The understanding of electron transfer across interfaces and nanostructures constitutes a major challenge in emerging nanodevices. Ultrafast injection of carriers through the interface at femtosecond scale has been reported in dye-TiO2 systems and in piezotronics devices based on ZnO nanotubes, followed by anomalous transport of the charges through the nanoporous network. These features which could not be expected on the basis of bulk models, motivated real-time theoretical studies of the injection dynamics and transport at the nanoscale to improving the overall efficiency. In this paper correlation functions are evaluated by the Fourier transform of the frequency-dependent conductivity of the system. Drude-Lorentz and Schmith models, fitted to experimental data, have been analyzed. We present results for TiO2 and ZnO oxides nanostructured films. It is found that the diffusion coefficient of carriers is usually very small, but can reach values comparable to the single crystal at early times after carriers are released, even in the presence of structural disorder, under conditions concerning the size of the nanoparticles, the strength of the coupling of the charges with the nanoparticles and the relaxation time. Our result for the current-current correlation function as a function of time is in agreement with the obtained result by ultrafast time THz spectroscopy.
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