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Systematic derivation of a surface polarisation model for planar perovskite solar cells. (English) Zbl 1431.78005

Eur. J. Appl. Math. 30, No. 3, 427-457 (2019); corrigendum ibid. 31, No. 1, 183-184 (2020).
Summary: Increasing evidence suggests that the presence of mobile ions in perovskite solar cells (PSCs) can cause a current-voltage curve hysteresis. Steady state and transient current-voltage characteristics of a planar metal halide \(\mathrm{CH_3 NH_3PbI_3}\) PSC are analysed with a drift-diffusion model that accounts for both charge transport and ion vacancy motion. The high ion vacancy density within the perovskite layer gives rise to narrow Debye layers (typical width \(\sim\)2 nm), adjacent to the interfaces with the transport layers, over which large drops in the electric potential occur and in which significant charge is stored. Large disparities between (I) the width of the Debye layers and that of the perovskite layer (\(\sim\)600 nm) and (II) the ion vacancy density and the charge carrier densities motivate an asymptotic approach to solving the model, while the stiffness of the equations renders standard solution methods unreliable. We derive a simplified surface polarisation model in which the slow ion dynamics are replaced by interfacial (nonlinear) capacitances at the perovskite interfaces. Favourable comparison is made between the results of the asymptotic approach and numerical solutions for a realistic cell over a wide range of operating conditions of practical interest.

MSC:

78A35 Motion of charged particles
78M35 Asymptotic analysis in optics and electromagnetic theory
82D37 Statistical mechanics of semiconductors
35Q60 PDEs in connection with optics and electromagnetic theory
35Q82 PDEs in connection with statistical mechanics
65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65L80 Numerical methods for differential-algebraic equations
65L04 Numerical methods for stiff equations
82M36 Computational density functional analysis in statistical mechanics

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References:

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