Interpretation of monoclinic hafnia valence electron energy-loss spectra by time-dependent density functional theory

摘要

We present the valence electron energy-loss spectrum and the dielectric function of monoclinic hafnia (m-HfO2) obtained from time-dependent density-functional theory (TDDFT) predictions and compared to energy-filtered spectroscopic imaging measurements in a high-resolution transmission-electron microscope. Fermi's golden rule density-functional theory (DFT) calculations can capture the qualitative features of the energy-loss spectrum, but we find that TDDFT, which accounts for local-field effects, provides nearly quantitative agreement with experiment. Using the DFT density of states and TDDFT dielectric functions, we characterize the excitations that result in the m-HfO2 energy-loss spectrum. The sole plasmon occurs between 13 and 16 eV, although the peaks similar to 28 and above 40 eV are also due to collective excitations. We furthermore elaborate on the first-principles techniques used, their accuracy, and remaining discrepancies among spectra. More specifically, we assess the influence of Hf semicore electrons (5p and 4f) on the energy-loss spectrum, and find that the inclusion of transitions from the 4f band damps the energy-loss intensity in the region above 13 eV. We study the impact of many-body effects in a DFT framework using the adiabatic local-density approximation (ALDA) exchange-correlation kernel, as well as from a many-body perspective using "scissors operators" matched to an ab initio GW calculation to account for self-energy corrections. These results demonstrate some cancellation of errors between self-energy and excitonic effects, even for excitations from the Hf 4f shell. We also simulate the dispersion with increasing momentum transfer for plasmon and collective excitation peaks.