We give an overview on the present status of self-assembled quantum structure fabrication by using the local droplet etching (LDE) technique during semiconductor molecular-beam epitaxy (MBE). LDE functionalizes nanodroplets to drill spatially well separated nanoholes into semiconductor surfaces. The mechanisms, the influence of substrate and droplet materials, and the control of the nanohole shape and size by the process parameters is discussed. LDE nanoholes in AlGaAs are filled for the creation of strain-free GaAs quantum dots (QDs). LDE QDs demonstrate a tunable emission wavelength, narrow exciton peaks, a low exciton fine-structure splitting, and single-photon emission which suggests them for applications in quantum information processing. The QD shape can be varied by the process parameters from cone-like to a shape where the probability distributions of the charge carriers are concentrated on a cone shell. For the cone-shell QDs, we predict the controlled transformation of either the electron or the hole from a quasi zero-dimensional dot into a one-dimensional quantum ring by a gate-voltage. Furthermore, also coupled quantum systems can be fabricated by a self-aligned vertical stacking into a LDE nanohole. A first example are GaAs quantum dot molecules (QDMs) which are formed from two QDs. LDE QDMs exhibit indirect excitons and anti-crossings which indicates strong coupling. A second example are hybrids composed of a single QD and a plasmonic nanostructure. Here, first results establish that self-assembled metallic nanostructures can be filled into nanoholes and that LDE QDs can be located very close to metallic structures clearly within their optical near-field.
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