Analytical evaluation of the charge carrier density of organic materials with a Gaussian density of states revisited

Selvaggi, Jerry P.

doi:10.1007/s10825-017-1113-5

Cited by 10 publications

(4 citation statements)

References 16 publications

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“…However, even with efficient functions to perform the integration and root-finding, this is computationally expensive and would result in J-V simulations taking minutes to hours instead of seconds to minutes motivating the need for more efficient schemes. Significant efforts have been made to find approximations to the Fermi-Dirac [9,26,64] and Gauss-Fermi integrals [52,58]. However, most approximations are either computationally expensive or lack accuracy.…”

Section: Fast and Accurate Evaluation Of Statistical Integrals And Th...mentioning

confidence: 99%

IonMonger 2.0: software for free, fast and versatile simulation of current, voltage and impedance response of planar perovskite solar cells

et al. 2022

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The second generation of the open-source MATLAB-based software tool , for solving drift–diffusion models of charge transport in planar perovskite solar cells, is presented here. This version is based upon a generalisation of the original drift–diffusion model of charge carrier and ion motion in the perosvkite cell, as described in Courtier (J Comput Electron 18:1435–1449, 2019). The generalised model has the flexibility to capture (1) non-Boltzmann statistics of charge carriers in the transport layers, (2) steric effects for the ions in the perovskite layer, (3) generation of charge carriers from light made up of a spectrum of different wavelengths and, (4) Auger recombination. The updated software is significantly more stable than the original version and also adds the ability to simulate impedance spectroscopy measurements as well as transient voltage and/or illumination protocols. In addition, it is fully backwards compatible with the original version and displays improved performance through refinement of the underlying numerical methods. Furthermore, the software has been made accessible to a wider user base by the addition of , a version that leverages MATLAB’s live scripts and eliminates the need for a detailed knowledge of MATLAB’s syntax.

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Section: Fast and Accurate Evaluation Of Statistical Integrals And Th...mentioning

confidence: 99%

IonMonger 2.0: software for free, fast and versatile simulation of current, voltage and impedance response of planar perovskite solar cells

et al. 2022

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“…Now, using the techniques in Selvaggi [13] to evaluate an approximation for this integral for calculation purposes. Let us consider integral…”

Section: B Solution Of the Integral Using Exact Techniquesmentioning

confidence: 99%

“…Also to bolster this claim it can be seen in [10][11][12] that when the current for a TFT is modeled using double exponential density of states it has more resemblance to the actual experimental data than when single exponential density of states is used. Currently the calculation of charge carrier density, which is basically the integral of f(E,T) and g(E) over all the energies from -∞ to 0, has been done by taking g(E) as Gaussian Density of States and Exponential Density of States as shown in [13] and by single exponential density of states as shown in [1]. Since we are developing Double Exponential Density of States so focus will be kept on Hart [1] in which he has taken the Fermi function: 𝑓(𝐸, 𝑇) =…”

Section: Introductionmentioning

confidence: 99%

Double exponential density of states and modified charge carrier transport in organic semiconductors

et al. 2022

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This paper discusses an approach to use an approximated charge carrier density for organic thin-film transistor (OTFT) using a double exponential density of states. Traditionally the literature has been published using a single exponential density of states and Gaussian density of states but this paper deals with using a double exponential density of states in the Fermi Integral to evaluate the charge carrier density for the OTFT. There are two exponential density of states related to the Tail region and Deep region and various parameters associated with it. The distribution of localized trap states between the highest and lowest orbital is expressed as a density of states. There are two states deep states and tail states. Tail states are better described by the Gaussian function, while Deep states are better described by the Exponential density of states. So, if we require that the two regions be defined by a single function then the function should be a sum of the two, the exponential and the Gaussian to accurately describe the complete region. The double exponential density of states is considered to evaluate and approximate the Fermi Integral using various Mathematical Methods, so that the error is lower for various parameters.

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“…The method developed in this paper has recently been employed for analytically evaluating the Gauss-Fermi integral [36]. This integral was previously known to not have a complete analytical solution [37].…”

Section: Remarks and Conclusionmentioning

confidence: 99%

The Application of Real Convolution for Analytically Evaluating Fermi-Dirac-Type and Bose-Einstein-Type Integrals

Selvaggi

Selvaggi²

2018

Journal of Complex Analysis

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The Fermi-Dirac-type or Bose-Einstein-type integrals can be transformed into two convergent real-convolution integrals. The transformation simplifies the integration process and may ultimately produce a complete analytical solution without recourse to any mathematical approximations. The real-convolution integrals can either be directly integrated or be transformed into the Laplace Transform inversion integral in which case the full power of contour integration becomes available. Which method is employed is dependent upon the complexity of the real-convolution integral. A number of examples are introduced which will illustrate the efficacy of the analytical approach.

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Analytical evaluation of the charge carrier density of organic materials with a Gaussian density of states revisited

Cited by 10 publications

References 16 publications

IonMonger 2.0: software for free, fast and versatile simulation of current, voltage and impedance response of planar perovskite solar cells

IonMonger 2.0: software for free, fast and versatile simulation of current, voltage and impedance response of planar perovskite solar cells

Double exponential density of states and modified charge carrier transport in organic semiconductors

The Application of Real Convolution for Analytically Evaluating Fermi-Dirac-Type and Bose-Einstein-Type Integrals

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