Understanding Mott’s law from scaling of variable-range-hopping currents and intrinsic current fluctuations

Abstract

Citation for published version (APA):Pasveer, W. F., & Michels, M. A. J. (2006). Understanding Mott's law from scaling of variable-range-hopping currents and intrinsic current fluctuations. Physical Review B, 74(19), 195129-1/8. [195129] Please check the document version of this publication:• A submitted manuscript is the version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website.• The final author version and the galley proof are versions of the publication after peer review.• The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.• Users may download and print one copy of any publication from the public portal for the purpose of private study or research.• You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal.If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the "Taverne" license above, please follow below link for the End User Agreement: www.tue.nl/taverne Take down policyIf you believe that this document breaches copyright please contact us at: openaccess@tue.nl providing details and we will investigate your claim. We have used the master equation to simulate variable-range hopping ͑VRH͒ of charges in a strongly disordered d-dimensional energy landscape ͑d =1,2,3͒. The current distribution over hopping distances and hopping energies gives a clear insight into the difference between hops that occur most frequently, dominate quantitatively in the integral over the mobility distribution, or are critical ones that still need to be considered in that integral to recover the full low-temperature mobility. The recently reported scaling with temperature of the VRH-current distribution over hopping distances and hopping energies is quantitatively analyzed in 1D and 2D, and accurately confirmed. Based on this, we present an analytical scaling theory of VRH, which distinguishes between a scaling part of the distribution and an exponential tail, separated by critical currents that set the scale and that follow self-consistently at each temperature. This naturally renders Mott's law for the low-temperature mobility, in a way and with a physical picture different from that of the established criticalpercolation-network approach to VRH. We argue that current fluctuations as observed in simulations are intrins...

Tunnelling and percolation in lattices and the continuum

“…where n b is the known radius of the particles in units of a nm. For the following comparison with the experimental data we do not consider the prefactor σ o in equations ( 2) and ( 6) as those are much harder to determine and depend on the finer details of the system [36,65]. On the other hand, the comparison to be made below appears sufficient for supporting our above suggestion regarding the hopping or percolation-like nature of the conducting mechanisms in composites.…”