Charge Transport in ${\hbox{TiO}}_{2}$ Films With Complex Percolation Pathways Investigated by Time-Resolved Terahertz Spectroscopy

The depolarization fields play an important role in terahertz experiments on nanostructured samples with complex nanoparticle morphologies and percolation pathways. Namely, their effects can hide or distort peculiarities of nanoscopic charge transport in the spectra measured on these structures. We calculate the local fields for a large number of percolated and non-percolated two-dimensional model structures by numerical solving of Maxwell equations in the quasi-static limit. The results strongly suggest that in a broad family of structures a simple effective medium approximation model can be applied to characterize the effective response. The model consists in an equivalent circuit composed of a resistance accounting for the percolated chains with an additional parallel RC-branch describing the non-percolated part. The physical meaning of this model is discussed in the frame of the Bergman spectral representation of effective medium. We show a recipe for the retrieval of a response connected to the depolarization fields and to the nanoscale transport mechanisms from transient terahertz spectra. Finally, we use the model to interpret our THz photoconductivity spectra in various ${\hbox{TiO}}_{2}$ films with nanofabricated percolation pathways.