A Model for the Operation of Perovskite Based Hybrid Solar Cells: Formulation, Analysis, and Comparison to Experiment

This work is concerned with the modeling of perovskite based hybrid solar cells formed by sandwiching a slab of organic lead halide perovskite (CH$_3$NH$_3$PbI$_{3-x}$Cl$_x$) photo-absorber between (n-type) acceptor and (p-type) donor materials---typically titanium dioxide and spiro. A model for the electrical behavior of these cells is formulated based on drift-diffusion equations for the motion of the charge carriers and Poisson's equation for the electric potential. It is closed by (i) internal interface conditions accounting for charge recombination/generation and jumps in charge carrier densities arising from differences in the electron affinity/ionization potential between the materials and (ii) ohmic boundary conditions on the contacts. The model is analyzed by using a combination of asymptotic and numerical techniques. This leads to an approximate---yet highly accurate---expression for the current-voltage relationship as a function of the solar induced photo-current. In addition, we show that this approximate current-voltage relation can be interpreted as an equivalent circuit model consisting of three diodes, a resistor, and a current source. For sufficiently small biases the device's behavior is diodic and the current is limited by the recombination at the internal interfaces, whereas for sufficiently large biases the device acts like a resistor and the current is dictated by the ohmic dissipation in the acceptor and donor. The results of the model are also compared to experimental current-voltage curves, and good agreement is shown.