SiGe-on-insulator (SGOI) structures were thermally oxidized to form Ge quantum dots (QDs) that are embedded in a SiO2 matrix, to systematically investigate possible structural factors that affect the properties of Ge QDs, such as size, density and even position. The properties of Ge QDs depend strongly on the layer thickness and the geometric pattern of SGOI structures, as well as on the thermal oxidation conditions and the Ge content of the SiGe alloy. Tiny dense (3 nm/2.8 × 1012 cm-2) Ge QDs are formed by oxidizing a Si0.95Ge0.05/Si-on- insulator 'plane' at 900°C, which is highly promising for nanocrystal nonvolatile memory device applications. A single Ge QD (∼10 nm) forms and is self-aligned with electrodes via SiO2 when a SGOI nanowire with a length of less than 150 nm is thermally oxidized. This meets the stringent criteria for a successful single-electron device. The growth kinetics of Ge QDs formed by the oxidation of SGOI planes and nanowires is discussed. Cathodoluminescence spectra were employed to investigate the origins of photoemission from the Ge QDs/SiO2 system. Ge QD resonant tunnelling diodes are also fabricated to elucidate the transport of electrons through such a system.