Exciton Impurity States in Molecular Crystals

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Abstract
The effect of impurities on Frenkel excitons in molecular crystals is studied with particular attention to impurity levels appearing outside exciton bands and virtual impurity levels lying in the continuum. A study is made of a specific case in which the transition dipole moments of the impurities are parallel to that of the host molecules. A secular equation which determines the energies of impurity levels due to any number of impurities is obtained, and a resonance form of the inverse relaxation time of excitons scattered by an impurity is derived. In the one‐impurity problem, a detailed discussion is made of the criterion for the appearance of impurity levels and virtual impurity levels. It is concluded that for excitons with fairly large effective masses these impurity states are very likely to occur. Numerical calculations are performed for a simple cubic lattice in which only interactions between nearest‐neighbor molecules are important. The results are then applied to a study of the interaction of impurity levels due to small but finite concentrations of impurities. It is shown that there can exist long‐range jumps of excitons from one impurity site to another due to the dipole—dipole interaction. An impurity‐induced energy transfer is suggested.

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