Chemical capacitance of nanostructured semiconductors: its origin and significance for nanocomposite solar cells

Interpenetrated networks of nanoscaled materials provide the opportunity to construct efficient solar cells from low purity materials and versatile fabrication processes. Instead on relying on long diffusion length in high purity crystals, the nanocomposite solar cells base their ability to convert photon energy to electricity on fast conversion of the photoexcitation to energetic carriers spatially separated in distinct nanoscaled phases, which enables their extraction. In this paper we discuss the general principles of operation of these solar cells. We start from the thermodynamic model of chemical capacitance, and we show its special role in the dynamic model of the solar cell in terms of equivalent circuits for small modulated perturbation. We argue that the concept of chemical capacitance is of critical importance for nanostructured semiconductor solar cells, because it describes the fundamental mechanism whereby photogenerated carriers store free energy and produce a voltage and current in the external circuit. The DSSC is so far the most efficient nanocomposite heterogeneous solar cell. In DSSC, the carriers transferring the chemical energy created in a photoexcited dye are electrons in nanocrystalline TiO2 , and redox species in a liquid electrolyte. The capacitance of DSSCs can be determined in several ways: electrochemical impedance spectroscopy (EIS), cyclic voltammetry, or integrating the current at differential voltage steps, and provides important information on the density of states (DOS) and the electron density. Normally, the concept of a capacitance relates to the textbook notion of an electrostatic geometric capacitance, determined by the electrical field between two metal plates with equal amounts of opposite charges. But this description is valid only insofar as the excess charge induced by the potential difference is confined to a very small region of the surface of the plates. Especially for mesoscopic systems, this is far from being generally true. In general, the change of electrochemical potential of electron reservoirs connected through leads to the mesoscopic plates, causes both an accomodation of the field by excess charges, and a variation of the Fermi level position with respect to the conduction band in the plates. Consequently, the more general electrochemical capacitance has been defined for small conductors connected to macroscopic reservoirs. The basic result is that the DOS contributes a factor to the capacitance given by