Electronic states and tunneling times in coupled self-assembled quantum dots (original) (raw)

Tunnel coupling in an ensemble of vertically aligned quantum dots at room temperature

Physical Review B, 2009

We report unambiguous observation of the formation of mixed electronic states in an ensemble of selfassembled vertically aligned quantum dots at room temperature. Three closely spaced layers containing stacked In͑Ga͒As/GaAs quantum dots are placed in the active region of a two-section semiconductor device, and investigations of the quantum-dot optical properties at different applied electric fields are carried out by means of differential-absorption spectroscopy. A simple semianalytical model, which describes absorption of two layers of coupled quantum dots with an account of the size dispersion, is developed. A comparison between our experimental and theoretical results allows clear attribution of the observed low-photon-energy field-dependent spectral features to the four mixed optical transitions due to the two upper quantum-dot layers. Interpretation of the experimental results reveals an anticrossing of spatially direct and indirect transitions characterized by the energy splitting of approximately 30 meV.

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

Coupled quantum dots: manifestation of an artificial molecule

Superlattices and Microstructures, 1998

Transport spectroscopy reveals the microscopic features of few-electron quantum dots which justify the name artificial atoms. New physics evolve when two quantum dots are coupled by a tunneling barrier. We study, both theoretically and experimentally, the tunneling spectroscopy on a double quantum dot. A detailed lineshape analysis of the conductance resonances proves that off-resonant coherent interdot tunneling governs transport through this system, while tunneling into the double quantum dot occurs resonantly. This coherent interdot tunneling witnesses the evolution of a delocalized electronic state which can be compared to a valence electron of this artificial molecule.

Coupling and Entangling of Quantum States in Quantum Dot Molecules

Science, 2001

We demonstrate coupling and entangling of quantum states in a pair of vertically aligned, self-assembled quantum dots by studying the emission of an interacting electron-hole pair (exciton) in a single dot molecule as a function of the separation between the dots. An interaction-induced energy splitting of the exciton is observed that exceeds 30 millielectron volts for a dot layer separation of 4 nanometers. The results are interpreted by mapping the tunneling of a particle in a double dot to the problem of a single spin. The electron-hole complex is shown to be equivalent to entangled states of two interacting spins.

Collective Properties of Electrons and Holes in Coupled Quantum Dots

NATO Science Series, 2005

We discuss the properties of few electrons and electron-hole pairs confined in coupled semiconductor quantum dots, with emphasis on correlation effects and the role of tunneling. We shall discuss, in particular, exact diagonalization results for biexciton binding energy, electron-hole localization, magnetic-field induced Wigner molecules, and spin ordering.

Electronic Properties of Self-Organized Quantum Dots

2007

Contents Part 1. Electronic Structure Calculations Chapter 1. Introduction Chapter 2. Method of calculation 2.1. Calculation of strain 2.2. Piezoelectricity and the reduction of lateral symmetry 2.3. Single Particle States 2.4. Many-Particle States 2.5. Optical Properties Part 2. InGaAs/GaAs Quantum Dots Chapter 3. Impact of Size, Shape and Composition on Piezoelectric Effects and Single-Particle States 3.1. The Investigated structures: Variation of size, shape and compostion 3.2. The Impact of the piezoelectric field 3.3. The vertical and lateral aspect ratio 3.4. Varying composition profiles 3.5. Conclusions Chapter 4. Few-particle Energies versus Geometry and Composition 4.1. Interrelation of QD-structure, strain and piezoelectricity, and Coulomb interaction 4.2. The Impact of QD size (series A and H) 4.3. The aspect ratio 4.4. Different composition profiles 4.5. Correlation vs. QD size, shape and particle type 4.6. Conclusions Chapter 5. Multimodal QD-size distribution: Theory and Experiment 5.1. Sample growth 5.2. Determination of QD-morphology and the spectrum of excited states 5.3. Predicted absorption spectra of truncated pyramidal InAs/GaAs QDs 5.4. Single-dot spectra obtained from cathodoluminescence spectroscopy 5.5. Results and Interpretation 5.6. Conclusion Chapter 6. Stacked quantum dots 6.1. Energetics of QD stacks 6.2. Role of strain and piezoelectricity 6.3. Strength of electronic coupling in pairs of identical QDs 6.4. Small perturbations of the size homogeneity 6.5. Asymmetric QD molecules: Coupling of different electronic shells 6.6. Tailoring the TE-TM ratio in semiconductor optical amplifiers 6.7. Conclusions 6 CONTENTS Part 3. Other Material Systems Chapter 7. Electronic and optical properties of InAs/InP quantum dots on InP(100) and InP(311)B substrates 7.1. Choice of model QDs 7.2. Absorption spectra for InAs/InP QDs 7.3. Impact of substrate orientation on the QDs optical properties 7.4. Conclusions Chapter 8. Inverted GaAs/Al x Ga 1−x As Quantum Dots 8.1. Choice of the model QDs 8.2. Influence of interface intermixing on the optical properties 8.3. External magnetic fields 8.4. Discussion 8.

Electronic Properties and Mid-Infrared Transitions in Self-Assembled Quantum Dots

Japanese Journal of Applied Physics, 1999

We present a detailed model of the electronic properties of single and vertically aligned self-assembled pyramidal InAs/GaAs quantum dots (SADs) which is based on the self-consistent solution of three-dimensional (3D) Poisson and Schroedinger equations within the local (spin) density approximation. Nonparabolicity of the band structure and a continuum model for strain between GaAs and InAs results in position and energy dependent effective mass. In single SADs, shell structures obeying Hund's rule for various occupation numbers in the pyramids agree well with recent capacitance measurements. The electronic spectra of SADs of various shapes have been determined with intraband level transitions and mid-infrared optical matrix elements. In the case of two vertically aligned pyramidal SADs, we show that quantum mechanical coupling alone between identical dots underestimates the magnitude of the coupling between the dots, which in large part is due to piezoelectricity and size difference between SADs.

ELECTRONIC STATES OF QUANTUM DOTS

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 themself to simulating of a pure single quantum dot. Moreover, many simulations settle for the linear model with constant instead of the rational eective mass. In this work we argue that the nonlinear model is necessary to correctly capture the interesting part of the spectrum. We advocate the eective one electronic band Hamiltonian with the energy and position dependent eective 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 eects 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 aect the electronic structure...

Hole states in Ge∕Si quantum-dot molecules produced by strain-driven self-assembly

Journal of Applied Physics, 2007

Space-charge spectroscopy was employed to study hole emission from the confined states in vertically self-aligned double Ge quantum dots separated by a Si barrier. From the temperature-and frequency-dependent measurements, the hole binding energy was determined as a function of the separation between the dots, t Si . Increasing of the ground state hole energy due to formation of a bonding molecular orbital was found to be as large as ϳ50 meV at t Si = 1.5 nm. For a dot layer separation exceeding 3 nm, the hole binding energy in double-dot molecule becomes smaller than the ionization energy of the single Ge dot, contrasting with a simplified quantum-mechanical molecular model. To analyze the experiment the electronic structure of two vertically coupled pyramidal Ge quantum dots embedded in Si was investigated by a nearest neighbor tight-binding single-particle Hamiltonian with the sp 3 basis. The elastic strain due to the lattice mismatch between Ge and Si was included into the problem. The three-dimensional spatial strain distribution was found in terms of atomic positions using a valence-force-field theory with a Keating interatomic potential. It was demonstrated that formation of single-particle hole states in self-organized molecules is governed by the interplay among two effects. The first is the quantum-mechanical coupling between the individual states of two dots constituting the molecule. The second one originates from asymmetry of the strain field distribution within the top and bottom dots due to the lack of inversion symmetry with respect to the medium plane between the dots. Analysis of the biaxial strain distribution showed that anomalous decreasing of the hole binding energy below the value of the single dot with increasing interdot separation is caused by the partial strain relaxation upon dot stacking accompanied by the strain-induced reduction of the hole confinement potential. We found that the molecule-type hole state delocalized fairly over the two dots is formed only at t Si Ͻ 3.3 nm and at t Si Ͼ 3.8 nm. For the intermediate distances ͑3.3 nmഛ t Si ഛ 3.8 nm͒, the hole becomes confined mostly inside the bottom, most strained Ge dot. The overall agreement between theory and experiment turns out to be quite good, indicating the crucial role played by strain fields in electronic coupling of self-assembled quantum-dot molecules.

Electronic structure of rectangular quantum dots

Physical Review B, 2003

We study the ground state properties of rectangular quantum dots by using the spin-densityfunctional theory and quantum Monte Carlo methods. The dot geometry is determined by an infinite hard-wall potential to enable comparison to manufactured, rectangular-shaped quantum dots. We show that the electronic structure is very sensitive to the deformation, and at realistic sizes the non-interacting picture determines the general behavior. However, close to the degenerate points where Hund's rule applies, we find spin-density-wave-like solutions bracketing the partially polarized states. In the quasi-one-dimensional limit we find permanent charge-density waves, and at a sufficiently large deformation or low density, there are strongly localized stable states with a broken spin-symmetry.