Electron Transport in Mesoscopic Semiconductor Nanostructures

Doctoral thesis, 1994

This thesis presents results from experimental studies, mostly at very low temperatures, and fabrication of very small electronic components made with GaAs/GaAlAs heterostructures. The components are so small that individual electrons are important to their characteristics. It is with this type of components possible to measure small fractions of the elementary charge and count each electron passing into an isolated conducting island. The wave-nature of the electrons play a signifi-cant role, because the electron wavelength is comparable to device sizes. An intermediate regime, with device dimensions ranging between atomic sizes up to the smallest things that we almost can see with our own eyes, is called mesoscopic. Electronic components in the mesoscopic regime exhibit a variety of new phenomena that have been extensively studied during the last years. Single electron effects originate from the charging energy associated with transport of electrons to very small conducting islands. Charging effects have been observed as periodic resonance peaks in the conductance through such small islands, referred to as Coulomb blockade oscillations. Each peak corresponds to the addition of one electron to the dot, an extraordinary charge sensitivity. Energy quantization is a manifestation of the wave-nature of the electron. The electron can, when the wavelength is comparable to the extent of the component, be considered as a standing wave. It can be restricted from moving in one, two or all three dimensions. In the latter case the component is referred to as a quantum dot. This system may be seen as an artificial atom, with a discrete number of electrons and a discrete spectrum of energy levels, with the possibility to attach leads and study one single artificial atom. We have shown that the eigenenergy spectrum of the dot is related to the geometric form of the boundary. We have found regularities of measured conductance variations as a function of magnetic field or size of a circular dot, which can be explained with a simplified model where the irregularities of the boundary and the contacts to the dot are neglected. The conductance reflects the density of states in the dot and is related to the zeroes of Bessel functions. Single electron charging effects was observed and we have examined the possibility of using the charge sensitivity of a quantum dot for making a single-electron tunneling electrometer, but found that the discrete energy spectrum results in a very complex behavior and gives the component an unwanted magnetic field dependence. The studied effects are of an intermediate, truly mesoscopic, regime; we cannot resolve the individual eigenenergy levels of the dot, but the conductance depends on the eigenenergy spectrum that reflect the geometry of the dot. A quantum dot in a semiconductor heterostructure is a system that provides us with excellent possibilities for investigations of phenomena that affect nanometer sized electronics.