Coherent energy migration in solids. I. Band-trap equilibria at Boltzmann and non-Boltzmann temperatures

Abstract

A model is presented which relates the dynamics of energy migration in crystals to the mechanism by which thermal equilibrium between delocalized band states and localized trap states is achieved. Central to this model is the requirement that coherent energy migration must be the dominant mode of migration at low temperatures in order to achieve Boltzmann equilibrium between band and trap states within the lifetime of the excited electronic state. Second, a stochastic model for detrapping is developed which is based on an irreversible radiationless relaxation process of a phonon-trap intermediate into the density of delocalized band states. Explicit account is taken of phonon-trap interactions in the formation of the excited trap intermediate. Further, the relation between detrapping and the ability of a crystal to achieve thermal equilibrium within the excited-state lifetime is developed and applied to one-dimensional crystals. Experimental results on molecular crystals representing examples of one-dimensional exciton bands are also presented. Specifically, the temperature dependence of phosphorescence from excited triplet trap states is interpreted in terms of the above considerations. From these experiments one can obtain both the sign of the intermolecular interaction and the dispersion of the first excited triplet band in addition to an estimate of the coherence length associated with exciton migration in the Frenkel limit. Finally, some new and unique methods for studying energy migration are presented which utilize optically detected magnetic-resonance techniques in zero field. They include experiments based on the measurement of electron-spin coherence in the rotating frame and the relationship of the spin coherence to the various rate processes important in trap-exciton interactions.