Abstract
We have extended an effective medium approximation theory [Fishchuk, Kadashchuk, Genoe, Ullah, Sitter, Singh, Sariciftci, and B\assler, Phys. Rev. B 81, 045202 (2010)] to investigate how polaron formation affects the Meyer-Neldel (MN) compensation behavior observed for temperature-dependent charge-carrier transport in disordered organic semiconductors at large carrier concentrations, as realized in organic field-effect transistors (OFETs). We show that the compensation behavior in organic semiconductor thin films can be consistently described for both nonpolaronic and polaronic hopping transport in the framework of the disorder formalism using either Miller-Abrahams or polaron Marcus rates, respectively, provided that the polaron binding energy is small compared to the width of the density of states (DOS) distribution in the system. We argue that alternative models based on thermodynamic reasoning, like the multiexcitation entropy (MEE) model, which assumes charge transport dominated by polarons with multiphonon processes and ignores the energy disorder, are inherently not applicable to describe adequately the charge-carrier transport in disordered organic semiconductors. We have suggested and realized a test experiment based on measurements of the compensation behavior for the temperature-dependent conductivity and mobility in OFET devices to check the applicability of these models. We point out that the MN behavior observed in thin-film OFETs has nothing to do with the genuine MN rule predicted by the MEE approach, but rather it is an apparent effect arising as a consequence of the functional dependence of the partial filling of the DOS in a disordered system with hopping transport. This fact is fully supported by experimental results. The apparent MN energy was found to depend also on the shape of the DOS distribution and polaron binding energy.
Highlights
Organic semiconductor films offer potential for emerging flexible large-area electronics, because they allow low-cost and low-temperature device fabrication compatible with flexible plastic substrates [1,2]
We show that the compensation behavior in organic semiconductor thin films can be consistently described for both nonpolaronic and polaronic hopping transport in the framework of the disorder formalism using either Miller-Abrahams or polaron Marcus rates, respectively, provided that the polaron binding energy is small compared to the width of the density of states (DOS) distribution in the system
We point out that the MN behavior observed in thin-film organic field-effect transistors (OFETs) has nothing to do with the genuine MN rule predicted by the multiexcitation entropy (MEE) approach, but rather it is an apparent effect arising as a consequence of the functional dependence of the partial filling of the DOS in a disordered system with hopping transport
Summary
Organic semiconductor films offer potential for emerging flexible large-area electronics, because they allow low-cost and low-temperature device fabrication compatible with flexible plastic substrates [1,2]. The compensation effect was experimentally observed for the temperature dependences of the OFET mobility μ(T ) upon varying the charge-carrier concentration, but it was not found in experiment by varying the width of the DOS [20]. It was proposed that the observed compensation phenomena in organic semiconductors can readily be explained by the MEE model [28,29], which is the best one to provide a correct and full description of the temperature-dependent charge-carrier mobility in OFET devices. We report on test experiments in which we are able to distinguish between the applicability of the EGD and MEE models to OFETs. We found that the isokinetic TMN temperature is distinctly different for mobility and conductivity, featuring normal- and inverted-MN effects, respectively, which naturally follow from hopping transport within a Gaussian DOS distribution. We focus here only on organic semiconductors; other situations where the MN behavior is observed are beyond the scope and ambition of this paper
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