Interpretation of the Time Constants Measured by Kinetic Techniques in Nanostructured Semiconductor Electrodes and Dye-Sensitized Solar Cells

Abstract

The processes of charge separation, transport, and recombination in dye-sensitized nanocrystalline TiO 2 solar cells are characterized by certain time constants. These are measured by small perturbation kinetic techniques, such as intensity modulated photocurrent spectroscopy (IMPS), intensity modulated photovoltage spectroscopy (IMVS), and electrochemical impedance spectroscopy (EIS). The electron diffusion coefficient, D n , and electron lifetime, τ n , obtained by these techniques are usually found to depend on steady-state Fermi level or, alternatively, on the carrier concentration. We investigate the physical origin of such dependence, using a general approach that consists on reducing the general multiple trapping kinetic-transport formalism, to a simpler diffusion formalism, which is valid in quasi-static conditions. We describe in detail a simple kinetic model for diffusion, trapping, and interfacial charge transfer of electrons, and we demonstrate the compensation of trap-dependent factors when forming steady-state quantities such as the diffusion length, L n , or the electron conductivity, σ n .

Electron Transport in Dye-Sensitized Solar Cells Based on ZnO Nanotubes: Evidence for Highly Efficient Charge Collection and Exceptionally Rapid Dynamics

“…The consequence of the smaller transfer factor for nt-ZnO relative to np-TiO 2 is a smaller fill factor in the nt-ZnO DSC. 37 It is common to discuss the collection efficiency in terms of the characteristic constants for electron transport (τ d ) and lifetime (τ n ) 38 since these time constants can be also obtained by alternative techniques, such as time transients of intensity modulated photocurrent spectroscopy (IMPS). 39 If the capacitance is taken to be strictly "chemical" in nature (reflecting density of states), it is reasonable to adopt a multiple trapping diffusion interpretation in which τ d ) R tr C µ ) L 2 /D n and τ n ) R ct C µ where D n is the chemical diffusion coefficient.…”

Physical electrochemistry of nanostructured devices

“…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. 95,136 The application of the multiple trapping model in DSC will be described in detail in section 3.4.…”

“…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. 95,136 The application of the multiple trapping model in DSC will be described in detail in section 3.4.…”

Observation of Diffusion and Tunneling Recombination of Dye-Photoinjected Electrons in Ultrathin TiO2 Layers by Surface Photovoltage Transients

“…Techniques operating in the intermediate time/ frequency range (10 mHz to 1000 Hz) such as impedance spectroscopy, 5 transient photocurrents, 4 and open-circuit photovoltage decays 6 provide macroscopic parameters that are timeand spatial-averaged with respect to the microscopic processes. 7 The latter are resolved separately in fast optical pump-probe experiments (10 ns to 10 ms), for example, monitoring the decay of the photoinduced dye cation excited by a laser pulse. 2 However, direct information about spatial distribution of carriers cannot be obtained from an optical measurement itself.…”