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Theory of excitonic optical properties of semiconductor quantum wells and Bragg structures

Zhenshan S. Yang

Published Jan 1, 2005• 0 citations
OpenAlex

Abstract

This dissertation addresses both fundamental aspects of the coherent exciton kinetics in single semiconductor quantum wells and more application-oriented aspects of the collective excitonic optical properties in quantum well Bragg structures. We use a bosonic theory to investigate the ultrafast coherent exciton dynamics after an optical excitation in a single semiconductor quantum well. It is shown that, on intermediate time scales, nonlinear mean-field interactions between excitons lead to a coherent, wave-like evolution in the momentum distribution of optically inactive excitons, which can survive for some time before dephasing sets in. Driven by two-exciton correlations, this coherent quantum kinetic effect bridges the well-known kinetics associated with optical excitation on the one hand and incoherent relaxation on the other. We also study more general dynamical properties of bosonic mean field systems with N-species of excitons (in a single semiconductor quantum well). We find that the momentum-conserving exciton mean field equations, including the coupling to external fields and fermionic corrections, have the dynamical structure su(N,N). We show that one can define a non-real generalized "Bloch vector" and a non-hermitian "density matrix" description, which allow us to explicitly obtain all the constants of motion associated with the su(N,N) symmetry. The many-body effects and correlations of excitons in a single quantum well are mainly induced by the Coulomb interactions. In the case of a semiconductor quantum well Bragg structure, the light induced coupling between different quantum wells also dramatically affects the excitons' behavior, especially through the collective excitations of excitons in the whole structure. We investigate the linear excitonic optical properties of the quantum well Bragg structure induced by the collective excitations using the transfer matrix approach. We show that the so called "intermediate band" (IB) created by the exciton resonance, which does not exist in conventional photonic crystals, can be used for the stopping, storing and releasing of light, which is important in information processing devices. We also discuss the compensation of the dispersive distortion in the light delay process through reversing the IB band structure. Other conceptual and practical issues such as the decay rate of the IB modes and the generalized anti-reflection coating are also investigated.

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This dissertation addresses both fundamental aspects of the coherent exciton kinetics in single semiconductor quantum wells and more application-oriented aspects of the collective excitonic optical properties in quantum well Bragg structures. We use a bosonic theory to investigate the ultrafast coherent exciton dynamics after an optical excitation in a single semiconductor quantum well. It is shown that, on intermediate time scales, nonlinear mean-field interactions between excitons lead to a coherent, wave-like evolution in the momentum distribution of optically inactive excitons, which can survive for some time before dephasing sets in. Driven by two-exciton correlations, this coherent quantum kinetic effect bridges the well-known kinetics associated with optical excitation on the one hand and incoherent relaxation on the other. We also study more general dynamical properties of bosonic mean field systems with N-species of excitons (in a single semiconductor quantum well). We find that the momentum-conserving exciton mean field equations, including the coupling to external fields and fermionic corrections, have the dynamical structure su(N,N). We show that one can define a non-real generalized "Bloch vector" and a non-hermitian "density matrix" description, which allow us to explicitly obtain all the constants of motion associated with the su(N,N) symmetry. The many-body effects and correlations of excitons in a single quantum well are mainly induced by the Coulomb interactions. In the case of a semiconductor quantum well Bragg structure, the light induced coupling between different quantum wells also dramatically affects the excitons' behavior, especially through the collective excitations of excitons in the whole structure. We investigate the linear excitonic optical properties of the quantum well Bragg structure induced by the collective excitations using the transfer matrix approach. We show that the so called "intermediate band" (IB) created by the exciton resonance, which does not exist in conventional photonic crystals, can be used for the stopping, storing and releasing of light, which is important in information processing devices. We also discuss the compensation of the dispersive distortion in the light delay process through reversing the IB band structure. Other conceptual and practical issues such as the decay rate of the IB modes and the generalized anti-reflection coating are also investigated.
This dissertation addresses both fundamental aspects of Coulomb correlations in semiconductor quantum wells and more practical aspects of theoretical analysis of semiconductor optoelectronic devices. After introducing the subject, we present and evaluate a state-of-the-art theory of the third order coherent optical response of a semiconductor quantum well based on the Dynamics Controlled Truncation (DCT) scheme. Already in the third order (the so-called chi (3)) regime, semiconductors exhibit a number of many-body Coulomb correlation effects. Their manifestation in various multi-pulse experimental configurations, customarily used in ultrafast semiconductor spectroscopy, has been an important component of this thesis. Coherent optical effects in a semiconductor 3-band system based on the heavy-hole, light-hole and conduction bands were investigated. The quantum beats in the time-integrated differential transmission signal were analyzed and compared with experimental data obtained at the University of Iowa. Fundamental differences from corresponding quantum beats in atomic 3-level systems were found. Also, the analysis of experimental data (obtained at the University of Arizona) of the coupled heavy-hole-light-hole optical Stark shift revealed evidence of intervalence band coherences, an analog of Raman coherences in atomic 3-levels systems. A scheme for realization of electromagnetically-induced transparency (EIT) based on the interference of excitonic and biexcitonic coherences was proposed. Corresponding experiments performed at the University of Oregon showed indeed a considerable coherent reduction of excitonic absorption. Furthermore, an extension of the chi(3) analysis revealed an energy renormalization of the biexciton, in good agreement with the corresponding experiment. A microscopic analysis of polarization dynamics in time-resolved four-wave mixing signals was performed, revealing interesting implications for the biexciton dephasing in addition to the significance of many-body correlations. In the case of four-wave mixing in semiconductor microcavities, our theoretical analysis in conjunction with experimental data obtained at the University of Tokyo gave us indications for a significant shortcoming of the second Born approximation (2nd BA) applied to two-exciton Coulomb correlations in a thin semiconductor quantum well, in agreement with the general knowledge of the qualitative failure of the 2nd BA in systems with short-range interaction in two dimensions. We also analyzed a novel all-optical switching technique based on the nonlinear polarization rotation. Apart from identifying the many-particle processes relevant for the switch operation in the chi(3) regime, we proposed ways to further optimize the switch.
Excitons, the bound states of an electron and a hole, in semiconductors are interesting objects and they continue to attract attention of researchers from all over the world. Despite intense research on exciton physics over last three-four decades, many interesting phenomena related to the dynamics and the nonlinear optical properties of excitons in semiconductors and their nanostructures in the coherent and incoherent regimes are still to be explored. This thesis presents our effort to study the nonlinear optical properties as well as the exciton dynamics in coherent and incoherent regime in semiconductor nanostructures including GaAs quantum wells (QWs) and InAs quantum dots (QDs). We have set up several time-resolved and steady-state optical spectroscopic measurement techniques in our laboratory to carry out our study on excitons dynamics in semiconductor QWs and QDs. We work out a clear and detailed theory of the pump-probe signal taking account of all aspect of the measurement, namely, the lock-in detection, spectral selection by the monochromator and time-integration at the slow photodetector. We have used the formalism of optical Bloch equations conventionally used to analyse wave mixing experiments. Our analysis puts the pump-probe technique on the same footing as the wave mixing experiments. We show that pumpprobe experiments can be used to study both coherent and incoherent dynamics. We also present a clear physical picture of the measured signal using the Lorentz harmonic oscillator model. We report the investigation of the coherent exciton dephasing dynamics using pumpprobe reflectivity measurement in GaAs QWs for resonant excitation. Two GaAs/AlGaAs QWs with well thicknesses 8 nm and 17.5 nm are used. We found a strong dependence of the dephasing rate of the excitons with increasing exciton density due to exciton-exciton scattering. We found that the exciton dephasing rate of 8 nm QWs at low excitation density and at low lattice temperature is larger than the corresponding dephasing rate of the 17.5 nm QWs, possibly due to larger effect of inhomogeneous broadening. We also report that the dephasing rates for both QWs are linear with the sample temperature below the 30 K. We report the study of ionization equilibrium between the exciton and the electronhole plasma population in the temperature and pressure (excitation density) phase space. Non-resonant excitation of semiconductor creates a nonequilibrium state of electron-hole plasma. We investigate this ionization equilibrium using steady state photoluminescence and time-resolved excitation correlation PL measurements. We present a clear phase diagram (in temperature and carrier density phase space) of this ionization process.A clear density-dependent increase in the ionization ratio is observed and its connection with the Mott transition is discussed. Semiconductor nanocrystals and QDs are another important area of research, mainly due to their huge potential for device application. We present a simple model which combines carrier loss kinetics, detailed balance principle in thermodynamic equilibrium and Pauli exclusion principle to quantitatively explain the observed behaviour of the experimental data.
Summary form only given. The optical properties of semiconductor quantum wells (QW) and, in particular, the coherent dynamics of excitons following resonant excitation with ultrafast laser pulses have attracted much attention in recent years. It is generally accepted that there is a transfer of coherence between the optical field and the QW that disappears in a characteristic time T/sub 2/ (picoseconds for GaAs) after the laser is turned off. However, the questions as to how the coherence is actually induced and that of the nature of the coherent state of the solid are poorly understood. In this work we address these points by re-examining the longstanding problem of the (classical vs. quantum) nature of the ubiquitous beats associated with the light-hole (LX) heavy-hole (HX) excitons, which are observed in transient optical experiments on QW. To this end, we consider the coherent behavior of excitons using the simplest albeit non-trivial model where they are treated as non-interacting bosons. Our results bear directly on studies for which nonlinear effects are not important and are not aimed directly at explaining the fourwave-mixing (FWM) experiments that dominate the field. Nevertheless, since nonlinear effects are, typically, weak compared with harmonic contributions, the free boson picture provides in all cases the correct lowest order wavefunction of the photoexcited solid.
Summary form only given. Effects of exciton-exciton correlations (e.g. bound biexciton, exciton-exciton scatterings) have been amply demonstrated in the /spl chi//sup (3)/ contributions to experiments measuring the interband polarization in semiconductor quantum wells. Increasing attention is currently being focussed on higher order excitonic correlation effects. One higher-order quantity is the incoherent exciton density (defined as total exciton density minus the interband polarization squared) which is created by excitons scattering each other out of the coherent component. Other than its role in the dephasing and relaxation of the system, the incoherent exciton density has not received much attention. In this contribution, we present results of our theoretical study on the behavior of this quantity and related correlation functions under conditions that inhibit relaxation. Our theory follows the general formulation of bosonic theories for excitons: the basic degrees of freedom are exact bosons, and the fermionic exchange effects are incorporated into the boson-boson and boson-photon effective Hamiltonians. We truncate the effective interaction at the two-boson level. No formal bosonization procedure is used: the matrix elements of our effective Hamiltonian are chosen in such a way that in the coherent /spl chi//sup (3)/ limit, our boson theory yields formally identical results as the standard fermionic dynamics controlled truncation formalism. Standard many-body techniques are used to derive equations of motion for densities, correlation functions, and measurable quantities such as the interband polarization.
The optical response of radiatively coupled semiconductor multiple-quantum-well structures is investigated theoretically. It is shown that the transverse optical field leads to a coupling of exciton states within each well which causes a radiative decay and a mixing of excitonic resonances. Simultaneously, the field-induced long-ranged coupling between different wells leads to collective effects that are very sensitive to the detailed geometry of the structure. For a quantum-well spacing equal to an integer multiple of half the optical wavelength inside the medium, it is predicted that the collective effects cause a stimulated decay of electronic excitations that should be observable in either transmission or reflection geometry. On the other hand, in a quarter wavelength structure, the light-induced coupling causes an interwell energy transport and a splitting of the excitonic resonances, that should be observable as quantum beats in the time-resolved transmitted or reflected signal.
A microscopic many-body theory for the optical and electronic properties of semiconductors is reviewed with an emphasis on the role of correlation effects. At the semiclassical level, the semiconductor Bloch equations include many-body effects via bandgap and field renormalization as well as correlation contributions representing two electron-hole pair amplitudes, excitonic populations, and coupled interband and intraband coherences. These Coulomb interaction induced carrier correlations lead to characteristic signatures in nonlinear semiconductor spectroscopy. At the fully quantum mechanical level the dominant light-matter correlations are described by coupled semiconductor Bloch and luminescence equations. Excitonic emission properties of quantum well and microcavity systems are discussed, including effects such as coherent signatures in the secondary emission and coherent control of the emitted light.