Dielectric study of the interplay between charge carriers and electron energy losses in reduced titanium dioxide

Abstract

The transport mechanism in titanium dioxide through polarons is an open issue. High-resolution electron energy-loss spectroscopy (HREELS) is in principle of great relevance in such context, provided the fingerprints on the loss spectrum of the charge carriers involved in the material are disclosed. This paper aims at evidencing those fingerprints. Through a suitable parametrization of the dielectric function, a theoretical analysis of EELS excitations in defective ${\mathrm{TiO}}_{2}$ rutile is developed in the framework of the semiclassical dielectric theory. The focus is put on the interplay between phonons, interband transitions, and defect-related excitations, namely, plasmon and band-gap states. Transport properties are demonstrated to be more efficiently grasped through the screening they induce on phonons than through the existence of a defined surface plasmon peak. While the corresponding imaginary part of the dielectric function only yields a slight broadening and temperature dependence of the quasielastic peak due to the large static dielectric function and electron effective mass, a sizable upward shift in energy and a decrease in intensity of phonons due to the real part are predicted. Band-gap states also screen phonons but with downward shift in energy loss. Due to its large oscillator strength, the high-energy-lying surface phonon at 95 meV is a very sensitive reporter of the combined effects of transport behavior and band-gap states. Finally, it is highlighted that extracting quantitative information out of EELS experiments requires an accurate modeling of the depth profile.