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Einstein's relationship for hopping electrons

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TLDR
In this article, it was shown that neither diffusion coefficient, D, nor mobility of carriers, μ, depend on temperature and the conventional form of the Einstein's relationship μ = eD kT is not valid.
Abstract
Photoconductivity in amorphous semiconductors at very low temperatures is temperature-independent, being determined by the energy-loss hopping of carriers through localized band-tail states. In such a hopping relaxation, neither diffusion coefficient, D , nor mobility of carriers, μ, depend on temperature and the conventional form of the Einstein's relationship μ = eD kT is not valid. The relationship between μ and D for the hopping relaxation of electrons in the exponential band tail is calculated and it is shown that it has the form μ ∝ eD ϵ 0 , where ϵ 0 is the energy scale of the exponential band tail.

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Journal ArticleDOI

Interpretation of electron diffusion coefficient in organic and inorganic semiconductors with broad distributions of states

TL;DR: This work examines in detail models for carrier transport in nanocrystalline semiconductors and organic materials with the following distributions: single and two-level systems, exponential and Gaussian density of states, and treats both the multiple trapping models and the hopping model in the transport energy approximation.
Journal ArticleDOI

Validity of the Einstein relation in disordered organic semiconductors.

TL;DR: It is demonstrated that the Einstein relation is violated only under nonequilibrium conditions due to deeply trapped carriers, as in diffusion-driven current measurements on organic single-carrier diodes.
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Simulating charge transport in organic semiconductors and devices: a review

TL;DR: An overview of common charge transport and device models; namely drift-diffusion, master equation, mesoscale kinetic Monte Carlo and quantum chemical Monte Carlo, and a discussion of the relative merits of each are presented.
Journal ArticleDOI

Diffusion-driven currents in organic-semiconductor diodes

TL;DR: Wetzelaer et al. as discussed by the authors discussed diffusion-driven currents in several types of organic diodes and demonstrated that the ideality factor of diffusion driven currents can be regarded as an effective tool for studying the recombination mechanisms in organic light-emitting Diodes (OLEDs) and solar cells.
Journal ArticleDOI

Theoretical description of hopping transport in disordered materials

TL;DR: In this article, a series of straightforward computer simulations for the percolation problem in hopping conduction was performed to verify the validity of analytical approaches, and the simulation results support the analytical approaches based on the transport energy concept and on per-colation arguments for the description of the dark conductivity at low temperatures.
References
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Book

Electronic processes in non-crystalline materials

TL;DR: The Fermi Glass and the Anderson Transition as discussed by the authorsermi glass and Anderson transition have been studied in the context of non-crystalline Semiconductors, such as tetrahedrally-bonded semiconductors.
Journal ArticleDOI

Electronic transport and recombination in amorphous semiconductors at low temperatures.

TL;DR: In this article, the problem of simultaneous diffusion and recombination of electron-hole pairs, photoexcited in noncrystalline semiconductors at low temperatures, is reduced to a universal mathematical problem whose solution does not depend on the density-of-states function.
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Electronic structure and transport in covalent amorphous semiconducting alloys

TL;DR: A brief review of the CFO model is given in this article, in which its principal features and what may be interpreted as its successes are listed and a few new results lending further support to features of the model are also reviewed.
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