Electronic structure and magneto-optics of self-assembled quantum dots

Atomic-Scale Multimodal Characterization of Self-Assembled InAs/InGaAlAs Quantum Dots

Self-assembled quantum dots (QDs) are potential candidates for photoelectric and photovoltaic devices, because of their discrete energy levels. The characterization of QDs at the atomic level using a multimodal approach is crucial to improving device performance because QDs are nanostructures with highly correlated structural parameters. In this study, scanning transmission electron microscopy, geometric phase analysis, and atom probe tomography were employed to characterize structural parameters such as the shape, strain, and composition of self-assembled InAs-QDs with InGaAlAs spacer layers. The measurements revealed characteristic AlAs-rich regions above the QDs and InAs-rich regions surrounding the QD columns, which can be explained by the relationship between the effect of strain and surface curvature around the QD. The methodology described in this study accelerates the development of future QD devices because its multiple perspectives reveal phenomena such as atomic-scale segregations and allow for more detailed discussions of the mechanisms of these phenomena.

Theory of Excitons in Atomically Thin Semiconductors: Tight-Binding Approach

Atomically thin semiconductors from the transition metal dichalcogenide family are materials in which the optical response is dominated by strongly bound excitonic complexes. Here, we present a theory of excitons in two-dimensional semiconductors using a tight-binding model of the electronic structure. In the first part, we review extensive literature on 2D van der Waals materials, with particular focus on their optical response from both experimental and theoretical points of view. In the second part, we discuss our ab initio calculations of the electronic structure of MoS2, representative of a wide class of materials, and review our minimal tight-binding model, which reproduces low-energy physics around the Fermi level and, at the same time, allows for the understanding of their electronic structure. Next, we describe how electron-hole pair excitations from the mean-field-level ground state are constructed. The electron-electron interactions mix the electron-hole pair excitations, resulting in excitonic wave functions and energies obtained by solving the Bethe-Salpeter equation. This is enabled by the efficient computation of the Coulomb matrix elements optimized for two-dimensional crystals. Next, we discuss non-local screening in various geometries usually used in experiments. We conclude with a discussion of the fine structure and excited excitonic spectra. In particular, we discuss the effect of band nesting on the exciton fine structure; Coulomb interactions; and the topology of the wave functions, screening and dielectric environment. Finally, we follow by adding another layer and discuss excitons in heterostructures built from two-dimensional semiconductors.

Morphology of wetting-layer states in a simple quantum-dot wetting-layer model

The excitation of semiconductor quantum dots often involves an attached wetting layer with delocalized single-particle energy eigenstates. These wetting-layer states are usually approximated by (orthogonalized) plane waves. We show that this approach is too crude. Even for a simple model based on the effective-mass approximation and containing one or a few lens-shaped quantum dots on a rectangular wetting layer, the wetting-layer states typically show a substantially irregular and complex morphology. To quantify this complexity we use concepts from the field of quantum chaos such as spectral analysis of energy levels, amplitude distributions, and localization of energy eigenstates.

Surface-Enhanced Molecular Electron Energy Loss Spectroscopy

Electron energy loss spectroscopy (EELS) in a scanning transmission electron microscope (STEM) is becoming an important technique in spatially resolved spectral characterization of optical and vibrational properties of matter at the nanoscale. EELS has played a significant role in understanding localized polaritonic excitations in nanoantennas and also allows for studying molecular excitations in nanoconfined samples. Here we theoretically describe the interaction of a localized electron beam with molecule-covered polaritonic nanoantennas, and propose the concept of surface-enhanced molecular EELS exploiting the electromagnetic coupling between the nanoantenna and the molecular sample. Particularly, we study plasmonic and infrared phononic antennas covered by molecular layers, exhibiting either an excitonic or vibrational response. We demonstrate that EEL spectra of these molecule-antenna coupled systems exhibit Fano-like or strong coupling features, similar to the ones observed in far-field optical and infrared spectroscopy. EELS offers the advantage to acquire spectral information with nanoscale spatial resolution, and importantly, to control the antenna-molecule coupling on demand. Considering ongoing instrumental developments, EELS in STEM shows the potential to become a powerful tool for fundamental studies of molecules that are naturally or intentionally located on nanostructures supporting localized plasmon or phonon polaritons. Surface-enhanced EELS might also enable STEM-EELS applications such as remote- and thus damage-free-sensing of the excitonic and vibrational response of molecules, quantum dots, or 2D materials.

Limited accuracy of conduction band effective mass equations for semiconductor quantum dots

Effective mass equations are the simplest models of carrier states in a semiconductor structures that reduce the complexity of a solid-state system to Schrödinger- or Pauli-like equations resempling those well known from quantum mechanics textbooks. Here we present a systematic derivation of a conduction-band effective mass equation for a self-assembled semiconductor quantum dot in a magnetic field from the 8-band k · p theory. The derivation allows us to classify various forms of the effective mass equations in terms of a hierarchy of approximations. We assess the accuracy of the approximations in calculating selected spectral and spin-related characteristics. We indicate the importance of preserving the off-diagonal terms of the valence band Hamiltonian and argue that an effective mass theory cannot reach satisfactory accuracy without self-consistently including non-parabolicity corrections and renormalization of k · p parameters. Quantitative comparison with the 8-band k · p results supports the phenomenological Roth-Lax-Zwerdling formula for the g-factor in a nanostructure.

Valence band offset, strain and shape effects on confined states in self-assembled InAs/InP and InAs/GaAs quantum dots

I present a systematic study of self-assembled InAs/InP and InAs/GaAs quantum dot single-particle and many-body properties as a function of the quantum dot-surrounding matrix valence band offset. I use an atomistic, empirical tight-binding approach and perform numerically demanding calculations for half-million-atom nanosystems. I demonstrate that the overall confinement in quantum dots is a non-trivial interplay of two key factors: strain effects and the valence band offset. I show that strain effects determine both the peculiar structure of confined hole states of lens type InAs/GaAs quantum dots and the characteristic 'shell-like' structure of confined hole states in the commonly considered 'low-strain' lens type InAs/InP quantum dot. I also demonstrate that strain leads to single-band-like behavior of hole states of disk type ('indium flushed') InAs/GaAs and InAs/InP quantum dots. I show how strain and valence band offset affect quantum dot many-body properties: the excitonic fine structure, an important factor for efficient entangled photon pair generation, and the biexciton and charged exciton binding energies.

Three-dimensional magneto-photoluminescence as a probe of the electronic properties of crystal-phase quantum disks in GaAs nanowires

Crystal-phase engineering has emerged as a novel method of bandgap engineering, made feasible by the high surface-to-volume ratio of nanowires. There remains intense debate about the exact characteristics of the band structure of the novel crystal phases, such as wurtzite GaAs, obtained by this approach. We attack this problem via a low-temperature angle-dependent magneto-photoluminescence study of wurtzite/zinc-blende quantum disks in single GaAs nanowires. The exciton diamagnetic coefficient is proportional to the electron-hole correlation length, enabling a determination of the spatial extent of the exciton wave function in the plane and along the confinement axis of the crystal-phase quantum disks. Depending on the disk nature, the diamagnetic coefficient measured in Faraday geometry ranges between 25 and 75 μeV/T(2). For a given disk, the diamagnetic coefficient remains constant upon rotation of the magnetic field. Along with our envelope function calculation accounting for excitonic effects, we demonstrate that the electron effective mass in wurtzite GaAs quantum disks is heavy, mostly isotropic and results from mixing of the two lower-energy conduction bands with Γ7 and Γ8 symmetries. Finally, we discuss the implications of the results of the angle dependent magneto-luminescence for the likely symmetry of the exciton states. This work provides important insight in the band structure of wurtzite GaAs for future nanowire-based polytypic bandgap engineering.

Proposed quenching of phonon-induced processes in photoexcited quantum dots due to electron-hole asymmetries

Differences in the confinement of electrons and holes in quantum dots are shown to profoundly impact the magnitude of scattering with acoustic phonons. Using an extensive model that includes the non-Markovian nature of the phonon reservoir, we show how the effect may be addressed by photoluminescence excitation spectroscopy of a single quantum dot. We also investigate the implications for cavity QED, i.e., a coupled quantum dot-cavity system, and demonstrate that the phonon scattering may be strongly quenched. The quenching is explained by a balancing between the deformation potential interaction strengths and the carrier confinement and depends on the quantum dot shape. Numerical examples suggest a route towards engineering the phonon scattering.

Limits and Properties of Size Quantization Effects in InAs Self Assembled Quantum Dots

In this paper we report on the limits and properties of size quantization effects in InAs self assembled quantum dots (QDs). Size, density and character of the InAs islands are investigated by transmission electron microscopy. The electronic and optical properties of the islands in the coherent and dislocated growth regime are studied using capacitance, photoluminescence, photovoltage and photocurrent spectroscopy. In the data measured with the different techniques, the change in dot size and density as well as the transition from coherent to dislocated island growth is clearly observable. An increasing QD size causes a red shift in the energetic position of the QD features while the density of the islands is reflected in the intensity of the QD signal. The decrease in intensity at high InAs coverage is attributed to dislocated island formation.

On the anomalous Stark effect in a thin disc-shaped quantum dot

The effect of a lateral external electric field F on an exciton ground state in an InAs disc-shaped quantum dot has been studied using a variational method within the effective mass approximation. We consider that the radial dimension of the disc is very large compared to its height. This situation leads to separating the excitonic Hamiltonian into two independent parts: the lateral confinement which corresponds to a two-dimensional harmonic oscillator and an infinite square well in the growth direction. Our calculations show that the complete description of the lateral Stark shift requires both the linear and quadratic terms in F which explains that the exciton possess nonzero lateral dipolar moment and polarizability. The fit of the calculated Stark shift permits us to estimate the lateral permanent dipole moment and the polarizability according to the disc size. Our results are compared to those existing in the literature. In addition the behavior of the optical integral shows that the exciton lifetime is greater than that under zero field which is due to the field-induced polarization.

Emission properties and photon statistics of a single quantum dot laser

A theoretical description for a single quantum-dot emitter in a microcavity is developed.We analyze for increasing steady-state pump rate the transition from the strong-coupling regime with photon antibunching to the weak-coupling regime with coherent emission. It is demonstrated how Coulomb interaction of excited carriers and excitation-induced dephasing can strongly modify the emission properties. Our theoretical investigations are based on a direct solution of the Liouville-von Neumann equation for the coupled carrier-photon system. We include multiple carrier excitations in the quantum dot, their Coulomb interaction, as well as excitation-induced dephasing and screening. Similarities and differences to atomic systems are discussed and results in the regime of recent experiments are interpreted.

Electronic States and light absorption in a cylindrical quantum dot having thin falciform cross section

Energy level structure and direct light absorption in a cylindrical quantum dot (CQD), having thin falciform cross section, are studied within the framework of the adiabatic approximation. An analytical expression for the energy spectrum of the particle is obtained. For the one-dimensional "fast" subsystem, an oscillatory dependence of the wave function amplitude on the cross section parameters is revealed. For treatment of the "slow" subsystem, parabolic and modified Pöschl-Teller effective potentials are used. It is shown that the low-energy levels of the spectrum are equidistant. In the strong quantization regime, the absorption coefficient and edge frequencies are calculated. Selection rules for the corresponding quantum transitions are obtained.

Effects of Shape and Strain Distribution of Quantum Dots on Optical Transition in the Quantum Dot Infrared Photodetectors

We present a systemic theoretical study of the electronic properties of the quantum dots inserted in quantum dot infrared photodetectors (QDIPs). The strain distribution of three different shaped quantum dots (QDs) with a same ratio of the base to the vertical aspect is calculated by using the short-range valence-force-field (VFF) approach. The calculated results show that the hydrostatic strain varepsilon(H) varies little with change of the shape, while the biaxial strain varepsilon(B) changes a lot for different shapes of QDs. The recursion method is used to calculate the energy levels of the bound states in QDs. Compared with the strain, the shape plays a key role in the difference of electronic bound energy levels. The numerical results show that the deference of bound energy levels of lenslike InAs QD matches well with the experimental results. Moreover, the pyramid-shaped QD has the greatest difference from the measured experimental data.

Characterization of strong light-matter coupling in semiconductor quantum-dot microcavities via photon-statistics spectroscopy

It is shown that spectrally resolved photon-statistics measurements of the resonance fluorescence from realistic semiconductor quantum-dot systems allow for high contrast identification of the two-photon strong-coupling states. Using a microscopic theory, the second-rung resonance of Jaynes-Cummings ladder is analyzed and optimum excitation conditions are determined. The computed photon-statistics spectrum displays gigantic, experimentally robust resonances at the energetic positions of the second-rung emission.

Theory of spontaneous emission of quantum dots in the linear regime

We develop a fully quantum-mechanical theory for the interaction of light and electron-hole excitations in semiconductor quantum dots. Our theoretical analysis results in an expression for the photoluminescence intensity of quantum dots in the linear regime. Taking into account the single-particle Hamiltonian, the free-photon Hamiltonian, the electron-hole interaction Hamiltonian, and the interaction of carriers with light, and applying the Heisenberg equation of motion to the photon number expectation values, to the carrier distribution functions and to the correlation term between the photon generation (destruction) and electron-hole pair, we obtain a set of luminescence equations. Under quasi-equilibrium conditions, these equations become a closed-set of equations. We solve them analytically, in the linear regime, and we find an approximate solution of the incoherent photoluminescence intensity. The validity of the theoretical analysis is tested by investigating the emission spectra in the high-temperature regime, interpreting the experimental findings for the emission spectra of a lens-shaped In(0.5)Ga(0.5)As self-assembled quantum dot. Our theoretical predictions for the interlevel spacing as well as for the dephasing time caused by electron-longitudinal optical phonon interactions are in good agreement with the experimental results.

Coupling and entangling of quantum states in quantum dot molecules

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.

Excitonic absorption in a quantum Dot

The excitonic absorption spectrum of a single quantum dot is investigated theoretically and experimentally. The spectrum is determined by an interacting electron-valence-hole complex. We show that the mixing of quantum configurations by two-body interactions leads to distinct absorption spectra controlled by the number of confined electronic shells. The theoretical results are compared with results of photoluminescence excitation spectroscopy on a series of single self-assembled In0.60Ga0.40As quantum dots.