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Publication# Electronic and Optical Properties of Semiconductor Quantum Dots

Abstract

This thesis is devoted to theoretically study the systems of single quantum dots (QDs) embedded in various photonic nanostructures, in close relation with experimental data. The word single is essential: due to their nanometer size, QDs have mainly been studied as ensembles. It is only recently that the experimental progress, in particular in the domain of QDs growth, has allowed to address single QDs. This helped to observe that the confined states in a QD resemble those of an atom, leading in turn to the macro-atom picture for QDs. It opened the path to the study of cavity quantum electrodynamics (CQED) in the solid state, as the analogous of a system of an atom in an electromagnetic cavity. However, already at the level of the QD (i.e. without a solid state cavity), the macro-atom picture has been proven to be oversimplified. Various effects related to the solid state environment of the QD have been experimentally and theoretically evidenced, like the influence of acoustic and optical phonons. These are channels of decoherence for the otherwise well isolated and confined QD levels. When adding the cavity, these effects are possibly enhanced, which can lead to very large deviations from the CQED ideal picture. Therefore the clear understanding of these effects is of essential importance, especially in view of the application of solid state systems to quantum information science. In Chapter 2, we address the radiation-matter coupling between two QDs in a nanocavity. This field of research combines the high quality of light resonators to the nonlinearities of the semiconductor material. It is promising in view of manipulating and transferring single long-lived excitations, an essential goal for quantum information science. Then, we study the deviations of a QD from the idealized macroatom picture. First, in Chapter 3, we include the influence of acoustic phonons on the light emitted by a QD-cavity system. We show that the QD modified susceptibility leads to the qualitative explanation of the cavity feeding effects, which is one of the most striking deviations of the QD-cavity system from the ideal CQED picture. In addition to phonons are extended two-dimensional states populated by the non resonant pumping laser in the QD's wetting layer (WL). In Chapters 4 and 5 we build a Monte-Carlo model of the excitation-decay mechanism in a QD-cavity system. We use it to describe the influence of WL states on the dynamics of the QD, leading in turn to a non-CQED behavior. This approach is particularly successful in the case of large QD-cavity detuning, where it predicts both time-dependent and spectral characteristics of the emitted light. Finally, in Chapter 6, we discuss our conclusions, emphasizing in particular that the knowledge of the actual solid state environment of the QD leads to a better control over the parameters allowing to reach the CQED regime. We also discuss the possible extensions of this work, in particular in relation to the analysis of the stimulated emission regime.

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A quantum dot is a semiconductor nanostructure that confines the motion of conduction band electrons and valence band holes in all three spatial directions, thus creating fully discrete energy levels. The confinement in the InAs/GaAs material system is generated by the bandgap difference for the two materials (∼ 0.4 eV for InAs, and ∼ 1.4 eV for GaAs) which provides a minimum of potential energy for both electrons and holes inside the InAs nanoparticle. The appearance of new nanoscale effects modifies the electro-optical properties of such a system which makes possible the improvement of existing device performance or even fascinating novel device applications. For the creation of coherent structures with very high purity and high density, as it is required for application in light emitting devices, self-assembling is a very important pathway. The quantum dot creation mostly relies on the relaxation of the strain accumulated during the growth of lattice mismatched materials, which happens in a non-equlibrium condition. This results in a statistical distribution of all the parameters characterizing the InAs nanocrystals as size, composition and strain, whose direct manifestation is the inhomogeneously broadened light emission deriving from quantum dot ensembles. At the dawning of the quantum dot development the broadening was considered as a limiting factor for application in semiconductor lasers. Today, it is considered favorably for all the applications where a broad gain spectrum is required as optical amplifiers, monolithic and external-cavity tunable lasers, and superluminescent diodes. The objective of this thesis is the application of InAs/GaAs self-assembled quantum dots to the active region of high power and broad-band superluminescent diodes emitting in the 1.3 μm wavelength region. Superluminescent diodes are edge-emitting semiconductor light sources based on the amplification of spontaneous emission along a waveguide where optical gain is achieved through current injection. They combine the high power and brightness of laser diodes with the low coherence of LEDs. The latter is a fundamental feature for the application in optical coherence tomography medical imaging, where the image resolution is related to the spectral bandwidth of the light source used. The achievement of bandwidths larger than 100 nm are demonstrated in this work through the optimization of molecular beam epitaxy growth conditions. This may be done optimizing the statistical size-dispersion of the dot ensemble, or through the use of different dot layers emitting at slightly different wavelengths. The large bandwidth emission is obtained also due to the peculiar energy structure of this material, for which a multi-state emission appears under particular injection conditions. As a term of comparison, best commercial single-chip superluminescent diodes for the imaging application at 1.3 μm show bandwidths around 60 nm. Moreover, the discrete nature of the energy levels in InAs quantum dots together with the implementation of a GaAs-based technology can be beneficial for the device temperature stability (the competing technology, based on InP, suffers from strong thermal degradation). The analysis and understanding of the device temperature characteristics will be detailed in the last chapter of the manuscript. Even though standard devices show an important temperature dependence, a better stability may be achieved through the use of p-doped active regions. In the last few years quantum dot devices have shown outstanding properties if compared to the competing quantum well technology. Low threshold currents, high temperature stability and low chirp in lasers, large bandwidths and low gain saturation in amplifiers have been demonstrated. However, in spite of the large interest among the scientific community, many of the microscopic processes at the origin of the electro-optical characteristics of this material are not completely understood yet. The physics of the quantum dot active material, will be modeled in this work through the use of systems of rate equations with different complexity depending on the system they are applied to. We will provide a mean-field rate equation model allowing to get insights about carrier dynamics in QD lasers. Also, we will develop two different traveling-wave rate equation models, one for the modeling of the L-I characteristics and the other for the modeling of the spectral characteristics of quantum dot superluminescent diodes. Considering the carrier and photon density distributions across the device cavity is essential in superluminescent diodes, where the high single pass gain results in large non-homogeneities of photon and carrier distributions. The work is motivated by an industrial cooperation with EXALOS AG, a leading company in the development, manufacturing, and sales of broadband superluminescent diodes.

This thesis presents the coherence properties of polaritons in semiconductor microcavities. Semiconductor microcavities are microstructures in which the exciton ground state of a semiconductor quantum well is coupled to a photonic mode of a microresonator. The strong coupling mixes the character of excitons and photons, giving rise to the lower and upper polariton branches, quasiparticles with an unusual energetic dispersion relation due to the extreme mass difference between exciton and photon. Particularly special is the dispersion of the lower polariton, which forms a dip in the 2-dimensional k-space around the lowest energy state with zero in-plane momentum. In this dip, which can be seen as a trap in momentum space, the polaritons are efficiently isolated from dephasing mechanisms involving phonons. Polaritons can be resonantly excited at desired points on the polariton dispersion by shining on the microcavity laser light at the appropriate angle and wavelength. Polaritons can interact and scatter pairwise with each other conserving energy and in plane momentum k, a process similar to parametric scattering of photons in a nonlinear crystal. One polariton from a pump reservoir scatters down to the signal state at k = 0 (corresponding to normal incidence) and a second takes away the excess energy and momentum of the first and scatters up to the idler position ({kP, kP} → {0, 2kP }). This process can be stimulated by a small amount of signal polaritons injected with a probe laser beam at normal incidence. Here the coherence properties of the polariton parametric scattering have been investigated using spectroscopy techniques sensitive to the optical phase, for example coherent control with phase-locked femtosecond probe pulses. Just above the threshold for the stimulated parametric scattering, the parametric amplification process is given by the linear superposition of the individual amplification processes of each probe pulse. The emission of signal, pump, and idler can be controlled by tuning the relative phase of the 150fs-long probe pulses, which are separated by a few picoseconds in time. Experiments are presented that deal with the real-time dynamics of the parametric scattering in the spontaneous and the stimulated regime. It is shown, that in the spontaneous regime the scattering is started by a small amount of polaritons which have relaxed to the band bottom by emitting phonons. In the regime where polariton scattering is stimulated by an external probe, the rise of the signal intensity is delayed with respect to the arrival time of both pump and probe, a feature that can be attributed to the complex phase-matching mechanism for the parametric scattering. In the second part of the thesis, the spontaneous build up of a macroscopic coherence in a CdTe microcavity under non-resonant laser excitation is analysed. The build up of a long-range spatial coherence easily exceeding the thermal wavelength of the polaritons is shown. This is the hallmark of Bose-Einstein condensation and the proof of a macroscopic wavefunction. Experimental data on the statistical distribution of the polaritons in time, the polarisation of the non-linear emission, and the quantum transition from a thermal to a coherent state1 confirm that Bose-Einstein condensation of microcavity polaritons has been observed. We regard these observations as the first bullet-proof evidence for spontaneous Bose-Einstein condensation in a solid state system, a phenomenon that has been the subject to many investigations and controversies during the past four decades. ------------------------------ 1 The data about the statistical distribution, the polarisation, and the transition from a thermal to a coherent state is by courtesy of Jacek Kasprzak of the University of Grenoble.

Semiconductor quantum dots are usually compared to artificial atoms, because their electronic structure consists of discrete energy levels as for natural atoms. These artificial systems are integrated in solid materials and can be localized with a spatial precision of the order of nanometers. Besides, they conserve their quantum properties even at quite high temperatures (∼ 10 K). These properties make quantum dots one of the most suitable systems for the realization of quantum devices and computers. However, the energy states and the optical properties of quantum dots are much more complicated than for atoms, because a quantum dot is never an isolated potential well. Instead, its electronic structure depends on the crystallin structure of the semiconductor material and on the Coulomb ion-electron and electron-electron correlations. In particular, the presence of several valence bands and their mixing, induced by quantum confinement, gives rise to novel properties which are still not completely understood and exploited in applications. To get a major advance in this field, a full deterministic control of the spatial shape of the quantum confinement is needed, combined with a deeper understanding of the connections between electronic and optical properties. This thesis work has these two main objectives. We realized and experimentally studied different quantum dot systems, in pyramidal hetero-structures grown with MOCVD techniques. These systems allowed the realization of several different geometries for the carrier confining potential, with a precision in the order of nanometers. The optical characterization has been obtained in particular by means of polarization-resolved microphotoluminescence, magneto-photoluminescence, excitation photoluminescence (PLE), and interferometry techniques. For single quantum dots, we have observed and characterized for the first time new excitonic complexes, arising from excited hole states. This allowed a full caracterizatioon of the valence band hole states in our peculiar system. By means of photon correlation measurements, we have also experimentally demonstrated that, even in presence of a large family of exciton states, these quantum dot systems can emit single photons. We have then realized much more complex quantum dot structures, double dot systems (quantum dot molecules) and a completely new system called Dot-in-Dot (DiD). This latter is composed by a small inner dot surrounded by an electrostatic potential well (which can be considered as an outer elongated dot). Such a composite system is characterized by a strong valence band mixing. This state superposition is however very sensitive to small variations of the confining potential. Therefore the degree of valence band mixing can be easily switched by the introduction of a week external field. Since the valence band mixing determines the polarization properties of the emitted light, the DiD changes the polarization properties of its emission spectrum under the action of an external field. In particular, we have experimentally demonstrated this effect for an external static magnetic field, while we have numerically predicted a very similar effect for a static electric field. In the latter case, the polarization switching is a direct consequence of the quantum confined Stark effect induced in the DiD. Hence the DiD appears to be an ideal candidate for realizing emitters of single photons with tunable and controllable polarization.