Exact analytical solutions describing quantum dot, ring and wire wavefunctions

We consider the several phenomena which are taking place in Quantum Dots (QD) and Quantum Rings (QR): The connection of the Quantum Chaos (QC) with the reflection symmetry of the QD, Disappearance of the QC in the tunnel coupled chaotic QD, electron localization and transition between Double Concentric QR in the transverse magnetic field, transition of electron from QR to the QD located in the center of QR. Basis of this consideration is the effective Schr\"odinger equation for the corresponding systems.

We have studied electron correlation effects in quantum dots and rings which include a repulsive scattering centre and aresubjected to a perpendicular magnetic field. The results for thedipole-allowed absorption spectrum show good qualitative agreement with the observed magnetoplasmon dispersion in similarsystems. This work provides a unified description of the electroncorrelations in quantum dots and quantum rings in a magnetic field. We also demonstrate that optical absorption is a direct route to explore the effects of impurity and interactions in a quantum ring.

The fabrication and optical measurement of Ge/Si nanostructure is presented. Atomic force microscopy (AFM) is employed to probe the surface morphology. It shows both quantum dots (QDs) and ring shape Ge nanostructure (quantum ring QRs). MicroRaman is performed to characterize the strain and composition QD and QR.

Laterally close-packed quantum dots (QDs) called quantum dot molecules (QDMs) are grown by modified molecular beam epitaxy (MBE). Quantum dots could be aligned and cross hatched. Quantum rings (QRs) created from quantum dot transformation during thin or partial capping are used as templates for the formations of bi-quantum dot molecules (Bi-QDMs) and quantum dot rings (QDRs). Preferable quantum dot nanostructure for quantum computation based on quantum dot cellular automata (QCA) is laterally close-packed quantum dot molecules having four quantum dots at the corners of square configuration. These four quantum dot sets are called quadra-quantum dots (QQDs). Aligned quadra-quantum dots with two electron confinements work like a wire for digital information transmission by Coulomb repulsion force, which is fast and consumes little power. Combination of quadra-quantum dots in line and their cross-over works as logic gates and memory bits. Molecular Beam Epitaxial growth technique called 'Droplet Epitaxy' has been developed for several quantum nanostructures such as quantum rings and quantum dot rings. Quantum rings are prepared by using 20 ML In-Ga (15:85) droplets deposited on a GaAs substrate at 390 o C with a droplet growth rate of 1 ML/s. Arsenic flux (7'8'10 - 6Torr) is then exposed for InGaAs crystallization at 200 o C for 5 min. During droplet epitaxy at a high droplet thickness and high temperature, out-diffusion from the centre of droplets occurs under anisotropic strain. This leads to quantum ring structures having non-uniform ring stripes and deep square-shaped nanoholes. Using these peculiar quantum rings as templates, four quantum dots situated at the corners of a square shape are regrown. Two of these four quantum dots are aligned either or, which are preferable crystallographic directions of quantum dot alignment in general.

We investigate the electron states and optical absorption in square- and hexagonal-shaped two-dimensional (2D) HgTe quantum dots and quantum rings in the presence of a perpendicular magnetic field. The electronic structure is modeled by means of the $s{p}^{3}{d}^{5}{s}^{*}$ tight-binding method within the nearest-neighbor approximation. Both bulklike and edge states appear in the energy spectrum. The bulklike states in quantum rings exhibit Aharonov-Bohm oscillations in magnetic field, whereas no such oscillations are found in quantum dots, which is ascribed to the different topology of the two systems. When magnetic field varies, all the edge states in square quantum dots appear as quasibands composed of almost fully flat levels, whereas some edge states in quantum rings are found to oscillate with magnetic field. However, the edge states in hexagonal quantum dots are localized like in rings. The absorption spectra of all the structures consist of numerous absorption lines, which substantially overlap even for small line broadening. The absorption lines in the infrared are found to originate from transitions between edge states. It is shown that the magnetic field can be used to efficiently tune the optical absorption of HgTe 2D quantum dot and quantum ring systems.

GaSb/GaAs quantum dots and rings grown under periodical growth mode by using molecular beam epitaxy

GaSb/GaAs quantum-ring-with-dot structures grown by droplet epitaxy

The nonlinear optical rectification coefficient of quantum dots and rings with a repulsive scattering center

The optical analysis of multilayer structures formed from the topmost layer of InGaAs/GaAs quantum rings (QRs) grown on a vertically stacked and laterally aligned InGaAs/GaAs quantum dot (QD) superlattice has been performed to elucidate the nature of the contribution from each layer. These hybrid structures representing a coupled QR chain layer and the layers of self-assembled QD chains display strong optical anisotropy. Unusually strong oscillations are observed in the circularly polarized photoluminescence (PL) intensities under magnetic field for emissions in the spectral range of the QD structure and these oscillations occur simultaneously with weaker oscillations related to the Aharonov-Bohm interference that modulates the emissions from the QR top layer of the structure. The behavior seen in the magneto-PL spectrum is interpreted in terms of joint effects associated to strain, spatial, and magnetic field confinements on the valence band states forming the magnetoexciton ground state of this multilayered structure. The result can be ascribed to a magnetically induced dark exciton contribution where the heavy-hole (type II) state becomes localized outside, whereas light-hole (type I) as well as electron states remain inside the spatial confinement area of the QD.

In this thesis the optical properties of self-assembled III-V semiconductor nanostructures are investigated by analyzing the photoluminescence (PL) with and without an external magnetic field. The studied PL is a result of the recombination of electrons and holes confined in the nanostructures. In this thesis we directly correlate the size, shape, composition and topology of the nanostructures to their magnetic and optical properties and study the influence of an electrical contact in the close proximity of these nanostructures. One of the most interesting nanostructures are quantum dots (QDs), which are able to confine charge carriers in all three dimensions. Both the exciton g-factor gex and the exciton diamagnetic coefficient ad determine the behavior of excitons confined in a QD in a magnetic field and provide further insight in the energy level structure of these nanostructures. The exciton Zeeman splitting is proportional to gex and is a result of the different spin configurations of the electron and hole, which constitute the exciton. The diamagnetic shift is a result of the additional confinement provided by the magnetic field B, and is proportional adB2, where ad scales with the lateral extend of the quantum dot. PL experiments on a large ensemble of InAs/GaAs QDs, as well as on individual InAs/GaAs QDs are performed. For these dots ad and gex have been determined. Importantly, there is a trend between gex and the emission energy E0: for larger emission energy a more negative value of the exciton g-factor is observed. From the power and temperature dependence of the ensemble PL it is shown that the sample consists of QDs with different height, where the highest dots correspond to the smallest emission energies. Moreover, QDs with larger ad have a more positive g-factor. From this it is inferred that quantum dots with an overall larger size have a less negative value of gex. By implementing the QDs in a Schottky device in close proximity to an electrical contact it is possible to tune the charged state of the exciton in the dot. We show that charge-tunable InAs/GaAs quantum dots also allow to study many-body interactions between a localized QD state and a Fermi sea of electrons. As a result of these many-body interactions new optical transitions are observed in the PL spectra. The same chargetunable quantum dots are also investigated in a magnetic field. Instead of the positive diamagnetic shift observed for the majority of the quantum dots, two different types of negative diamagnetic shift are reported. The shallow character of our quantum dots causes a negative quadratic diamagnetic shift for the highly negatively charged exciton complexes in line with predictions for shallow quantum dots. The second type of negative diamagnetic shift is observed even for the neutral exciton and is strongly linearly dependent on the magnetic field. We also investigated quantum dots grown from different semiconductor materials. InAs/InP quantum dots are studied using AFM, X-STM, macro-PL and micro-PL. Macro PL and X-STM measurements show that the studied InAs/InP dots have a multimodal height distribution. Single quantum dot luminescence, carried out on a large number of dots, shows a strong correlation between exciton g-factor, diamagnetic coefficient and emission energy. In fact, the strong dependence of gex on the emission energy results in a sign change of the exciton g-factor. In correspondence with what we found on the InAs/GaAs QDs, we find that dots having a smaller overall size will have a more negative gex as compared to quantum dots of larger overall size. We also show that for several quantum dots the exciton g-factor is quenched. A theoretical model is used to calculate the effect of the quantum dot size on the g-factor. The model is both qualitatively and quantitatively in good agreement with the experimental obtained results. Nanostructures of a different topology are self-assembled InAs/GaAs quantum rings (QRs). Using magnetization measurements on a large ensemble of quantum rings we demonstrate the presence of the Aharonov-Bohm (AB) effect in these nanostructures. Moreover, a model based on the X-STM measurements on these nanostructures reproduces the magnetic field position of this oscillation. The optical properties of these QRs are investigated for magnetic fields up to 30T for a large ensemble of quantum rings and for individual rings. Although the excitonic AB effect is suppressed in these nanostructures, the ring character of our nanostructures gives rise to non-equidistant energy level splittings and into a magnetic field induced splitting of each excited state into two states in the ensemble PL. This is different to what has been observed in measurements on quantum dots. The calculations based on the same model show a qualitative agreement with the experimental data, and allow us to identify the different PL peaks. Furthermore, analyzing exciton lines with high resolution revealed an anomalous quadruplet splitting, which is different as the one reported for InAs/GaAs quantum dots. Although the origin of this splitting is still unclear, it is most likely related to the singlet to triplet transition of singly charged excitons. Finally the magneto-luminescence experiments on type II self-assembled InP/GaAs quantum dots are discussed. For these dots the hole is located outside the quantum dot, whereas the electron is confined inside the quantum dot creating a type II exciton. The magneto-luminescence of the ensemble of dots did not resolve any oscillatory behavior related to the AB effect in contrast to experiments reported on the same sample. Decisive magneto-luminescence measurements on individual dots did also not reveal any AB related phenomena within the experimental resolution of 40 µeV. These results show the necessity to study subtle magneto-luminescence properties of nanostructures on an individual dot level, rather than on a large ensemble of dots.

In this chapter we discuss the details of the spatial structure of GaSb/GaAs(001) quantum rings, and how the observed nanostructures were achieved during the self-assembled growth and formation process. In contrast to the In(Ga)As/GaAs material system, for which thin capping of quantum dots followed by a longer growth interruption is necessary to initiate the quantum-dot to quantum-ring transformation, GaSb quantum rings occur already after the material deposition on GaAs(001), sometimes even without capping. Upon capping almost all quantum dots are transformed into quantum rings. The GaSb quantum rings are found to exhibit a clear central opening, which is filled by the pure GaAs capping material. The more direct formation process of the GaSb/GaAs(001) quantum rings can be understood by analyzing the details of the energies acting during the self-assembled growth. Hence, these more distinct quantum-ring structures are even more promising to show corresponding electronic states, as e.g., the Aharonov-Bohm effect.

We investigate the strain profiles and electronic structures of a novel quantum ring capped by a material different from the substrate. By comparing the novel quantum ring with an ordinary quantum dot and quantum ring, which are capped by the same material as the substrate, we find that the novel quantum ring exhibits noticeably different properties, such as an anomalous strain relaxation, band alignments, and blueshift of the emission energy. We investigate the novel properties of our quantum ring by separating the ring evolution process into (i) the step of geometric change from a dot to ring and (ii) the step of GaAs capping. The GaAs embedded in the In0.53Ga0.47As matrix provides sufficient space for the relaxation of InAs and, thus, individual strain and biaxial strain of the InAs ring are considerably reduced by the GaAs layer. We show that the blueshift in the emission energies due to ring formation is mainly caused by (i) the geometric change from a dot to ring and (ii) the weakened heavy hole–light hole splitting, and not by the enhanced compressive strain. The relaxation of the ring along the radial direction also considerably enhances the shear strain and piezoelectric potential, and the piezoelectric potential partially compensates for the blueshift resulting from the ring evolution and GaAs capping. We also show that the tensile–strained GaAs selectively acts as a potential well for light holes and as potential barriers for both the electrons and heavy holes. As a consequence, the GaAs layer considerably enhances the light-hole character of the hole states in our quantum ring.

The size uniformity of self-assembled SiGe quantum rings, which are formed by cappingSiGe quantum dots with a thin Si layer, is found to be greatly influenced by the growthtemperature and the areal density of SiGe quantum dots. Higher growth temperaturebenefits the size uniformity of quantum dots, but results in low Ge concentration as well asasymmetric Ge distribution in the dots, which induces the subsequently formedquantum rings to be asymmetric in shape or even broken somewhere in the ridge ofrings. Low growth temperature degrades the size uniformity of quantum dots, andthus that of quantum rings. A high areal density results in the expansion andcoalescence of neighboring quantum dots to form a chain, rather than quantum rings.Uniform quantum rings with a size dispersion of 4.6% and an areal density of7.8×108 cm − 2 are obtained at the optimized growth temperature of640°C.

The first part of this work evaluates Al-doped ZnO (AZO) as an optically transparent top-gate material for studies on semiconductor quantum dots. In comparison with conventional Ti gates, samples with AZO gates demonstrate a more than three times higher intensity in the quantum dot emission under comparable excitation conditions. On the other hand, charges inside a process-induced oxide layer at the interface to the semiconductor cause artifacts at gate voltages above 1 V. The second part describes an optical and simulation study of a vertical electric-field (F)-induced switching from a strong to an asymmetric strong–weak confinement in GaAs cone-shell quantum dots (CSQDs), where the charge carrier probability densities are localized on the surface of a cone. These experiments are performed at low U and show no indications of an influence of interface charges. For a large F, the measured radiative lifetimes are substantially shorter compared with simulation results. We attribute this discrepancy to an F-induced transformation of the shape of the hole probability density. In detail, an increasing F pushes the hole into the wing part of a CSQD, where it forms a quantum ring. Accordingly, the confinement of the hole is changed from strong, which is assumed in the simulations, to weak, where the local radius is larger than the bulk exciton Bohr radius. In contrast to the hole, an increasing F pushes the electron into the CSQD tip, where it remains in a strong confinement. This means the radiative lifetime for large F is given by an asymmetric confinement with a strongly confined electron and a hole in a weak confinement. To our knowledge, this asymmetric strong–weak confinement represents a novel kind of quantum mechanical confinement and has not been observed so far. Furthermore, the observed weak confinement for the hole represents a confirmation of the theoretically predicted transformation of the hole probability density from a quantum dot into a quantum ring. For such quantum rings, application as storage for photo-excited charge carriers is predicted, which can be interesting for future quantum photonic integrated circuits.

Topological defects generally they occur in a system when phase transitions take place. We have examples of arrangements with these defects both in Gravitation and Condensed Matter. Depending on how they are generated, this kind of defects make the space present curvature or torsion. There is a wide literature about this matter, much from a gauge field point of view [1, 2, 3], and probing different aspects [6] as the existence of Landau levels [4, 5] or quantum phases [7], for example. However, there is not an unique fundamental theory for describing defects in solids. In our work we follow the Geometric Thery of Defects (TGD) which has the work by Katanaev [8] as a good way of describing continuum media with topological defects. This last theoretical framework is our compass. Besides, we are interested in mesoscopic systems, an important subject right before the role played by nanodevices. In our work we study quantum rings in a space with a screw dislocation. This kind of space presents torsion. The confinement is modelled by a potential that describes different kinds of mesoscopic systems (quantum dots, antidots and quantum wires). We found some results showing the changes in the behaviour of properties as energy eigenvalues and magnetization.