CHAPTER 1. FLUORESCENT SILICON CLUSTERS 9 Figure 1.2: Schematic of a nanoscale crystal (quantum dot) embedded in a material of larger band gap energy. E$_{g}$$_{1}$ and E$_{g}$$_{2}$ refer to the band gap energies of the nanocrystal and host material  respectively. can be minimised for such a system . It is assumed that the nanocrystal structure fits well with that of the host and that a minimum of additional interface states are produced. Ideally  this would mean that an electron promoted across E$_{g}$$_{1}$ from the valence band of the nanocrystal to its conduction band would remain confined within the nanocrystal. The electron would have no other choice than to fluoresce to the ground state because no discrete states are available within the gap. To better account for non-radiative decay in real systems  vibrational relax- ation is often considered. Because of the possibility of surface reconstruction  vibrational relaxation at surfaces is particularly important for free nanoscale crystals and clusters. Figure 1.3 illustrates the cycle of excitation  electronic migration and relaxation within the conduction band and vibrational relax- ation at the surface. In this simple picture  a high density of vibrational states