Modified charge carrier density for organic semiconductors modeled by an exponential density of states
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Modified charge carrier density for organic semiconductors modeled by an exponential density of states Kevin Hart1 · Sean Hart1 · Jerry P. Selvaggi1 Received: 16 February 2020 / Accepted: 3 August 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract Charge-transport models are usually developed by first finding an appropriate density of states (DOS) which is extracted from experimental data. For organic materials, two of the more common ones include the Gaussian density of states and the exponential density of states (EDOS). This article will focus on the latter. Charge-transport models which employ an EDOS have been extensively researched, and many articles are still being published. However, from an analytical point of view, only approximate mathematical expressions for the charge carrier density are ever used. This, in general, forces a chargetransport model to be valid only within a limited temperature range. This article illustrates a more mathematically exact way to handle an organic semiconductor whose DOS can be represented by an exponential function. Keywords Density of states · Disordered organic semiconductors · Conductivity · Carrier mobility · Seebeck coefficient · Fermi–Dirac-type integral
1 Introduction There are a number of different approaches for developing charge-transport models. The one common denominator among them is to choose an appropriate DOS. This, in itself, is an area of intense research. The DOS employed in this article is an EDOS. A similar procedure was employed by Selvaggi [1] for a GDOS. A knowledge of the charge density usually forms the basis for finding such properties as macroscopic dc conductivity, effective mobility, Seebeck coefficient, etc. One of the more well-known and well-researched mathematical models was developed by Vissenberg et al. [2] . They employed an EDOS model in order to derive approximate expressions for the macroscopic dc conductivity and effective mobility based upon the experimental results found by Brown et al. [3] and Garnier et al. [4]. Both Brown et al. [3] and Garnier
* Jerry P. Selvaggi [email protected] Kevin Hart [email protected] Sean Hart [email protected] 1
SUNY New Paltz, New Paltz, USA
et al. [4] give a readable discussion of the physics of organic thin-film transistors. Of course, no “exact” mathematical model for the DOS has yet been found which can explain all the properties listed above. This would most certainly require a more in-depth quantum-mechanical description. However, approximate mathematical models are continually being developed which attempt to incorporate more physics in order to more closely match experimental data. This article will concentrate on one particular mathematical model developed by Vissenberg et al. [2]. However, the mathematics employed is general enough to handle more complex models as illustrated in Selvaggi [1] The authors will concentrate on the Vissenberg and Matters (VM) model in order to provide a benchmark for more complex models that may
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