Reaction Order and Ideality Factor in Dye-Sensitized Nanocrystalline Solar Cells: A Theoretical Investigation

Nonlinear recombination in dye-sensitized solar cells was studied from a fundamental point of view. A model based on Marcus theory was used to describe the recombination from both conduction band and trap states. By combination of this model with the empirical form of nonlinear recombination, dependency of the reaction order (β) on the microscopic parameters of the solar cell was investigated. It was analytically shown that β is always less than unity and also depends on the quasi Fermi-level in semiconductors. By this nonconstant β, the dependency of the ideality factor ( m ), electron diffusion length ( L n ), and the electron lifetime (τ n ) on the Fermi-level were studied. It was discussed that the nonconstant β can explain the flattening of the L n at high Fermi-level, as observed in some recent experimental works. For the lifetime, it was shown that only the quantity τ n / m is accessible in the common open-circuit voltage decay method. It was also shown that the lifetime and the ideality factor can be obtained by the well-known charge extraction method.