Intensity Dependence of the Back Reaction and Transport of Electrons in Dye-Sensitized Nanocrystalline TiO₂Solar Cells

Abstract

The lifetime τ n and diffusion coefficient D n of photoinjected electrons have been measured in a dye-sensitized nanocrystalline TiO2 solar cell over 5 orders of magnitude of illumination intensity using intensity-modulated photovoltage and photocurrent spectroscopies. τ n was found to be inversely proportional to the square root of the steady-state light intensity, I 0, whereas D n varied with I 0 0.68. The intensity dependence of τ n is interpreted as evidence that the back reaction of electrons with I3 - may be second order in electron density. The intensity dependence of D n is attributed to an exponential trap density distribution of the form N t(E) ∝ exp[−β(E − E c)/(k B T)] with β ≈ 0.6. Since τ n and D n vary with intensity in opposite senses, the calculated electron diffusion length L n = (D n τ n )1/2 falls by less than a factor of 5 when the intensity is reduced by 5 orders of magnitude. The incident photon to current efficiency (IPCE) is predicted to decrease by less than 10% over the same range of illumination intensity, and the experimental results confirm this prediction.

Physical electrochemistry of nanostructured devices

“…72,134 The MT model, in combination with the quasistatic approximation 136 also provides an explanation for the observed compensation between chemical diffusion coefficient and lifetime 129 dependence on Fermi level, to give a nearly constant electron diffusion length as reported by L. M. Peter and other authors. 6,15,72,95,135,196 Characteristic experimental results of the main parameters, obtained by EIS in several DSCs, 66 are shown in Fig. 22.…”

“…Detailed information on the physical parameters related to transport in DSC has been obtained using small perturbation techniques at a fixed steady state such as IMPS 72,73 and EIS. 38,65,66,78 Short range electron displacement in nanoporous semiconductors and DSC has been described in terms of the continuous time random walk (CTRW) formalism, 124 but the most widely used approach to long range electronic motion, involving macroscopic transport equations, is the MT model, which has been described in a number of papers.…”

“…38,65,66,78 Short range electron displacement in nanoporous semiconductors and DSC has been described in terms of the continuous time random walk (CTRW) formalism, 124 but the most widely used approach to long range electronic motion, involving macroscopic transport equations, is the MT model, which has been described in a number of papers. 68,72,[125][126][127] It was found that both the effective electron diffusion coefficient, D n , and the effective electron lifetime, t n , 128,129 that are measured become a function of the steady state. 13,68,72,[129][130][131][132][133][134][135] Using quasi-equilibrium arguments, the variations of both diffusion coefficient and lifetime were attributed to the statistics of electrons in the material, which deviates from dilution, as described by thermodynamic factors.…”

“…68,72,[125][126][127] It was found that both the effective electron diffusion coefficient, D n , and the effective electron lifetime, t n , 128,129 that are measured become a function of the steady state. 13,68,72,[129][130][131][132][133][134][135] Using quasi-equilibrium arguments, the variations of both diffusion coefficient and lifetime were attributed to the statistics of electrons in the material, which deviates from dilution, as described by thermodynamic factors. 136 The varying D n was recognized as a chemical diffusion coefficient, 55,127 and the correlation between variations of D n and t n , 135 was explained by a common origin of their variations in an exponential distribution in the bandgap.…”

Electrochemical Impedance Spectroscopic Analysis of Dye-Sensitized Solar Cells

“…The hole was sealed with a microscope cover slide and Bynel to avoid leakage of the electrolyte solution. There were two electrolytes used in this paper: electrolyte 1, 0. η ) J SC ‚V OC ‚ff/I Ph (16) potentiostat (EG&G, M273) equipped with a frequency response analyzer (EG&G, M1025). The frequency range is 0.005-100 kHz.…”