CHAPTER 1. FLUORESCENT SILICON CLUSTERS 5 Figure 1.1: Schematic of fluorescence emission in direct and indirect band gap semiconductors. The scheme shows the valence (bottom) and conduction bands (top) of a direct (left) and an indirect band gap semiconductor (right). The arrows indicate the magnitude of the energy band gap, E$_{g}$, the pathways of excitation of an electron from the valence band to the conduction band, electronic relaxation, fluorescence and absorption of phonons (see text). tered because of the relatively short timescale on which electronic relaxation occurs in the conduction and valence bands. The fluorescence intensity will be unchanged because both electron and hole have the same momentum. This situation changes in indirect band gap semiconductors, as shown on the right hand side in figure 1.1. In indirect band gap semiconductors, the minima of the conduction band and maxima of the valence band are shifted. As a consequence, electrons that are photoexcited into the conduction bands quickly undergo electronic relaxation to the minimum of the conduction band. However, any subsequent direct, vertical decay to the valence band is not possible because all states with similar momenta, ¯ hk , are populated with electrons; in other words, hole states for direct recombination with the excited electrons are not available. ’Diagonal’ recombination with the available, original hole state at the maximum of the valence band is not an option because momentum would no longer be conserved. So, in order for diagonal recombination to happen, a phonon with matching momentum has to be absorbed during fluorescence, but