Quantum dots: when nano becomes colourful

Abstract

The ground state energy of an electron-hole pair confined in a nanometre semiconductor particle (quantum dots) has been studied as a function of size. Three different methods have been used depending on the importance of the quantum confinement. In the regime of weak quantum confinement, the system reduces to a one-body problem, and can be treated as a hydrogen-like atom. In the intermediate regime, the variational method provides an acceptable upper bound of the ground state energy. The trial function used has been properly designed to take into account both the confinement effect and the Coulomb interaction. In the strong confinement regime, the Coulomb interaction can be neglected, and the problem can be solved analytically as a system of two independent particles confined by an infinite ”square” potential. The results evidence the strong dependence of the ground state energy on the particle size, which can be applied to tune optical properties at will. Finally, the results have been compared with experimental data.