Accumulation of ionic charge carriers and the influence of steric potential in perovskite solar cells
Andreas Schiller a b, Balthasar Blülle b, Christoph Kirsch a, Martin Neukom a b, Beat Ruhstaller a b
a Institute of Computational Physics, Zurich University of Applied Sciences (ZHAW), 8401 Winterthur (Switzerland)
b Fluxim AG Katharina-Sulzer-Platz 2, 8400 Winterthur, Switzerland
Proceedings of International Conference on Hybrid and Organic Photovoltaics (HOPV19)
Roma, Italy, 2019 May 12th - 15th
Organizers: Prashant Kamat, Filippo De Angelis and Aldo Di Carlo
Oral, Andreas Schiller, presentation 105
Publication date: 11th February 2019

Modeling perovskite cells with the drift-diffusion approach including both electronic and ionic charge carriers can qualitatively reproduce several characteristic measurement results including IV curve hysteresis [1,2], dark current decay transients [3] and negative capacitance [4]. Up to now, however, no parameter set has been published which quantitatively matches multiple experiments. This raises the question, whether and how the model needs to be extended or adapted further.

The commonly used drift-diffusion approach makes use of the Boltzmann statistics for both electronic and ionic charge carriers. This model typically leads to a strong accumulation of ionic charge carriers at layer interfaces and thus a very fine space discretization is required in order to achieve numerical results of sufficient precision. More importantly, the exceedingly high ion density close to interfaces contradicts the physical understanding of ions as particles or vacancies with a certain volume requirement. S. van Reenen et al [5] described this behavior for OLECs but they circumvented the problem of strong accumulation by using a coarse space discretization.

We propose to model the interaction among ionic charge carriers as a purely geometrical effect. The steric potential derived in that way leads to a Fermi-like model [6], which effectively takes into account the limited amount of available states for ions in a given volume.

In this presentation, we shall discuss the suggested model and its implementation for both, steady-state and transient drift-diffusion simulations. In a detailed case study for a Methyl Ammonium Lead Iodide (MAPI) perovskite solar cell, we investigate the influence of the steric potential on the charge carrier profiles and we discuss the impact of the charge carrier statistics on the device properties of a solar cell.

The proper understanding of ion accumulation at the interfaces of perovskite devices will be a significant step towards the description of the full steady-state and dynamic device characteristics by a single set of parameters.

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