Effect of electric field on diffusion in disordered materials. I. One-dimensional hopping transport

Abstract

An exact analytical theory is developed for calculating the diffusion coefficient of charge carriers in strongly anisotropic disordered solids with one-dimensional hopping transport mode for any dependence of the hopping rates on space and energy. So far such a theory existed only for calculating the carrier mobility. The dependence of the diffusion coefficient on the electric field evidences a linear, non-analytic behavior at low fields for all considered models of disorder. The mobility, on the contrary, demonstrates a parabolic, analytic field dependence for a random-barrier model, being linear, non-analytic for a random energy model. For both models the Einstein relation between the diffusion coefficient and mobility is proven to be violated at any finite electric field. The question on whether these non-analytic field dependences of the transport coefficients and the concomitant violation of the Einstein's formula are due to the dimensionality of space or due to the considered models of disorder is resolved in the following paper [Nenashev et al., arXiv:0912.3169], where analytical calculations and computer simulations are carried out for two-and three-dimensional systems.

Полевая Диффузия В Неупорядоченных Органических Материалах В Условиях Заполнения Глубоких Состояний

“…второе слагаемое в правой части уравнения (2)) [10,11]. Ранее [4,6,7,12] коэффициент ПД был найден для предельного случая малой концентрации носителей, т. е. в пренебрежении вторым слагаемым в квадратных скобках в правой части уравнения (2). Далее будет получена зависимость коэффициента ПД от концентрации, с учетом заполнения глубоких ловушек.…”

“…Рассмотрим квазиравновесный режим перено-са [4,7,8,14]. В нулевом приближении (∂ρ/∂t = 0) решение уравнения (2) имеет следующий вид [14]:…”

“…Его причина в статистическом разбросе времен освобождения носите-лей с глубоких состояний, прежде всего за счет разброса энергий состояний. Этот эффект был неоднократно опи-сан теоретически [4,6,7], но при условии низкой концен-трации носителей, когда можно пренебречь заполнением глубоких состояний. В недавней работе [8] показано, что коэффициент ПД значительно убывает с ростом концентрации носителей.…”

Low-temperature spark plasma sintering of alumina by using SiC molding set

“…The low sintering temperatures in SPS, compared to other sintering techniques, are certainly related to the electric field applied for heating. The electric field may enhance the densification by accelerating diffusion, 1),2) suppressing grain growth 3) or softening particle surfaces. 4) Though the exact mechanism is unclear, it was proven experimentally that the application of electric field contributes to lower the sintering temperature by enhancing densification.…”

Note: On the relation between Lifson-Jackson and Derrida formulas for effective diffusion coefficient

“…Examples range from hopping transport in semiconductors to single-molecule enzyme kinetics and intracellular transport by molecular motors. [1][2][3][4][5][6][7][8][9][10] When (1) the random walk occurs on a periodic lattice and (2) the observation time is sufficiently long so that a typical displacement exceeds the lattice period, one can use a coarse-grained description of the motion. In this description, all information about the underlying random walk is packed into the effective drift velocity, V eff , and diffusion coefficient, D eff .…”