Quantum Dots: Inelastic Light Scattering from Electronic Excitations


Christian Schüller Institut für Angewandte Physik und Zentrum für Mikrostrukturforschung, Universität Hamburg

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Electrons confined in semiconductor quantum systems are a field of enormous and still growing research interest because they allow, in specially tailored systems, the investigation of fundamental properties, such as many-particle interactions of electrons in reduced dimensions. In this article, we give an overview of experimental and theoretical investigations of electronic excitations in semiconductor quantum dots. Optical spectroscopy techniques, such as far-infrared (FIR) transmission and resonant Raman scattering, i.e., inelastic light scattering (ILS), are ideal tools to study the spectrum of elementary excitations of these systems. Since the work of Pinczuk et al. on 2-D intersubband excitations in GaAs–AlGaAs quantum wells, it has been known that besides collective spin-density (SDEs) and charge-density excitations (CDEs), one can observe nearly unrenormalized excitations—the so-called single-particle excitations (SPEs)—in ILS experiments. Both SDEs and CDEs are collective excitations; SDEs are affected by exchange interaction while CDEs are affected by the full Coulomb interaction of the electrons. However, the origin of the SPEs, which seem to be unaffected by the particle–particle interaction, has posed a puzzle. Electronic excitations, and also SPEs in particular, could subsequently be observed in lower-dimensional systems, based on modulation-doped GaAs–AlGaAs quantum wells, and also particularly in quantum dots. In an experimental work, it was shown that SPEs can be observed in low-dimensional electron systems under conditions of extreme resonance, when the laser energy is close to the fundamental band gap of the structures. Thus SPEs are created in a resonant density-fluctuation scattering process, whereas collective SDEs and CDEs ensue from an excitonic third-order scattering process. Many theories of nonresonant Raman scattering accurately describe the energetic positions of the collective excitations, as well as the wave-vector and magnetic-field dependence of the CDE and SDE. However, they fail in predicting the experimentally observed relative strengths of the different modes. Furthermore, the occurrence of SPE cannot be explained within the confines of these theories. It has been known for a long time that valence-band states play a crucial role in carrying out a correct treatment of the resonant scattering cross section. Recent theoretical papers on quantum wires and quantum dots showed that inclusion of the valence-band states indeed significantly changes the intensities of the excitations. During the past decade, self-assembled InAs quantum dots (SAQDs) have also proven to be highly interesting quantum structures, both from a technological as well as from a fundamental physics point of view. They exhibit relatively large quantization energies in the range of about 50 meV. In most experiments reported so far, SAQDs have been investigated by optical spectroscopy, in particular photoluminescence (PL). Nowadays, PL experiments on single dots are well established, which overcome the inhomogeneously broadened linewidths in typical ensemble measurements.a

aFor a recent review, see Ref. .

It has also been demonstrated that it is possible to charge SAQD with single electrons via the application of external gate structures. So far, there are only two reports in literature about ILS experiments on electronic excitations in InGaAs SAQD. In this contribution, ILS experiments on collective CDEs in InAs SAQD with tunable electron numbers N are described. In these experiments, N can be controlled at N = 1–6.

The article is organized as follows. In the section “Characteristics of Quantum Dots and Experimental Details,” we describe the quantum-dot structures under investigation: modulation-doped GaAs–AlGaAs quantum dots and InAs SAQD, and give a brief discussion of the electronic structure and the excitations of these systems. Furthermore, the experimental realization of ILS is outlined in this section. In the section “Scattering Mechanisms,” a summarized description of the scattering mechanisms, which lead to the creation of electronic excitations in quantum dots, is provided. In the section “Experiments on GaAs–AlGaAs Deep-Etched Quantum Dots,” we start to discuss experiments on modulation-doped GaAs–AlGaAs quantum dots. There, basics such as parity selection rules are elaborated. The section “Experiments on InAs Self-Assembled Quantum Dots” summarizes recent experiments on InAs SAQD, which contain only a small number of electrons and which can be regarded as artificial atoms.