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Voltage statistics of variable-range hopping transport

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##manager.scheduler.room##: Auditorio San Agustin

Date: 2019-07-08 11:45 AM – 03:30 PM

Last modified: 2019-06-15

#### Abstract

Since Mott showed the temperature dependence of conductance of amorphous materials [1], the mechanism of variable-range hopping transport (VRH) has been discussed extensively with a variety of theoretical models. The standard description of VRH is the formation of percolation networks which are sets of the bonds whose conductance is larger than a threshold value [2]. In this work, we pay more attention to the voltage distribution at local sites. To this end, we have numerically solved the linearized rate equations for the Miller-Abraham type hopping transport [3] in 2-dimensional random lattices and obtained local chemical potential μ which is defined as the difference between site voltage and electric potential created by an external field. In the calculations, the site density is kept to be 1 and the site energies are uniformly distributed between -<span style='font-style: italic;'>W</span>/2 and <span style='font-style: italic;'>W</span>/2. At high temperatures (<span style='font-style: italic;'>kT</span> > 0.1 <span style='font-style: italic;'>W</span>, <span style='font-style: italic;'>T</span>: temperature and <span style='font-style: italic;'>k</span>: Boltzmann constant), the variance of μ is small and independent of T. With decreasing <span style='font-style: italic;'>T</span>, the variance of μ is getting larger and larger, following a power law <span style='font-style: italic;'>T</span><sup><span style='font-style: italic;'>p</span></sup> (<span style='font-style: italic;'>p</span> ≈ -2). The rate equations for hopping can be described by an equivalent circuit consisted by resistors and capacitors. In this perspective, μ are determined to minimize the power generated in the circuit under an electric field . In other words, the gradient of μ should be as small as possible under the Kirchhoff’s current law. Since the distribution of hopping rates is getting wider and wider with decreasing <span style='font-style: italic;'>T</span>, μ changes slowly in space but largely in magnitude to satisfy the conditions.<br />[1] N. F. Mott, J. Non-Cryst. Solids <span style='font-weight: bold;'>1</span>, 1 (1968).<br />[2] B. Shklovskii and A. Efros, Electronic Properties of Doped Semiconductors (Springer-Verlag, 1984).<br />[3] V. Ambegaokar, S. Cochran, and J. Kurkijärvi, Phys. Rev. B <span style='font-weight: bold;'>8</span>, 3682 (1973).<br />

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