MONTE-CARLO TREATMENT OF THE NONRADIATIVE ENERGY-TRANSFER PROCESS FORNONRANDOM PLACEMENTS OF DOPANTS IN SOLIDS

The nonradiative energy transfer process from donor-to-acceptor ions i s simulated for the garnet lattice using the Monte Carlo (MC) method. The probabilities of the events which occur after a donor is excited a re calculated, i.e., the donor and acceptor emission transients. Two d ifferent simulation results are reported. One is obtained under the Fo rster and Dexter (FD) assumptions-dopants are randomly distributed in the crystal, no donor-to-donor and no acceptor-to-donor transfers occu r, and the transfer is proportional to (1/R)(S) with s a unique intege r. The second is obtained by replacing the random spatial distribution of dopants in the FD model by a nonrandom distribution. The nonrandom placements result from a short-range interaction between donors and a ccepters which may be attractive or repulsive. For both distributions, the FD assumptions that s is a unique integer is relieved and transie nts are obtained for an arbitrary multipolar expression. The FD model was found to give a rather good approximation to the donor emission tr ansient determinated by the MC simulations for the FD assumptions. The donor luminescence decay is faster for an attractive interaction betw een donors and accepters than for the random distribution. It is slowe r for a repulsive interaction. Using the arbitrary multipolar expressi on and using random and nonrandom spatial distributions of dopants giv e distinguishably different decay transients. However, better discrimi nation among causes for some particular given transient is afforded by using different dopant levels.