Exciton percolation I. Migration dynamics

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Abstract
The exciton transfer, via migration and trapping, in binary and ternary mixed crystals is formulated in terms of percolation theory and the cluster structure for binary randomly mixed crystals. An important limiting case (exciton supertransfer) is derived for long exciton lifetime, relative to jumping and trapping time. The exciton supertransfer case is solved analytically [in terms of the functions derived by J. Hoshen and R. Kopelman, Phys. Rev. B (in press)] and the solutions involve neither physical parameters nor physical constants. Other limiting cases are derived, as well as an algorithm for the general energy transfer case. This algorithm relates the migration and trapping in binary and ternary systems with the trapping‐free migration in binary systems. The algorithm involves the use of empirical information, i.e., the parameters describing the exciton dynamics in a pure crystal. The various formulations are valid for concentrations both above and below the critical (’’percolation’’) concentration, with due emphasis on small, medium, and large cluster contributions. Sample calculations are given (for the square lattice with site percolation).