Abstract
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 CH3NH3PbI3PSC 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 ~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 (~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 simplifiedsurface polarisationmodel in which the slow ion dynamics are replaced by interfacial (non-linear) 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.
Highlights
Since the first use of methylammonium lead tri-halide perovskite as a sensitizer in a dye-sensitized solar cell [15], and its subsequent incorporation into a novel thin film solar technology as a bulk solar absorber [14, 17], the efficiency of perovskite solar cells (PSCs) has increased extremely rapidly from around 3% to above 20% [6], a level that is comparable to the standard crystalline silicon devices
We outlined a model for charge carrier transport and ion vacancy motion in a tri-layer planar PSC
Using parameters extracted from the literature, we were able to identify two key small dimensionless parameters that characterise the model: λ, which gives the ratio of the Debye length in the perovskite to the width of perovskite layer, and δ, the ratio of the typical charge carrier densities to the typical ion vacancy density
Summary
Since the first use of methylammonium lead tri-halide perovskite as a sensitizer in a dye-sensitized solar cell [15], and its subsequent incorporation into a novel thin film solar technology as a bulk solar absorber [14, 17], the efficiency of perovskite solar cells (PSCs) has increased extremely rapidly from around 3% to above 20% [6], a level that is comparable to the standard crystalline silicon devices. Absorption of light occurs predominantly within the perovskite layer and is associated with the generation of an exciton which, due to its weak binding energy (∼50 meV) [16], rapidly dissociates into a free electron in the conduction band, and a hole in the valence band, of the perovskite. These charge carriers move both in response to random thermal excitations (diffusion) and to internal electric fields (drift). The valence band energy in the ETL is significantly below that in the perovskite, so that a potential barrier exists to the entry of holes into this material from the perovskite
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