of coherent strained InP islands grown on GaP have been investigated with a hybrid approach that has been previously applied to InAs islands on GaAs. This combines calculations of the surface energies by density functional theory and the bulk deformation energies by continuum elasticity theory. The calculated equilibrium shapes for different chemical environments exhibit the {101}, {111}, {\=1\=1\=1} facets and a (001) top surface. They compare quite well with recent atomic-force microscopy data. Thus in the InP/GaInP-system a considerable equilibration of the individual islands with respect to their shapes can be achieved. We discuss the implications of our results for the Ostwald ripening of the coherent InP islands. In addition we compare strain fields in uncapped and capped islands.Comment: 10 pages including 6 figures. Submitted to Phys. Rev. B. Related publications can be found at http://www.fhi-berlin.mpg.de/th/paper.htm