In the last decades, many researchers have focused on improving the efficiency of existing photovoltaic techniques. In that direction, the study of the flexoelectric phenomena [1] has opened the path to another line of research referred to as flexo-photovoltaics [2]. However, there is very scarce work done in its computational modeling and solution. In this work, a simple yet revealing model consisting on coupling the flexoelectricity [3] and the semiconductor modeling equations [4] is considered together with its Finite Element solution.
The photovoltaic part of the model is discretized by means of standard C0-FE. However, flexoelectricity is modeled by 4th order PDE and, consequently, standard finite element formulations cannot be used. Instead, its solution is carried out by means of the C0-Interior Penalty Method described in [5] for infinitesimal deformations. The extension of the C0-IPM formulation in [5] for the finite deformations framework [6] is currently under development.
References:
[1] Pavlo Zubko, Gustau Catalan, Alexander K. Tagantsev. Flexoelectric Effect in Solids. The Annual Review of Materials Research 33, 1, pp. 387-421. 2013.
[2] Ming-Min Yang, Jik Kim, Marin Alexe. ’Flexo-photovoltaic effect’. Science, vol. 360. 2018.
[3] D. Codony, O. Marco, S. Fernàndez-Méndez, I. Arias. An immersed boundary hierarchical B-spline method for flexoelectricity. Computer method in applied mechanics and engineering 354, 1, pp. 750-782. 2019.
[4] W. R. Van Roosbroeck. ’Theory of flow of electrons and holes in germanium and other semiconductors’. Bell System Technical J, 29: 560–607. 1950.
[5] Jordi Ventura, David Codony, Sonia Fernàndez-Méndez. ’A C0 Interior Penalty Finite Element Method for Flexoelectricity’. Journal of Scientific Computing. 2021
[6] D. Codony, P. Gupta, O. Marco, I. Arias. ‘Modeling flexoelectricity in soft dielectrics at finite deformation’. Journal of the Mechanics and Physics of Solids, 146. 2021
