Extended Foerster-Dexter model for correlated donor-acceptor placement in solid-state materials

In models of nonradiative energy transfer applied to doped solid-state laser materials, the distance between excited donors and neighboring acceptors critically affects the calculated energy transfer rates. In the generally successful formulation of nonradiative transfer theory,1 the donors and acceptors are taken to be distributed evenly throughout the crystal and are independent (uncorrelated) in position. We derive a general expression to treat donor-acceptor transfer rates for locally correlated donor-acceptor placement. Several specific cases appropriate to actual laser materials are (1) an excluded volume around a donor diminished in acceptor concentration and (2) an enhanced volume around a donor in which acceptors preferentially locate. Physical effects which can lead to such microscopic distributions are discussed.