confinement term in equation 1.2 and the original particle-in-a-box equation 1.1 is remarkable, and strongly supports the presence of quantum confinement. 

Park and co-workers investigated amorphous silicon quantum dots embedded in silicon nitride. They observed fluorescence in the form of a single band whose maximum shifted with average quantum dot size. The size dependence of flu- orescence energy fit to the equation was found as E ( eV ) = 1 . 56 + 2 . 40 d − 2 eV, which confirmed the earlier observed band gap energy of amorphous silicon (Lockwood et al., 1996) in the limit of large dot sizes. However, the depen- dence on quantum confinement, 2 . 40 d − 2 eV, was much larger. The discrepancy with work on conducted on Si/SiO$_{2}$ superlattices was attributed to the three- dimensional confinement of the quantum dots in silicon nitride (Park et al., 2001). 

Summarising, we have so far seen that with reduction of size of a crystal translational symmetry is gradually lost with the consequence that indirect band gap semiconductors become quasi-direct semiconductors at the nanoscale. At the same time the band gap energy increases because of quantum confinement. 

A further important factor determining the ability to fluoresce is the elec- tronic structure at the surface of nanocrystals. Surfaces break translational symmetry, a consequence of which is that one cannot expect the same energy band structure as might be observed for ’infinite’ crystals. Band gap energies may be smaller, or may not even exist. For nanocrystals, this means that surface effects may compete with quantum confinement. In the following, non-radiative decay at nanocrystal surfaces will be discussed. 

To prevent non-radiative decay at its surface, a nanocrystal may be embed- ded in another semiconductor or insulator of larger band gap energy. This effect is illustrated in figure 1.2. 

In broadest terms, one can expect that surface effects on the band gap energy 

