GENERALIZED PLANCKS RADIATION LAW FOR LUMINESCENCE VIA INDIRECT TRANSITIONS

Based on microscopic transition probabilities and on the principle of detailed balance, absorption and emission rates are calculated for ind irect transitions. It is found that the emission rate at a photon ener gy ($) over bar hw can be expressed by the absorption coefficient for the same photon energy in the same way as for direct transitions. This relation is quite generally valid including cases where the electrons in the exited state (conduction band) and the electrons in the ground state (valence band) are distributed according to two different quasi -Fermi distributions. A generalized Planck's law is formulated for lum inescence which contains a nonzero chemical potential of the emitted p hotons as the only difference to the description of thermal radiation.