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

Abstract

Abstract. 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 Clx) 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 photocurrent. 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.

IonMonger: a free and fast planar perovskite solar cell simulator with coupled ion vacancy and charge carrier dynamics

“…At the interface between the perovskite and the ETL, (1) the electron flux (and its associated current density) is conserved, (2) the hole flux (and its associated current density) is conserved, (3) there is no flux of halide ion vacancies, (4) and (5) both the electrostatic potential and electric displacement field are continuous, and (6) the majority carrier density (in this case the electrons) at the edge of the ETL is related to the neighbouring carrier density in the perovskite by a factor, k E , which depends upon the relevant band offset and change in effective density of states [11]. Therefore, at the interface between the ETL and the perovskite, the following conditions are applied…”

“…Due to the existence of mobile ion vacancies, the perovskite layer must be treated as a mixed ionic-electronic conductor for the purpose of device simulation. The first works [2,11,25] to apply numerical methods to PSC modelling reported that their simulations suffered from prohibitively long calculation times and inaccuracies in solution for realistic values of the parameters. A combined analytic/numerical method was used by Richardson et al [5,18] to reveal how iodide ion vacancies accumulate/deplete in very narrow layers (called Debye layers) adjacent to the perovskite boundaries.…”

Towards the maximum efficiency design of a perovskite solar cell by material properties tuning: A multidimensional approach

“…This section provides the detailed understanding of the charge generation and recombination processes within a perovskite solar cell. Sun et al 32 [35][36][37][38] . With both the analytical and the numerical model, the total generation of charges is obtained by the integration of the locally-generated charges over the whole absorber layer thickness.…”

Exponential decay of a finite volume scheme to the thermal equilibrium for drift–diffusion systems

“…Dissipativity and convergence to the thermal equilibrium for large time have also been established for this generalized model [26]. Let us underline that more recently, driven by applications like organic semiconductors, there is an increased interest in drift-diffusion models with arbitrary statistical distribution functions [11,40].…”