Electrochemical and photoelectrochemical characterization of porous semiconducting electrodes
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CaNb2O6 particles with crystallite sizes from 24 to 64 nm have been produced by solgel synthesis. The flatband potential was by impedance measurements determined to be around -0.4 V vs. NHE for a bulk sample, which is in fair agreement with theoretical predictions. For a film electrode both anodic and cathodic photocurrents were observed, and the transition between the two implies a flatband potential at 670 mV. The difference between pellet and the film was interpreted as being due to unpinning of the energy bands in the large surface area film electrode. Measured photocurrents show a maximum response at 280 nm (4.4 eV). The Poisson-Boltzmann equation has been solved for spherical geometry by use of Green’s functions, resulting in an analytical (closed form) integral expression that could be solved iteratively using a solution to the linearized Poisson-Boltzmann equation as the first order approximation for the potential. Practically identical results were produced when solving the governing equation by finite differences. Concentration and potential profiles for both extrinsic and intrinsic semiconductor particles were calculated. They can be used to determine at which combination of carrier concentration and radius a particle is too small to sustain a significant space charge layer. Also, the surface capacitance-potential behaviour has been obtained. For the intrinsic case the behaviour had a minimum value at the flatband potential. Extrinsic particles approached Mott-Schottky behaviour at high dopant levels or large radii. For smaller radii curved Mott-Schottky plots resulted. Although more complicated than the Mott-Schottky plots for the large particles these may still be useful as a basis for estimates of the flatband potential from measurements. The effect of the secondary current distribution on the impedance of a disk electrode has been solved analytically for four different local admittances: a capacitance, a capacitance in parallel with a resistance, a capacitance in a porous electrode and a porous intercalation electrode with mixed conductivity. A general formula has been derived for the impedance of a disk electrode as a function of the local admittance (Y, which is again a function of the angular frequency, ω) the electrolyte conductivity (κ) and the disk radius (a) which serves as a practical first approximation to the more complete result. The effect of a secondary current distribution on the impedance of a (square) plate has been obtained by finite differences with the four local admittances as input. At high frequencies the current distribution causes apparent constant phase element behaviour for the disk electrode while the effect on a plate electrode is to give an inductive loop. From the analytical expression for the first approximation it was found that the current distribution starts to influence the total measured impedance at the disk when aY (ω) / K >>1. The same relation was found to hold for a square plate electrode with a being the length of the plate.