Abstract
Driftdiffusion models that account for the motion of ion vacancies and electronic charge carriers are important tools for explaining the behaviour, and guiding the development, of metal halide perovskite solar cells. Computing numerical solutions to such models in realistic parameter regimes, where the short Debye lengths give rise to boundary layers in which the solution varies extremely rapidly, is challenging. Two suitable numerical methods, that can effectively cope with the spatial stiffness inherent to such problems, are presented and contrasted (a finite element scheme and a finite difference scheme). Both schemes are based on an appropriate choice of nonuniform spatial grid that allows the solution to be computed accurately in the boundary layers. An adaptive time step is employed in order to combat a second source of stiffness, due to the disparity in timescales between the motion of the ion vacancies and electronic charge carriers. It is found that the finite element scheme provides significantly higher accuracy, in a given compute time, than both the finite difference scheme and some previously used alternatives (Chebfun and pdepe). An example transient sweep of a currentvoltage curve for realistic parameter values can be computed using this finite element scheme in only a few seconds on a standard desktop computer.
Original language  English 

Pages (fromto)  329348 
Journal  Applied Mathematical Modelling 
Volume  63 
Early online date  3 Jul 2018 
DOIs  
Publication status  Published  Nov 2018 
Keywords
 RCUK
 EPSRC
 EP/L01551X/1
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Data availability statement for 'A fast and robust numerical scheme for solving models of charge carrier transport and ion vacancy motion in perovskite solar cells'.
Courtier, N. E. (Creator), Richardson, G. (Creator) & Foster, J. (Creator), Elsevier BV, 3 Jul 2018
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