Modelling charge transport in perovskite solar cells: Potential-based and limiting ion depletion

Abdel, Dilara; Vágner, Petr; Fuhrmann, Jürgen; Farrell, Patrick E.

doi:10.1016/j.electacta.2021.138696

Cited by 17 publications

(23 citation statements)

References 36 publications

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“…On the other hand, the electric contribution to the total energy is given by the electrostatic field energy. Lastly, assuming an ideal lattice gas [3] we can derive a consistent energy contribution of anion vacancies which extends the electric free energy formulation in [29]. Hence, in total the free energy functional for the PSC model reads…”

Section: Thermodynamic Free Energymentioning

confidence: 89%

“…The density of a charge carrier is denoted by n α , α ∈ {n, p, a}. We examine the model for the charge transport in PSCs formulated in [3], where for t ≥ 0 the mass balances are given by…”

Section: Charge Transport Model For Perovskite Solar Cellsmentioning

confidence: 99%

“…Such a choice necessarily leads to nonlinear diffusion for the densities in (2.1a). For anion vacancies in PSCs the Fermi-Dirac integral of order −1 is chosen to reflect the limitation of ion concentration by the lattice sites available in the crystal [3]. This particular statistics function reads…”

Section: Statistics Functionsmentioning

confidence: 99%

“…Because of the differences and new features compared to classical semiconductors, there is a need for new mathematical and numerical modeling and analysis for these devices. Several models have been proposed recently in the literature -with the exception of [3], nearly all of them are in one dimension [10,15].…”

Section: Introductionmentioning

confidence: 99%

“…The main goal of this paper is the analysis of an implicit in time two-point flux approximation (TPFA) finite volume scheme for the perovskite model. The model and the scheme originate from [3]. The scheme relies on the the excess chemical potential flux scheme which appears to be used for the first time in [40] and was later numerically analyzed in [11,23] and compared in [1,28].…”

Section: Introductionmentioning

confidence: 99%

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Numerical analysis of a finite volume scheme for charge transport in perovskite solar cells

Abdel¹,

Chainais-Hillairet²,

Farrell³

et al. 2022

Preprint

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In this paper, we consider a drift-diffusion charge transport model for perovskite solar cells, where electrons and holes may diffuse linearly (Boltzmann approximation) or nonlinearly (e.g. due to Fermi-Dirac statistics). To incorporate volume exclusion effects, we rely on the Fermi-Dirac integral of order −1 when modeling moving anionic vacancies within the perovskite layer which is sandwiched between electron and hole transport layers. After nondimensionalization, we first prove a continuous entropy-dissipation inequality for the model. Then, we formulate a corresponding two-point flux finite volume scheme on Voronoi meshes and show an analogous discrete entropy-dissipation inequality. This inequality helps us to show the existence of a discrete solution of the nonlinear discrete system with the help of a corollary of Brouwer's fixed point theorem and the minimization of a convex functional. Finally, we verify our theoretically proven properties numerically, simulate a realistic device setup and show exponential decay in time with respect to the L 2 error as well as a physically and analytically meaningful relative entropy.

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Section: Thermodynamic Free Energymentioning

confidence: 89%

Section: Charge Transport Model For Perovskite Solar Cellsmentioning

confidence: 99%

Section: Statistics Functionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Numerical analysis of a finite volume scheme for charge transport in perovskite solar cells

Abdel¹,

Chainais-Hillairet²,

Farrell³

et al. 2022

Preprint

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The Role of Vacancy Dynamics in Two‐Dimensional Memristive Devices

Spetzler,

Abdel,

Schwierz

et al. 2023

Adv Elect Materials

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Two‐dimensional layered transition metal dichalcogenides (TMDCs) are promising memristive materials for neuromorphic computing systems. Despite extensive experimental work, the underlying switching mechanisms are still not understood, impeding progress in material and device functionality. This study reveals the dominant role of defect dynamics in the switching process of 2D TMDC materials. The switching process is governed by the formation and annihilation dynamics of a local vacancy depletion zone. It explains the distinct features of the device characteristics observed experimentally, including fundamentally different device behavior previously thought to originate from multiple mechanisms. Key influence factors are identified and discussed with a fully coupled and dynamic charge transport model for electrons, holes, and ionic point defects, including image‐charge‐induced Schottky barrier lowering (SBL). Thermal effects and local Joule heating are considered by coupling the transient heat transfer equation to the electronic properties. The model is validated with hysteresis and pulse measurements for various lateral 2D MoS2‐based devices, strongly corroborating the relevance of vacancy dynamics in TMDC devices and offering a new perspective on the switching mechanisms. The insights gained from this study can be used to extend the functional behavior of 2D TMDC memristive devices in future neuromorphic computing applications.

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Understanding the Full Zoo of Perovskite Solar Cell Impedance Spectra with the Standard Drift‐Diffusion Model

Clarke,

Richardson,

Cameron

2024

Advanced Energy Materials

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The impedance spectra of perovskite solar cells frequently exhibit multiple features that are typically modelled by complex equivalent circuits. This approach can lead to the inclusion of circuit elements without a sensible physical interpretation and create confusion where different circuits are adopted to describe similar cells. Spectra showing two distinct features have already been well explained by a drift‐diffusion model incorporating a single mobile ionic species but spectra with three features have yet to receive the same treatment and have even been dismissed as anomalous. This omission is rectified here by showing that a third (mid‐frequency) impedance feature is a natural consequence of the drift‐diffusion model in certain scenarios. Our comprehensive framework explains the shapes of all previously published spectra, which are classified into six generic types, each named for an animal resembling the Nyquist plot, and approximate solutions to the drift‐diffusion equations are obtained in order to illustrate the specific conditions required for each of these types of spectra to be observed. Importantly, it is shown that the shape of each Nyquist plot can be linked to specific processes occurring within a cell, allowing useful information to be extracted by a visual examination of the impedance spectra.

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Modelling charge transport in perovskite solar cells: Potential-based and limiting ion depletion

Cited by 17 publications

References 36 publications

Numerical analysis of a finite volume scheme for charge transport in perovskite solar cells

Numerical analysis of a finite volume scheme for charge transport in perovskite solar cells

The Role of Vacancy Dynamics in Two‐Dimensional Memristive Devices

Understanding the Full Zoo of Perovskite Solar Cell Impedance Spectra with the Standard Drift‐Diffusion Model

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