ABSTRACT
Equations for the exciton Bohr radius, the decisive length for quantum confinement, as well as electron and hole Bohr radii are derived. Weak, moderate, and strong regimes of quantum confinement are distinguished. After discussing the energy dispersion relation for excitons, the solution of the Schrodinger equation for particle-in-a-spherical box is applied to determine the confinement energy of electrons and holes. The solutions are roots of the Bessel function of the first kind as the Bessel functions of the second kind are found to be physically untenable. The electrons can occupy discrete energy levels and the energy difference representing the bandgap is increased. The energy equations for weak and strong confinement are applied to show why these regimes are so named. Corrective terms that owe their origin to Brus and Kayunama are included. Finally, the evolution of the energy band structure of nanocrystals is looked upon from a bottom-up perspective.
