It is assumed that the elementary transport step is the charge transfer between adjacent molecules or sites, and both the hopping site energies and intersite distances are subject to distribution. Electronic states of the polymer are considered to be completely localized, and the density of states (DOS) distribution is assumed to be Gaussian and given by:

where ε is the site energy relative to the center of DOS, and σ is its Gaussian width.

Under Miller-Abrahams treatment,O. Ostroverkhova, "Organic and Polymeric Photorefractive Materials and Devices", in "Introduction to Organic Electronic and Optoelectronic Materials and Devices" (Eds. S. Sun and L. Dalton, CRC Press, 2008), P. M. Borsenberger and D. S. Weiss, "Organic photoreceptors for xerography" (Marcel Dekker: New York, 1998), J. L. Bredas, et al., Chem. Rev., 104, 4971-5003 (2004). for a hole transport, the downward energy jumps increase the hole's energy and thus have to be thermally activated, while the upward energy jumps are nonactivated, and the probability of such jump does not depend on the energy difference between the sites.

The rate of movement between transport sites varies with the sites' differences in both energy and physical distance. Also note that although preferential direction of the motion is that along the electric field, backward jumps are also possible. In the example to the right, the transport sites are distributed with the standard deviation σ, which you can change in the range between ~0.01 and 0.2 eV (typical for organic materials) and view the change in the hole drift velocity. The drift velocity is also affected by the applied electric field and temperature. The sliders allow you to change these parameters in the range typically used in photorefractive measurements and observe the increase in the hole drift velocity as the electric field or temperature increase.

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