Injection Efficiency in Dye-Sensitized Solar Cells within a Two-Band Model

The injection efficiency in dye-sensitized solar cells is investigated theoretically within a general two-band model, which consists of a conduction band in semiconductor anode and an energy level for the lowest unoccupied molecular orbit (LUMO) in dye molecule. Formulas for the calculation of injection efficiency are derived by using a thermodynamical statistics on the injection current at steady state. The dependence of injection efficiency on various electronic structure parameters, such as the LUMO level relative to conduction band edge, density of states, and so forth, is examined. An approximate expression is obtained for a qualitative description of injection efficiency in the dye-sensitized solar cell operated at a normal conditions. Our results demonstrate that the thermodynamical competition between forward transfer current (from LUMO level to conduction band) and backward transfer current (from conduction band to LUMO level) should be considered in the evaluation of injection efficiency, and the competition results in a lower injection efficiency than unity. The previous experimental results on injection efficiency, such as the weak electron density dependence (or bias dependence), the effect of LUMO delocalization, and so forth, can be well interpreted by using our formula.