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Mechanisms of the low density nonlinear optical response of excitons in gallium arsenide and the study of exciton transport.

A. C. Schaefer

Published Jan 1, 1996• 0 citations
OpenAlex

Abstract

The study of the nonlinear optical response of excitons in semiconductors is important for both scientific and technological applications. Although the nonlinear optical properties of bulk semiconductors and heterostructures have been studied for almost three decades, with most of the research focusing on heterostructures, the mechanisms leading to the nonlinearities in these systems are not completely understood. Determining these mechanisms and developing a theoretical picture which describes the most dominant effects remains a challenge and an active area of study. Although optical interactions in semiconductors is a genuine many-body problem, a description of this system similar to the optical Bloch equations used in atomic studies has shown some success, but more work is needed to make this model complete. Experimental work, particularly in the bulk system uncomplicated by the interface disorder present in heterostructures, will provide the guidance to extend this formalism. In this dissertation, the frequency domain resonant nonlinear optical response of excitons in bulk gallium arsenide at low density is studied to gain insight into the dominant mechanisms leading to the response, as well as the dynamics of the nominally three-dimensional excitonic system. Specifically, the nonlinear response was probed with differential transmission (DT) and four-wave mixing (FWM) experiments, which measure to lowest order the third-order susceptibility, $\chi\sp{(3)}.$ Using these various tools, three specific areas were studied and the results will be presented. First, the role of the biexciton, the state of two bound excitons, in determining the bulk nonlinear response was explored. The observation of a red-shifted nonlinear resonance suggests the importance of this state at moderate densities. Second, a new response, characterized by a resonant increase in exciton absorption induced by optical pumping with initial superlinear growth and a transition to behavior described by simple line broadening with increased pump intensity, was studied in detail. A model considering increased polariton absorption with increased exciton-exciton interactions explains these effects. Finally, nonlinear optical spectroscopy was used to study exciton transport, where near-ballistic behavior was revealed. The effect of exciton transport, thermalization and radiative recombination on the nonlinear optical response was explored.

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•Jan 1, 1990•0 citations
The study of the nonlinear optical response of excitons in semiconductors is important for both scientific and technological applications. Although the nonlinear optical properties of bulk semiconductors and heterostructures have been studied for almost three decades, with most of the research focusing on heterostructures, the mechanisms leading to the nonlinearities in these systems are not completely understood. Determining these mechanisms and developing a theoretical picture which describes the most dominant effects remains a challenge and an active area of study. Although optical interactions in semiconductors is a genuine many-body problem, a description of this system similar to the optical Bloch equations used in atomic studies has shown some success, but more work is needed to make this model complete. Experimental work, particularly in the bulk system uncomplicated by the interface disorder present in heterostructures, will provide the guidance to extend this formalism. In this dissertation, the frequency domain resonant nonlinear optical response of excitons in bulk gallium arsenide at low density is studied to gain insight into the dominant mechanisms leading to the response, as well as the dynamics of the nominally three-dimensional excitonic system. Specifically, the nonlinear response was probed with differential transmission (DT) and four-wave mixing (FWM) experiments, which measure to lowest order the third-order susceptibility, χ\sp(3).\chi\sp{(3)}.χ\sp(3). Using these various tools, three specific areas were studied and the results will be presented. First, the role of the biexciton, the state of two bound excitons, in determining the bulk nonlinear response was explored. The observation of a red-shifted nonlinear resonance suggests the importance of this state at moderate densities. Second, a new response, characterized by a resonant increase in exciton absorption induced by optical pumping with initial superlinear growth and a transition to behavior described by simple line broadening with increased pump intensity, was studied in detail. A model considering increased polariton absorption with increased exciton-exciton interactions explains these effects. Finally, nonlinear optical spectroscopy was used to study exciton transport, where near-ballistic behavior was revealed. The effect of exciton transport, thermalization and radiative recombination on the nonlinear optical response was explored.
Optically induced coherences reveal key features of nonlinearities in the optical response of semiconductors and can be employed to obtain information about dynamical processes via such techniques as transient four-wave mixing and differential transmission. This thesis presents experimental observations of three previously unrecognized aspects of coherent nonlinear optical phenomena occurring in gallium arsenide and multiple quantum wells: excitation-induced dephasing, two-photon biexcitonic coherence, and electronic Raman coherence. Results are analyzed using optical Bloch equations, which emphasize the potential generalization to other semiconductor systems. Excitation-induced dephasing is similar to classical line broadening. The work in this thesis shows for the first time that this incoherent effect is directly responsible for the dominant coherent optical nonlinearity in bulk gallium arsenide. Exact analytic models show that excitation-induced dephasing accounts for the previously unexplained polarization and density dependence of four-wave mixing signals obtained at the 1s exciton resonances in gallium arsenide. This thesis also presents the first observation of the two-photon biexcitonic coherence in a gallium arsenide multiple quantum well using a modified Michelson phase-conjugate interferometer to directly observe the 770-Terahertz oscillation of the nonradiative superposition of the electronic ground state and the biexciton state. The contribution of the two-photon coherence to the nonlinear optical response is thereby confirmed, in addition to the well-known stepwise biexcitonic response. Finally, the short-lived electronic Raman coherence between the light- and heavy-hole 1s excitons in gallium arsenide is conclusively demonstrated for the first time. The Raman coherence provides direct access to dephasing processes not detectable in conventional linear spectroscopy. Similar non-radiative coherences are related to population trapping, electromagnetically induced transparency, and lasing without inversion in atomic systems, and the new observations in gallium arsenide suggest that analogous phenomena may occur in semiconductors.
The purpose of this research is to study the relaxation of optically generated excitons and carriers in semiconductor microstructures using four wave mixing (FWM) spectroscopy. The systems studied include CdSSe microcrystallite doped glasses and GaAs/AlGaAs multiple quantum well structures (MQWS). Exposing a semiconductor to optical radiation near the fundamental band gap results in the creation of populations of elementary excitations including electrons, holes, and excitons, and also results in the creation of a superposition state between the ground and excited state of the solid. The work in this dissertation examines the relaxation of the populations of elementary excitations and the relaxation of the coherence between the ground and excited state using four wave mixing spectroscopy. First, the nonlinear optical response of simple two level systems is examined in order to provide insight into the types of line shapes expected from semiconductors. It is shown that the line shape is strongly dependent on how the system is coupled to the reservoir and the consequences of coupling to a reservoir are examined in a FWM measurement made in atomic sodium. The first semiconductor system studied is CdSSe microcrystallite doped glass. This system is shown to have a very slow component to the nonlinear response which has a optical intensity dependence and temperature dependence which suggests that the FWM response in these materials is trap mediated. Room temperature FWM measurements in GaAs MQWS enables the measurement of the carrier recombination time and the ambipolar diffusion coefficient. Using the technique of correlated optical fields, a slow component to the nonlinear response was measured showing an interference profile which suggests a possible shift of the exciton resonance due to the optically generated carriers. At low temperatures (2-20 K), measurements of the exciton line shape and relaxation time were made and evidence for exciton spectral diffusion was found. The low temperature line shapes can be qualitatively reproduced using Modified Optical Bloch equations which include the effects of spectral diffusion.
This dissertation presents investigations of fundamental optical nonlinearities in semi-conductor microstructures. Two distinct effects are studied. In the first part the excitonic optical Stark effect in InGaAs and GaAs multiple quantum-well structures is investigated by means of pump-probe spectroscopy. For nonresonant excitation below the excitonic transition the direction of the shift of the resonance depends on the polarization of the pump and probe pulses. In particular, for anti-circular polarization a surprising red-shift is observed. For resonant excitation, induced absorption energetically above and below the exciton transition and bleaching of the resonance is found. Experiments using both resonant and nonresonant excitation reveal the importance of bound and unbound two-exciton states in absorption changes of the 1s heavy-hole exciton resonance. It is found that higher-order Coulomb contributions determine the intensity as well as the time dependence of the differential excitonic absorption. In addition, the influence of light-hole excitons is analyzed. It is shown that the direction of the optical Stark shift for nonresonant excitation depends also sensitively on the heavy-hole to light-hole splitting and the detuning of the pump pulse. For very high pump intensities and nonresonant excitation the absorption is split when a circularly polarized pump and a linearly polarized probe beam are used. For co-circular excitation traces of hyper-Raman gain are observed. In the second part of this dissertation, the nonlinear optical response of semiconductor microcavities in the nonperturbative regime is studied in resonant single-beam transmission and pump-probe experiments. In both types of experiment, a pronounced third transmission peak lying spectrally between the two normal modes is observed. Its dependence on the probe intensity, pump intensity, pump-probe delay, exciton-cavity detuning and pump detuning is investigated. For single-beam transmission, the energy of the third peak parallels the position of the cavity resonance. It is more pronounced for circularly polarized excitation and lasts longer than the two normal modes. For pump-probe experiments, the third peak increases with decreasing probe intensity and increasing pump intensity. Its energy is close to the low-energy side of the pump spectrum and virtually unaffected by the cavity-exciton detuning. The appearance of the third peak requires temporal overlap of pump and probe pulses. The origin of this complex nonlinearity is the quantum nature of light, which induces intraband polarizations in the presence of a coherent driving field and a finite carrier density. It is found that the coupling of the intraband polarizations via guided modes to the polarization of the fundamental longitudinal mode is responsible for the third transmission peak. A fully quantized theory reproduces the experimental observations.
Ultrafast nonlinear optical spectroscopy is used to study the coherent dynamics of optically excited electron-hole pairs in semiconductors. Coulomb interaction implies that the optical inter-band transitions are dominated, at least at low temperatures, by excitonic effects. They are further enhanced in quantum confined lower-dimensional systems, where exciton and biexciton effects dominate the spectra even at room temperature. The coherent dynamics of excitons are at modest densities well described by the optical Bloch equations and a number of the dynamical effects known from atomic and molecular systems are found and studied in the exciton-biexciton system of semiconductors. At densities where strong exciton interactions, or many-body effects, become dominant, the semiconductor Bloch equations present a more rigorous treatment of the phenomena. Ultrafast degenerate four-wave mixing is used as a tool to study the coherent exciton dynamics, and the importance of performing transform limited spectroscopy is demonstrated throughout.
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.
This work presents new results of experimental studies of exciton relaxation in GaAs/AlGaAs multiple quantum well materials, using transient nonlinear laser spectroscopy techniques. In the low excitation regime, effective optical Bloch equations similar to the density matrix formalism of a two-level system describe the response. Solutions of these equations appropriate for three-pulse scattering studies are presented, along with a discussion of new experimental techniques used in this work. Non-ideal conditions present in the molecular beam epitaxy growth process introduce monolayer fluctuations in the quantum well thickness, leading to inhomogeneous broadening and exciton localization at sites of minimum energy. Localized excitons are separated in energy from extended, quasi-delocalized states by the mobility edge. Studies of localized exciton relaxation indicate that these excitons relax on a much slower timescale than delocalized excitons. The temperature dependence of the localized exciton relaxation rate shows that above 15K, the excitons are thermally activated to extended states above the mobility edge. Below 15K the excitons relax by phonon assisted migration between localization sites. For temperatures above 5K, and for exciton energies greater than 1 meV below line center, an extra dephasing mechanism characterizes the exciton relaxation. The inhomogeneous broadening of the exciton leads to the emission of stimulated photon echoes in the experimental geometry used in this work. The time-resolved emission demonstrates the stimulated photon echo nature at low excitation densities. At higher excitation densities, the decay dynamics is more complex. The time-resolved emission shows the presence of a stimulated photon echo and a free polarization decay. This unusual result suggests that both a homogeneous and an inhomogeneous exciton distribution comprise the exciton resonance. Exciton relaxation at low excitation densities represents the interaction of the exciton with the lattice. At higher excitation densities, exciton-exciton and exciton-free carrier interactions modify the relaxation rates. The dependence of the exciton relaxation rate on excitation density shows that many-body effects play an important role in the exciton physics. Free carrier interactions are more efficient at increasing the exciton relaxation rate; both types of interactions are more important in quantum well systems than in bulk materials.