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

The nonradiative energy transfer process from donor-to-acceptor ions is simulated for the garnet lattice using the Monte Carlo (MC) method. The probabilities of the events which occur after a donor is excited are calculated, i.e., the donor and acceptor emission transients. Two different simulation results are reported. One is obtained under the Forster and Dexter (FD) assumptions-dopants are randomly distributed in the crystal, no donor-to-donor and no acceptor-to-donor transfers occur, and the transfer is proportional to (1/R)(S) with s a unique integer. 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 accepters which may be attractive or repulsive. For both distributions, the FD assumptions that s is a unique integer is relieved and transients are obtained for an arbitrary multipolar expression. The FD model was found to give a rather good approximation to the donor emission transient determinated by the MC simulations for the FD assumptions. The donor luminescence decay is faster for an attractive interaction between donors and accepters than for the random distribution. It is slower for a repulsive interaction. Using the arbitrary multipolar expression and using random and nonrandom spatial distributions of dopants give distinguishably different decay transients. However, better discrimination among causes for some particular given transient is afforded by using different dopant levels.