Dokument

Summary:
This work consists of two parts which are entitled "One-Dimensional Resonant Fibonacci Quasicrystals" and "Resonant Tunneling of Light in Silicon Nanostructures". A microscopic theory has been applied to investigate the optical properties of the respective semiconductor nanostructures. The studied one-dimensional resonant Fibonacci quasicrystals consist of GaAs quantum wells (QW) that are separated by either a large spacer L or a small one S. These spacers are arranged according to the Fibonacci sequence LSLLSLSL... The average spacing satisfies a generalized Bragg condition with respect to the 1s-exciton resonance of the QWs. A theory, that makes use of the transfer-matrix method and that allows for the microscopic description of many-body effects such as excitation-induced dephasing caused by the Coulomb scattering of carriers, has been applied to compute the optical spectra of such structures. Based on an appropriate single set of fixed sample parameters, the theory provides reflectance spectra that are in excellent agreement with the corresponding measured linear and nonlinear spectra. A pronounced sharp reflectivity minimum is found in the vicinity of the heavy-hole resonance both in the measured as well as in the calculated linear 54-QW spectra. Such sharp spectral features are suitable for application as optical switches or for slow-light effects. Hence, their properties have been studied in detail. Specifically, the influence of the carrier density, of the QW arrangement, of a detuning away from the exact Bragg condition, of the average spacing as well as of the ratio of the optical path lengths of the large and small spacers L and S, respectively, and of the QW number on the optical properties of the samples have been studied. The features of measured spectra could have been attributed to different sample properties related to the sample setup. Additionally, self-similarity among reflection spectra corresponding to different QW numbers that exceed a Fibonacci number by one is observed, which identifies certain spectral features as true fingerprints of the Fibonacci spacing. In the second part, resonant tunneling of light in stacked structures consisting of alternating parallel layers of silicon and air have been studied theoretically. While usually total internal reflection is expected for light shined on a silicon-air interface under an angle larger than the critical angle, light may tunnel through the air barrier due to the existence of evanescent waves inside the air layers if the neighboring silicon layer is close enough. This tunneling of light is in analogy to the well-known tunneling of a quantum particle through a potential barrier. In particular, the wave equation and the stationary Schrödinger equation are of the same form. Hence, the resonant tunneling of light can be understood in analogy to the resonant tunneling of e.g. electrons as well. The characteristic feature of resonant tunneling is a complete transmission through the barrier at certain resonance energies. The transmission, reflection, and propagation properties of the samples have been determined numerically using a transfer-matrix method. Analytical expressions for the energetic resonance positions have been derived and are in excellent agreement with the numerical simulations. Special attention has been drawn to the lowest resonance out of a series of resonant-tunneling resonances. There, light has been observed to be concentrated within silicon layers the extension of which is smaller than the corresponding wavelength of the light. Specifically, the quality factor is large at the resonance energies, so that the resonant light leaves the sample delayed, which allows for the study of slow light. A detailed investigation of how the sample geometry influences the optical properties of the sample has been presented. In particular, it has been outlined how to design a sample to obtain certain desired optical properties. The optical properties that are related to the resonant tunneling strongly rely on the (mirror-)symmetry of the samples. If asymmetries - especially of the silicon wells inside the air barrier - are present in the sample setup, the resonant-tunneling efficiency is diminished. Such asymmetries are unavoidable in the production of the samples. Therefore, a parameter range has been identified in which reasonable transmission above a transmission probability of 50% can be expected taking typical fluctuations caused by the production process into account. Silicon-based resonant-tunneling structures of a setup proposed by the presented theory have already been fabricated and first experiments are under way. This will allow for theory-experiment comparisons.

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