Field-induced trapping as a probe of dimensionality in molecular crystals

Abstract

The combined effect of an electric field and reduced dimensionality on the hopping motion of a charge carrier in. an anisotropic molecular crystal is determined.'New, exnct -expressions for S(t), the number of distinct sites occupied by a carrier'in time t, are presented for two-dimensional and iree-dimensional anisotropic lattices. The general results are used to model the unusual phenomenon of field-induced charge carrier trapping reported to occur in a quasi-one-dimensional moleculan crystal. An analytic expression for the carrier lifetime r, as a function of the anisotropy in the molecular hopping rates and electric field, is developed and is shown to be in excellent agteement with experimental results. A major conclusion of'the theory is that E~, the electric field characterizing the 9 dependence of Tr, can'be a more direct probe of the'intrinsic anisotropy than is the observed mobility ratio. Considerable interest exists in low-dimension solids such as anisotropic molecular crystals (1), polymeric materials (2, 3), super lattices (4, 5), and inversion layers'(6). Qne and two dimensionality offer opportunities to investigate novel phenomena: consequences of Peierls-Fr6hlich condensation in I-dimensional (1d) (7,8) (20). We show the measured field dependence of the trapping time r(E) to be a direct probe of the hopping rate anisotropy q = wl/w2, wi being the hopping rate along the stack axis and W2 the rate normal to it.Many aspects of triplet-exciton energy transfer and charge-carrier transport of these crystals have been investigated. (22), is 10-2 cm2/V s at room temperature and shows an activated temperature dependence ,rith an activation energy A = 0.11 eV. The electron mobility is interpreted to be intrinsic because the trap concentration needed' for (shallow) trapdominated transport must exceed 1.0%, which is unrealistic for a high-purity zone-refined crystal. An intrinsic mobility exhibiting activated temperature dependence can be a small polaron in the hopping regime (23). The observed mobility ratio A 1/IU2 iS somewhat variable and is typically about 10; this corresponds to an anisotropy in the hopping rates W1/t02 <-102.The details of the hopping motion are not known. It has-been suggested that the donor-acceptor pair, along the stack axis, could act as a single molecular entity. i.e., the excesselectron is partially delocalized on the donor (22). Thus, the electron hopping motion is not primarily from acceptor to nearest acceptor (which is not along the stack axis) as'is the case for the amorphous (trinitrofluorenone-polyvinylcarbazole TNF-PVK) systems (2-4), but rather along the stack axis. If the electron is localized on the pair (A1D1), the hopping transition could be (A1D1) -'(D1A2). A small polaron theory, involving localization on a pair of molecular sites, has been applied to solid rare gases (25,26). ' The'transient photocurrents i (t) for a group of phenanthrene-PMDA crystals is found to be marginally range limited-i.e., ip(t) a exp(-t/r) fort I to, the transit time and the (...

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