ELECTRONIC STATES OF QUANTUM DOTS (original) (raw)
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Numerical simulation of electronic properties of coupled quantum dots on wetting layers
Nanotechnology, 2008
The self-assembled quantum dots are grown on wetting layers and frequently in an array-like-assembly of many similar but not exactly equal dots. Nevertheless, most simulations disregard these structural conditions and restrict themselves to simulating of a pure single quantum dot. For a reason of numerical efficiency we advocate the effective one-band Hamiltonian with the energy and position dependent effective mass approximation and a finite height hard-wall 3D confinement potential for computation of the energy levels of the electrons in the conduction band. Within this model we investigate the geometrical effects mentioned above on the electronic structure of a pyramidal InAs quantum dot embedded in a GaAs matrix. We find that the presence of a wetting layer may affect the electronic structure noticeably. Furthermore, we establish that in spite of the large band gap of the InAs/GaAs heterostructure if the dots in a vertically aligned array are sufficiently close stacked there is a considerable interaction between their eigenfunctions. Moreover, the eigenfunctions of such an array are quite sensitive to certain structural perturbations.
Electronic States in Three Dimensional Quantum Dot/Wetting Layer Structures
Lecture Notes in Computer Science, 2006
Although self-assembled quantum dots are grown on wetting layers, most simulations exclude the wetting layer. The neglected effects on the electronic structure of a pyramidal InAs quantum dot embedded in a GaAs matrix are investigated based on the effective one electronic band Hamiltonian, the energy and position dependent electron effective mass approximation, and a finite height hard-wall 3D confinement potential. By comparing quantum dots with wetting layers and a dot without a wetting layer, we find that the presence of a wetting layer may effect the electronic structure essentially.
2000
A single-band, constant-confining-potential model is applied to self-assembled InAs/GaAs pyramidal dots in order to determine their electronic structure. The calculated energy eigenvalues and transition energies agree well with those of more sophisticated treatments which take into account the microscopic effects of the strain distribution on band mixing, confining potentials, and effective masses. The predictions of the model are compared with several spectra reported in the literature by different authors. Very good agreement with both energy position and number of peaks in such spectra is found. The hole energy splitting between ground and first excited states deduced from capacitance and photoluminescence measurements is in excellent agreement with our calculated values. The simplicity and versatility of the model, together with its modest computational demands, make it ideally suited to a routine interpretation and analysis of experimental data.
Surface Science, 2002
The ground-state electronic structure of unsupported three-dimensional cylindrical quantum dots is investigated using a simple free electron model with a step potential. Detailed analysis of the electron structure is presented for different sizes of the quantum dot. The possibility to gain information about the adlayer growth mode from photoemission measurements is discussed and a comparison with experiments is made for the system Na on Cu(1 1 1). We show that an electron structure model study in combination with a STM-dI=dV measurement could give information about the symmetry of the electron states. Such a combined study would make it possible to predict molecular reactivity on quantum dots.
Numerical study of 2-D quantum dots
We present a numerical study of the chemical potential and of the capacitance in a model quantum dot. Our model includes the electron-electron interaction and exchange and correlation effects within the framework of density functional theory. Our results exhibit the typical features observed in experiments, such as the increase in the capacitance for increasing number of electrons and the presence of irregularities in the succession of the chemical potential values vs. the electron number.
Physical Review B, 1998
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 ͑-spin͒-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 ͑1996͔͒ shows good agreement. ͓S0163-1829͑98͒02008-6͔
Numerical calculation of the electronic structure for three-dimensional quantum dots
Computer Physics Communications, 2006
In some recent papers Li, Voskoboynikov, Lee, Sze and Tretyak suggested an iterative scheme for computing the electronic states of quantum dots and quantum rings taking into account an electron effective mass which depends on the position and electron energy level. In this paper we prove that this method converges globally and linearly in an alternating way, i.e. yielding lower and upper bounds of a predetermined energy level in turn. Moreover, taking advantage of the Rayleigh functional of the governing nonlinear eigenproblem, we propose a variant which converges even quadratically thereby reducing the computational cost substantially. Two examples of finite element models of quantum dots of different shapes demonstrate the efficiency of the method.
Electronic structure and many-body effects in self-assembled quantum dots
Journal of Physics: Condensed Matter, 1999
A detailed model for the electronic properties of self-assembled InAs/GaAs quantum dots (SADs) is presented, with emphasis on inter-level transitions and many-body effects. The model is based on the self-consistent solution of three-dimensional Poisson and Schrödinger equations within the local (spin-) density approximation. Nonparabolicity of the band structure and a continuum model for the strain between GaAs and InAs results in position-and energydependent effective mass. The electronic spectra of SADs of various shapes have been determined with intraband level transitions and mid-infrared optical matrix elements. Shell structures obeying Hund's rule for various occupation numbers in pyramidal SADs agree well with recent capacitance measurements. It is shown that many-body interactions between orbital pairs of electrons are determined in a first approximation by classical Coulomb interaction. 0953-8984/99/315953+15$30.00
Numerical simulation of a coupling effect on electronic states in quantum dots
Lasers operating at 1.3 µm have attracted considerable attention owing to their potential to provide efficient light sources for next-generation high-speed communication systems. InAs/GaAs quantum dots (QDs) were pointed out as a reliable low-cost way to attain this goal. However, due to the lattice mismatch, the accumulation of strain by stacking the QDs can cause dislocations that significantly degrade the performance of the lasers. In order to reduce this strain, a promising method is the use of InAs QDs embedded in InGaAs layers. The capping of the QD layer with InGaAs is able to tune the emission toward longer and controllable wave-lengths between 1.1 and 1.5 µm. In this work, using the effective-mass envelope-function theory, we investigated theoretically the optical properties of coupled InAs/GaAs strained QDs based structures emitting around 1.33 µm. The calculation was performed by the resolution of the 3D Schrödinger equation. The energy levels of confined carriers and the optical transition energy have been investigated. The oscillator strengths of this transition have been studied with and without taking into account the strain effect in the calculations. The information derived from the present study shows that the InGaAs capping layer may have profound consequences as regards the performance of an InAs/GaAs QD based laser. Based on the present results, we hope that the present work make a contribution to experimental studies of InAs/GaAs QD based structures, namely the optoelectronic applications concerning infrared and mid-infrared spectral regions as well as the solar cells.
Multiscale Modeling of a Quantum Dot Heterostructure
2011
ABSTRACT A multiscale approach was adopted for the calculation of confined states in self-assembled semiconductor quantum dots (QDs). While results close to experimental data have been obtained with a combination of atomistic strain and tight-binding (TB) electronic structure description for the confined quantum states in the QD, the TB calculation requires substantial computational resources.