Understanding electronic systems in semiconductor quantum dots

Abstract

Systems of confined electrons are found everywhere in nature in the form of atoms where the orbiting electrons are confined by the Coulomb attraction of the nucleus. Advancement of nanotechnology has, however, provided us with an alternative way to confine electrons by using artificial confining potentials. A typical structure of this nature is the quantum dot, a nanoscale system which consists of few confined electrons. There are many types of quantum dots ranging from self-assembled to miniaturized semiconductor quantum dots. In this work we are interested in electrostatically confined semiconductor quantum dot systems where the electrostatic confining potential that traps the electrons is generated by external electrodes, doping, strain or other factors. A large number of semiconductor quantum dots of this type are fabricated by applying lithographically patterned gate electrodes or by etching on two-dimensional electron gases in semiconductor heterostructures. Because of this, the whole structure can be treated as a confined two-dimensional electron system. Quantum confinement profoundly affects the way in which electrons interact with each other, and external parameters such as a magnetic field. Since a magnetic field affects both the orbital and the spin motion of the electrons, the interplay between quantum confinement, electron–electron correlation effects and the magnetic field gives rise to very interesting physical phenomena. Thus, confined systems of electrons in a semiconductor quantum dot represent a unique opportunity to study fundamental quantum theories in a controllable atomic-like setup. In this work, we describe some common theoretical models which are used to study confined systems of electrons in a two-dimensional semiconductor quantum dot. The main emphasis of the work is to draw attention to important physical phenomena that arise in confined two-dimensional electron systems under various quantum regimes.