Pyramidal Quantum Dots Research Articles

Strain-energy distribution and electronic structure of InAs pyramidal quantum dots with uncovered surfaces: Tight-binding analysis

The strain energy distribution and electronic structure of InAs pyramidal quantum dots (QD's) with uncovered surfaces have been analyzed theoretically. The strain in the QD's, which simulate self-assembled QD's on GaAs, is calculated using the Keating potential. The strain energy per inside atom is largest at the lowest layer, while the several layers near the pyramid top have practically no strain. Using the ${\mathrm{sp}}^{3}{s}^{*}$ tight-binding method, we calculate the densities of states for the inside states and the surface states. The density of the inside states shows a large energy gap; $2.71--1.74$ eV for $161--1222$-atom QD's. At the same time, we find the surface states in the gap.

Comparison of the electronic structure ofInAs/GaAspyramidal quantum dots with different facet orientations

Using a pseudopotential plane-wave approach, we have calculated the electronic structure of strained InAs pyramidal quantum dots embedded in a GaAs matrix, for a few height $(h)$-to-base$(b)$ ratios, corresponding to different facet orientations ${101}$, ${113},$ and ${105}$. We find that the dot shape (not just size) has a significant effect on its electronic structure. In particular, while the binding energies of the ground electron and hole states increase with the pyramid volumes ${(b}^{2}h)$, the splitting of the $p\ensuremath{-}$like conduction states increases with facet orientation $(h/b),$ and the $p\ensuremath{-}$to-$s$ splitting of the conduction states decreases as the base size $(b)$ increases. We also find that there are up to six bound electron states (12 counting the spin), and that all degeneracies other than spin, are removed. This is in accord with the conclusion of electron-addition capacitance data, but in contrast with simple k\ensuremath{\cdot}p calculations, which predict only a single electron level.

Self-consistent calculation of the electronic structure and electron-electron interaction in self-assembled InAs-GaAs quantum dot structures

We have performed a detailed self-consistent calculation of the electronic structure and electron-electron interaction energy in pyramidal self-assembled InAs-GaAs quantum dot structures. Our model is general for three-dimensional quantum devices without simplifying assumptions on the shape of the confining potential nor fitting parameters. We have used a continuum model for the strain, from which the position-dependent effective mass and band diagram are calculated. The number of electrons in the dot is controlled by applying an external voltage to a metal gate on the top of a complete multilayer device containing a single dot. In order to determine the electron occupation number in the dot that minimizes the total energy of the system, we have adopted the concept of transition state as defined by Slater for shell filling in atoms. We have calculated the exchange and correlation terms of the many-body Hamiltonian using the local (-spin) -density approximation. By accounting for spins we have been able to determine the shell structure in the pyramid and to calculate the energy differences between the various spin configurations. We have also calculated the different contributions to the total electronic energy in the dot, i.e., the single-particle energies, the exchange-correlation energy, and the classical electrostatic electron-electron repulsion energy as a function of the gate voltage and number of electrons in the dot. Comparison with recent experimental data of Fricke et al. [Europhys. Lett. 36, 197 (1996)] shows good agreement.

Asymmetric Stark shifts of exciton in [formula omitted] pyramidal quantum dots

Within the framework of the single-band effective-mass envelope-function theory, the effect of electric field on the electronic structures of pyramidal quantum dot is investigated. Taking the Coulomb interaction between the heavy holes and electron into account, the quantum confined Stark shift of the exciton as functions of the strength and direction of applied electric field and the size of the quantum dot are obtained. An interesting asymmetry of Stark shifts around the zero field is found.

A simple method for calculating strain distributions in quantum dot structures

A simple method is presented for calculating the stress and strain distributions arising from an initially uniformly strained quantum dot of arbitrary shape buried in an infinite isotropic medium. The method involves the evaluation of a surface integral over the boundary of the quantum dot and is therefore considerably more straightforward to implement than alternative stress evaluation techniques. The technique is ideally suited to calculating strain distributions within disordered arrays of pyramidal quantum dots prepared by Stranski–Krastanow growth. The strain distribution for a cuboidal quantum dot is presented and compared to that of a rectangular quantum wire.

Multiphonon-relaxation processes in self-organized InAs/GaAs quantum dots

We report on optical studies of relaxation processes in self-organized InAs/GaAs quantum dots (QDs). Near resonant photoluminescence excitation spectra reveal a series of sharp lines. Their energy with respect to the detection energy does not depend on QD size and their energy separations are close to the InAs LO phonon energy of 32.1 meV estimated for strained pyramidal InAs QDs. The shape of the PLE spectra is explained by multiphonon relaxation processes involving LO phonons of the QD as well as of the wetting layer, an interface mode, and low frequency acoustical phonons.

Pyramidal quantum dot structures by self-limited selective area metalorganic vapor phase epitaxy

We have fabricated AlGaAs GaAs quantum dot structures using selective area metalorganic vapor phase epitaxy (MOVPE). First, GaAs pyramidal structures with four-fold symmetric [lcub]011[rcub] facet side walls are formed on SiN x masked (001) GaAs with square openings. After the pyramidal structures were completely formed, no growth occurs on the top or side walls of the pyramids. Furthermore, the shape and width of the top area observed by a scanning electron microscope (SEM) and an atomic force microscope (AFM) is shown to be highly uniform. This indicates that self-limited growth occurs. Next, using these uniform pyramids, GaAs quantum dots are overgrown on top of the pyramids using different growth conditions. Sharp photoluminescence (PL) spectra are observed from uniform quantum dots.

InAs/GaAs pyramidal quantum dots: Strain distribution, optical phonons, and electronic structure.

The strain distribution in and around pyramidal InAs/GaAs quantum dots (QD's) on a thin wetting layer fabricated recently with molecular-beam epitaxy, is simulated numerically. For comparison analytical solutions for the strain distribution in and around a pseudomorphic slab, cylinder, and sphere are given for isotropic materials, representing a guideline for the understanding of strain distribution in two-, one-, and zero-dimensional pseudomorphic nanostructures. For the pyramidal dots we find that the hydrostatic strain is mostly confined in the QD; in contrast part of the anisotropic strain is transferred from the QD into the barrier. The optical-phonon energies in the QD are estimated and agree perfectly with recent experimental findings. From the variation of the strain tensor the local band-gap modification is calculated. Piezoelectric effects are additionally taken into account. The three-dimensional effective-mass single-particle Schr\"odinger equation is solved for electrons and holes using the realistic confinement potentials. Since the QD's are in the strong confinement regime, the Coulomb interaction can be treated as a perturbation. The thus obtained electronic structure agrees with luminescence data. Additionally AlAs barriers are considered.