An analytical model for organic bulk heterojunction solar cells based on Saha equation for exciton dissociation

The power conversion efficiencies of organic solar cells (OSCs) have been greatly improved in recent years. However, latest experimental data of high efficiency OSCs, the sublinear relationship between the short circuit current density (J_sc) and light intensity (P_in), and the effects of energetic disorder in bulk heterojunction organic solar cells have not been understood. An analytical model for high-efficiency OSCs is proposed, which takes most physical factors into account that have been ignored in most previous models, including practical solar spectra and absorption spectra, degeneracy effect, exciton effect, space charge limited current, and unified mobility expression dependent on temperature, electric field and density, etc. Three analytical iterative methods are proposed to solve the strong non-linear Poisson equation and the drift-diffusion equations. The method for the drift-diffusion equations involves introducing two constant coefficients and determining their values self-consistently by demanding the space averages of approximate drift and diffusion currents equal to the averages of accurate ones. The theoretical results for five high-efficiency OSCs are in good agreement with experimental data, including current-voltage curves, light intensity-dependent J_sc and open-circuit voltage (V_oc) curves. The effects of energetic disorder in bulk heterojunction organic solar cells, and the sublinear relationship J_sc ∝ Pαin (α < 1) can be well explained. The Saha equation for exciton dissociation and the space-charge-limited-current (SCLC) effect are important for modelling high-efficiency OSCs. The V_oc ∼ P_in relationship can be influenced by many factors. But, the J_sc ∼ P_in relationship can be mainly and slightly influenced by the exciton effect and energetic disorder, respectively. When aiming to realize higher performance OSCs, one should decrease six material parameters, including the energetic disorder, exciton mass, deep level impurity concentration, the ratios of electron and hole mobilities, densities of states for electrons and holes, and potential barriers at the anode and cathode. The performance parameters of 15 triad compounds are predicted by using ab initio E_g and absorption spectra from the literature along with other input parameters taken from previous optimized values, and the efficiency of two compounds was found to exceed 35%.