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Title: A very general rate expression for charge hopping in semiconducting polymers

Abstract

We propose an expression of the hopping rate between localized states in semiconducting disordered polymers that contain the most used rates in the literature as special cases. We stress that these rates cannot be obtained directly from electron transfer rate theories as it is not possible to define diabatic localized states if the localization is caused by disorder, as in most polymers, rather than nuclear polarization effects. After defining the separate classes of accepting and inducing nuclear modes in the system, we obtain a general expression of the hopping rate. We show that, under the appropriate limits, this expression reduces to (i) a single-phonon rate expression or (ii) the Miller-Abrahams rate or (iii) a multi-phonon expression. The description of these limits from a more general expression is useful to interpolate between them, to validate the assumptions of each limiting case, and to define the simplest rate expression that still captures the main features of the charge transport. When the rate expression is fed with a range of realistic parameters the deviation from the Miller-Abrahams rate is large or extremely large, especially for hopping toward lower energy states, due to the energy gap law.

Authors:
; ;  [1]
  1. Department of Chemistry and Centre for Scientific Computing, University of Warwick, Coventry CV4 7AL (United Kingdom)
Publication Date:
OSTI Identifier:
22415761
Resource Type:
Journal Article
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 142; Journal Issue: 18; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9606
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; CHARGE TRANSPORT; ELECTRON TRANSFER; ENERGY GAP; PHONONS; POLARIZATION; POLYMERS; SEMICONDUCTOR MATERIALS; STRESSES

Citation Formats

Fornari, Rocco P., Aragó, Juan, and Troisi, Alessandro. A very general rate expression for charge hopping in semiconducting polymers. United States: N. p., 2015. Web. doi:10.1063/1.4920945.
Fornari, Rocco P., Aragó, Juan, & Troisi, Alessandro. A very general rate expression for charge hopping in semiconducting polymers. United States. doi:10.1063/1.4920945.
Fornari, Rocco P., Aragó, Juan, and Troisi, Alessandro. Thu . "A very general rate expression for charge hopping in semiconducting polymers". United States. doi:10.1063/1.4920945.
@article{osti_22415761,
title = {A very general rate expression for charge hopping in semiconducting polymers},
author = {Fornari, Rocco P. and Aragó, Juan and Troisi, Alessandro},
abstractNote = {We propose an expression of the hopping rate between localized states in semiconducting disordered polymers that contain the most used rates in the literature as special cases. We stress that these rates cannot be obtained directly from electron transfer rate theories as it is not possible to define diabatic localized states if the localization is caused by disorder, as in most polymers, rather than nuclear polarization effects. After defining the separate classes of accepting and inducing nuclear modes in the system, we obtain a general expression of the hopping rate. We show that, under the appropriate limits, this expression reduces to (i) a single-phonon rate expression or (ii) the Miller-Abrahams rate or (iii) a multi-phonon expression. The description of these limits from a more general expression is useful to interpolate between them, to validate the assumptions of each limiting case, and to define the simplest rate expression that still captures the main features of the charge transport. When the rate expression is fed with a range of realistic parameters the deviation from the Miller-Abrahams rate is large or extremely large, especially for hopping toward lower energy states, due to the energy gap law.},
doi = {10.1063/1.4920945},
journal = {Journal of Chemical Physics},
issn = {0021-9606},
number = 18,
volume = 142,
place = {United States},
year = {2015},
month = {5}
}