Fractal Charge Carrier Kinetics in TiO2

Charge carrier recombination kinetics of TiO2 powder samples were analyzed in the time domain ranging from 50 ns to 1 ms. The transient reflectance signals of the charge carriers observed by laser flash photolysis spectroscopy do not fit to simple second order kinetics as expected for the recombination of trapped electrons and holes. The deviation from second order reaction dynamics could rather be explained by the segregation of charge carriers and the fractal dimension of the semiconductor agglomerates. According to the fractal reaction kinetics, the time dependent rate coefficient k f (k f = k 2,f t –h ) has been employed instead of the second order rate constant k 2, where the fractal parameter h describes the dimension of the system. This model could successfully be used to describe charge carrier signals in all observed time domains. Moreover, the model was compared with the concept developed by Shuttle et al., which proposes that the charge carrier signals decay following a power-law. The benefits of the fractal model proposed here include the possibility to describe and analyze influences of the morphology on the fractal parameter h and its applicability over a broad range of time domains and excitation energies.