Theory of radiative and nonradiative transitions for semiconductor nanocrystals

Existing calculations on the radiative and nonradiative transitions in semiconductor crystallites are reviewed with particular emphasis on indirect band-gap materials like silicon for which the quantum confinement effects are more spectacular. It is shown that the crystallite gaps and radiative recombination rates can be predicted with fair accuracy. Effects related to atomic relaxation in the excited state (Stokes shift) are calculated and it is shown that small enough crystallites lead to self-trapped excitons which provide another source of luminescence, much less dependent on size effects. Nonradiative processes are then 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 screening is studied, justifying the use of a reduced internal dielectric constant and providing an estimate of the Coulomb shift due to charging effects.