## ABSTRACT

Nearly four decades ago, Neugebauer and Webb
^{1}
recognized that when capacitance is reduced, the electrostatic energy required to charge the capacitance (e^{2}/2C) can be made to be of the order of magnitude of thermal voltage (10s of meV) at dimensions in the 10-nm range which results in a capacitance in the aF (10^{-18} F) range. This implies that discrete single-electron transmission or storage events can be observed, and unless the electrostatic energy is available to the electron from an energy source such as a power supply, the transition is prohibited. This is known as Coulomb blockade. Figure 8.1 shows an illustrative schematic, with band-diagrams for such a confined system. For a confined system in a semiconductor, quantum effects can also be significant due to a reduced number of states. In three-dimensionally confined semiconductor structures, the order of magnitude of the confinement energy can be similar to that due to Coulomb blockade. Fulton and Dolan,
^{2}
in 1987, demonstrated the first single-electron transistor by showing the modulation of the Coulomb blockade region by an applied bias voltage, and in recent times, there has been tremendous interest in understanding of this mesoscopic system,
^{3}
From a device point of view, an important consequence of the use of single-electron and quantum effects is the reduction in the number of charged carriers.