We now turn to transport in nanostructure systems in which the electronic states are completely quantized. In Section 2.3.2 we briefly introduced quantum dots (sometimes referred to as quantum boxes) in which confinement was imposed in all three spatial directions, resulting in a discrete spectrum of energy levels much the same as an atom or molecule. We can therefore think of quantum dots and boxes as artificial atoms, which in principle can be engineered to have a particular energy level spectrum. In Section 4.1, we first consider models for the electronic states of quantum dots and boxes, and then compare these to experimental data. As in atomic systems, the electronic states in quantum dots are sensitive to the presence of multiple electrons due to the Coulomb interaction between electrons. In addition, magnetic fields serve as an experimental probe that one can use to elucidate the energy spectrum of such artificial atoms discussed below.

The primary focus of our attention in this book is on the transport properties in nanostructures; quantum dots provide some of the most interesting experiments in this regard. Transport in quantum dots and boxes implies an external coupling to these structures from which charge may be injected, as discussed in Chapter 3. Rich phenomena are observed not only because of quantum confinement and the resonant structure associated with this confinement, but also due to the granular nature of electric charge. In contrast to quantum wells and quantum wires, quantum dot structures are sufficiently small that even the introduction of a single electron is sufficient to dramatically change the transport properties due to the charging energy associated with this extra electron.