Faradaic impedance of dye-sensitized solar cells

Theoretical equations of the Faradaic impedance of the photoelectrode and the counter electrode of dye-sensitized solar cell (DSC) were derived. The Faradaic impedance is the frequency dependent resistance related to the time constants of elementary electrode processes like photoexcitation, electron transfer, charge transfer reaction and diffusion. The typical cell impedance spectrum describes the locus of three semicircles on the Nyquist plane. The locus of three semicircles is generally analyzed by using the equivalent circuit composed of charge transfer resistance (R_ct,1) and capacitance (C_dl,1) of counter electrode, charge transfer resistance (R_ct,2) and capacitance (C_dl,2) of photoelectrode, the finite diffusion impedance due to the diffusion of I₃⁻ on the counter electrode (Z_w), and total resistance of the substrate and solution (R_s). The physical meanings of R_ct,1 and R_ct,2 can be elucidated by the interpretations of Faradaic impedance derived in the present paper. The R_ct,1 is represented as the function of the potential-dependent rate constants of I₃⁻ reduction and I⁻ oxidation. On the other hand, the R_ct,2 is the function of the photoelectrode potential, the surface concentration of I₃⁻ and the potential-independent rate constant of the back electron transfer reaction. The theoretical expressions of the current-voltage (I-V) curve of the DSC can be also derived. In the present paper, the relations between the impedance and I-V curve of the DSC are discussed.