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

Abstract

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 TiO films with nanofabricated percolation pathways.

Microscopic origin of the Drude-Smith model

“…23,29,[34][35][36]39,71,73,76 Alternatively, the Drude-Smith model has also been used as an EMT in its own right and fit directly to the measured THz conductivity. [9][10][11][12][13][14][15][16][17][18][19]21,22,[25][26][27]30,31,33,38,[41][42][43][44][45]48 Each approach begins with a different physical process and leads to its own difficulties when one interprets the subsequent fits to the data.…”

“…In isolated nanoparticles this resonance can be described by a Lorentz oscillator model, [64][65][66][67] and in systems of non-percolated nanoparticles an appropriate EMT can in some cases connect the macroscopic conductivity of the system to the microscopic conductivity inside the nanoparticles. [70][71][72][73][74] . However, since the modified Drude-Smith conductivity represents the microscopic response of an entire nanoparticle (or even a nanoparticle network) and not the intrinsic conductivity of the material inside it, it is unclear whether it can be combined with conventional EMTs to account for depolarization fields.…”

“…91 Notably, simulations in Ref. 71 revealed that depolarization fields in percolated nanoparticle networks are minimal. Local-field corrections to the modified Drude-Smith model are therefore relevant mainly for non-percolated systems.…”

Accessing the fundamentals of magnetotransport in metals with terahertz probes

“…We note that although the Drude model is shown to accurately describe the high-frequency conductivity in certain metals 11,31 , it does not always hold for complex metal structures 44 , and hence the observed Drude behaviour could not have been assumed a priori for our multilayer GMR sample. Importantly for us, the pure Drude model, free from any effective parameters reflecting, for example, sample morphology [44][45][46] , simultaneously yields the magnetic field-dependent sheet d.c. conductivity σ s,d.c. (B) and the electron momentum scattering time τ (B) of our GMR sample, as shown in Fig.…”

Picosecond charge transport in rutile at high carrier densities studied by transient terahertz spectroscopy

“…For bulk samples with a thin photoexcited layer, the 69 measured transient transmittance E/E in the frequency 70 domain is directly related to the transient sheet conductivity 71 as follows [7][8][9]:…”