Interpretation of Diffusion and Recombination in Nanostructured and Energy-Disordered Materials by Stochastic Quasiequilibrium Simulation

The main electronic feature of many nanocrystalline semiconductors and I organic materials is the presence of a distribution of localized states in the system with a broad energy dispersion. Carrier transport and recombination in these energetically disordered systems have raised increasing attention, in relation to applications in novel optoelectronic devices. We provide a general view of the physical interpretation of carrier transport coefficients (diffusion coefficient and mobility) and recombination lifetime in the presence of the localized states. We aim to carefully distinguish between the quantities that appear in the continuity equation for a small perturbation of the charge carriers (collective diffusion coefficient and lifetime) and those that are related to the behavior of the individual carriers (single-particle quantities). As an important example, charge-carrier transport and recombination in the case of multiple trapping model will be discussed in detail, for both exponential and Gaussian distributions. We address important aspects of the interpretation of lifetime and charge-transfer rates related to recombination in nanostructured organic and hybrid solar cells. Finally, to clarify different definitions for diffusion coefficient and lifetime, we use Monte Carlo simulation to calculate the diffusion coefficient, the mobility, and the lifetime (for both linear and nonlinear recombination) in the Gaussian DOS. We also justify the validity of the generalized Einstein relation in the case of a non-Boltzmann distribution of the carriers. Definitions and calculations provided in this paper have important consequences for both the interpretation of measurements and the calculation with advanced transport and recombination models.