Existing calculations on the radiative and nonradiative transitions in
semiconductor crystallites are reviewed with particular emphasis on i
ndirect band-gap materials like silicon for which the quantum confinem
ent effects are more spectacular. It is shown that the crystallite gap
s and radiative recombination rates can be predicted with fair accurac
y. Effects related to atomic relaxation in the excited state (Stokes s
hift) are calculated and it is shown that small enough crystallites le
ad to self-trapped excitons which provide another source of luminescen
ce, much less dependent on size effects. Nonradiative processes are th
en examined: intrinsic, due to Auger recombination, and extrinsic, due
to dangling bond surface states. Both are found to play an essential
role in the interpretation of experimental data. Finally, dielectric s
creening is studied, justifying the use of a reduced internal dielectr
ic constant and providing an estimate of the Coulomb shift due to char
ging effects.