Valence Electron Energy-loss Spectra Research Articles

Beyond the random phase approximation (RPA): First principles calculation of the valence EELS spectrum for KBr including local field, quasiparticle, excitonic and spin orbit coupling effects

The low energy region (< 50 eV) of the electron energy loss spectrum (EELS) can contain a great deal of spectral detail associated with excitations of the valence electrons. Calculation of the spectra from first principles can assist with interpretation and the most widely used method is the random phase approximation (RPA), usually neglecting local field effects (LFE). For KBr this approach is insufficient due to the importance of quasiparticle and excitonic effects. Calculations including these multi-electron effects are shown to give much improved agreement with the experimental spectra, and the inclusion of spin-orbit coupling (SOC) reproduces the excitonic doublet just above band-edge onset. A review of the complex theory behind these methods is given along with practical guidance on performing these calculations.

Measurement of dielectric function and bandgap of germanium telluride using monochromated electron energy-loss spectroscopy

Using a monochromator in transmission electron microscopy, a low-energy-loss spectrum can provide inter- and intra-band transition information for nanoscale devices with high energy and spatial resolutions. However, some losses, such as Cherenkov radiation, phonon scattering, and surface plasmon resonance superimposed at zero-loss peak, make it asymmetric. These pose limitations to the direct interpretation of optical properties, such as complex dielectric function and bandgap onset in the raw electron energy-loss spectra. This study demonstrates measuring the dielectric function of germanium telluride using an off-axis electron energy-loss spectroscopy method. The interband transition from the measured complex dielectric function agrees with the calculated band structure of germanium telluride. In addition, we compare the zero-loss subtraction models and propose a reliable routine for bandgap measurement from raw valence electron energy-loss spectra. Using the proposed method, the direct bandgap of germanium telluride thin film was measured from the low-energy-loss spectrum in transmission electron microscopy. The result is in good agreement with the bandgap energy measured using an optical method.

A consistent picture of excitations in cubic BaSnO3 revealed by combining theory and experiment

Among the transparent conducting oxides, the perovskite barium stannate is most promising for various electronic applications due to its outstanding carrier mobility achieved at room temperature. However, most of its important characteristics, such as band gaps, effective masses, and absorption edge, remain controversial. Here, we provide a fully consistent picture by combining state-of-the-art ab initio methodology with forefront electron energy-loss spectroscopy and optical absorption measurements. Valence electron energy-loss spectra, featuring signals originating from band gap transitions, are acquired on defect-free sample regions of a BaSnO3 single crystal. These high-energy-resolution measurements are able to capture also very weak excitations below the optical gap, attributed to indirect transitions. By temperature-dependent optical absorption measurements, we assess band-gap renormalization effects induced by electron-phonon coupling. Overall, we find for the effective electronic mass, the direct and the indirect gap, the optical gap, as well as the absorption onsets and spectra, excellent agreement between both experimental techniques and the theoretical many-body results, supporting also the picture of a phonon-mediated mechanism where indirect transitions are activated by phonon-induced symmetry lowering. This work demonstrates a fruitful connection between different high-level theoretical and experimental methods for exploring the characteristics of advanced materials.

Quantitative analysis of Li distributions in battery material Li1-xFePO4 using Fe M2,3-edge and valence electron energy loss spectra

The spatial distribution of Li ions in a lithium iron phosphate (Li1-xFePO4) single crystal after chemical delithiation is quantitatively investigated using Fe M2,3-edge and valence electron energy loss (EEL) spectroscopy techniques. Li contents between those of end-member compositions LiFePO4 and FePO4 are found to correspond to reproducible changes in Fe M2,3-edge and valence EEL spectra across an interface between LiFePO4 and FePO4 regions. Quantitative analysis of these changes is used to estimate the local valence states of Fe ions, from which the Li concentration in the intermediate phase can be deduced. The faster recording time for valence EEL spectra than Fe M2,3-edge spectra makes measurement of the former a more efficient and reproducible means of estimating Li distributions.

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

We present the valence electron energy-loss spectrum and the dielectric function of monoclinic hafnia (m-HfO$_2$) 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-HfO$_2$ energy loss spectrum. The sole plasmon occurs between 13-16 eV, although the peaks $\sim$28 and above 40 eV are also due to collective excitations. We furthermore elaborate on the first-principles techniques used, their accuracy, and remaining discrepancies among spectra. More specifically, we assess the influence of Hf semicore electrons (5$p$ and 4$f$) on the energy-loss spectrum, and find that the inclusion of transitions from the 4$f$ 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 a $GW$-derived electronic structure 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.

On the validity of the Čerenkov limit as a criterion for precise band gap measurements by VEELS

The generation of Čerenkov photons, contributions from retardation and surface effects, and the excitation of guided light modes can complicate the analysis of valence electron energy-loss spectroscopy (VEELS) data. In recent works it was argued that working below the so-called Čerenkov limit unwanted spectral contributions can be avoided, simplifying the reliable measurement of band gap energies and the extraction of the dielectric function by the Kramers–Kronig analysis. Here, relativistic simulations of valence electron energy-loss spectra of GaAs are employed in order to identify different spectral contributions. It is found that for electron energies below the Čerenkov limit the spectra can still be affected by the excitation of guided light modes and retardation effects. These spectral contributions can influence the position of the apparent band gap signal and can be problematic for the Kramers–Kronig analysis when working below or above the Čerenkov limit.

Spectroscopic evidence in the visible-ultraviolet energy range of surface functionalization sites in the multilayerTi3C2MXene

Valence electron energy-loss (VEEL) spectroscopy in the transmission electron microscope is combined to ab initio calculations to investigate the dielectric properties of multilayer (ML) two-dimensional ${\mathrm{Ti}}_{3}{\mathrm{C}}_{2}{T}_{2}$ ($T\ensuremath{\equiv}\text{OH}$ or F) MXene. Besides evidencing important similarities between the ${\mathrm{ML}\ensuremath{-}\mathrm{Ti}}_{3}{\mathrm{C}}_{2}{T}_{2}$ and TiC valence electron gas behaviors, a clear interband transition characteristic of the most stable site of the $T$ functionalization groups is identified in the VEEL spectrum. This signature, highly dependent on the $T$-group localization on the surface, has a prominent effect on the optical properties of the ML, leading to $40%$ variations in the optical conductivity in the middle of the visible spectrum. Such a dependence could be of crucial interest for optical transparent thin films or sensing applications.

Optical guided modes coupled with Čerenkov radiation excited in Si slab using angular-resolved electron energy-loss spectrum

Retardation effects in the valence electron energy-loss spectrum (EELS) of a Si slab are analyzed by angular-resolved EELS. The dispersion curves of the valence spectra excited in a slab are directly observed from a specimen area with several different thicknesses and are interpreted by performing a calculation of the dispersion relation using Kröger's formula. The dispersion curves observed below about 3 eV are attributed to guided modes coupled with Čerenkov radiation (ČR). The coupling between guided modes and ČR is found to be dependent on the sample thickness (t). For the sample with t &amp;gt; 150 nm, the intensity of the guided modes increased linearly with thickness, revealing the coupling with ČR. For t &amp;lt; 150 nm, however, the intensity of the guided modes rapidly decreased due to a diminished coupling with ČR, resulting from the thickness-dependent dispersion curves of the guided modes.

Origin of valence and core excitations inLiFePO4 andFePO4

Electronic structures of LiFePO4 and FePO4 have been investigated using valence and core electron energy loss spectroscopy(EELS) supported by ab initio calculations. Valence electron energy loss spectra ofFePO4 are characterized by interband transitions found between 0 and 20 eV, which are not observed inLiFePO4. Spectra are fully analysed using band structure calculations and calculateddielectric functions. In particular, we show that interband transitions observed inFePO4 spectra originate from the states at the top of the valence band, which have mainlyoxygen p character. From core-loss EELS, it is observed that the O-K edge inFePO4 has apre-edge peak below the threshold of the main O-K edge. This pre-edge peak is not observed in the O-Kspectra of LiFePO4. The position of the pre-edge peak is determined by a charge transfer process, whichshifts the position of the iron 3d bands with respect to the conduction band. Theintensity of the pre-edge peak is also determined by the changes in the hybridizationof iron 3d and oxygen states as a result of extraction of lithium ions from theLiFePO4 lattice. We show that the extraction of lithium ions fromLiFePO4 results in large changes in the electronic structure, such thatFePO4 can be considered to be a charge transfer insulator whileLiFePO4 is a typical Mott–Hubbard insulator.

Scaling Dopant States in a Semiconducting Nanostructure by Chemically Resolved Electron Energy-Loss Spectroscopy: A Case Study on Co-Doped ZnO

Dilute dopant introduces foreign states to the electronic structures of host semiconductors and imparts intriguing properties to the materials. Identifying and positioning the dopant states are of crucial importance for seeking the underlying mechanism in the doped systems. However, such determination has still been challenging, particularly for individual nanostructured materials, due to the lack of the spectroscopic probe that possesses both nanometer spatial resolution and chemical resolution. Here, we shall demonstrate the successful scaling of dopant states of individual semiconducting nanostructures by chemically resolved electron energy-loss spectroscopy (EELS), taking the individual Co-doped ZnO nanorods as an example. Guided by the Co dopant spatial distribution mapped by the core-loss EELS technique, chemical resolution is achieved in the accumulated valence electron energy-loss spectra. Three Co dopant states are successfully identified and positioned in the host ZnO bands. Furthermore, the electron extension degrees of the Co dopant states are assessed on the basis of the multiple-atom effect. The above experimental inputs optimize the density functional theoretical calculations, which generates the corrected full electronic structures of (Zn,Co)O dilute magnetic semiconductors. These results give a carrier-mediated interpretation for the room-temperature ferromagnetism of Co-doped ZnO nanostructures based on a recent theory.

Valence electron energy-loss spectroscopy of nanoporous MgO

This work reports experimental evidence for a redshift in the main peak in the valence electron energy loss spectrum of nanoporous MgO. An interpretation is given based on effective-medium response theory. We find that the main peak energy depends on the density of nanopores within the illuminated area. As a result, by combining electron energy loss spectroscopy with transmission electron microscopy imaging, the loss peak position may be used to measure the porosity of nanoporous materials.

Fast determination of phases in LixFePO4 using low losses in electron energy-loss spectroscopy

Experimental valence electron energy-loss spectra, obtained on different phases of LixFePO4, are analyzed with first principles calculations based on density functional theory. In the 4–7 eV range, a large peak is identified in the FePO4 spectrum but is absent in LiFePO4, which allows the easy formation of energy filtered images. The intensity of this peak, nonsensitive to the precise orientation of the crystal, is large enough to rapidly determine existing phases in the sample and permit future dynamical studies.

Determination of complex dielectric functions at HfO2/Si interface by using STEM-VEELS

The complex dielectric functions and refractive index of atomic layer deposited HfO2 were determined by the line scan method of the valence electron energy loss spectrum (VEELS) in a scanning transmission electron microscope (STEM). The complex dielectric functions and dielectric constant of monoclinic HfO2 were calculated by the density functional theory (DFT) method. The resulting two dielectric functions were relatively well matched. On the other hand, the refractive index of HfO2 was measured as 2.18 by VEELS analysis and 2.1 by DFT calculation. The electronic structure of HfO2 was revealed by the comparison of the inter-band transition strength, obtained by STEM-VEELS, with the density of states (DOS) calculated by DFT calculation.

Retrieving the dielectric function of diamond from valence electron energy-loss spectroscopy

A data-acquisition and data-processing method is proposed that aims at minimizing the effect of retardation on the Kramers--Kronig analysis of valence electron energy-loss spectra. This method is applied to diamond, which, due to its high dielectric constant, is a material that shows strong retardation effects and thus is a challenging material to be studied by valence electron energy-loss spectroscopy. The results obtained show a significant improvement but still show small discrepancies with respect to optical data, which are most likely due to the residual retardation contributions and the fact that nonzero momentum transfers are measured.

Electron energy-loss spectroscopy in the low-loss region as a characterization tool of electrode materials

Energy losses below 100 eV are by far less exploited than higher losses in electron energy-loss spectroscopy. Two new examples are given to illustrate the characterization possibilities offered by spectra in this energy range. Typical materials that could be used as electrodes in electrochemical cells were chosen as application cases. Through the use of calculations based on density functional theory, we first demonstrate that the first peak present at the lithium K edge in LixTiP4 can give access to the precise localisation of inserted Li atoms in the f.c.c. structure. In particular, different tetrahedral sites could be differentiated according to their distance to the Ti site. Secondly, calculations of valence electron energy-loss spectra of perovskite materials indicate that a characteristic peak for regular perovskite (Pm \(\overline 3 \)m space group) exists in the 10–15 eV range. The high sensitivity of this peak to the distortion of the octahedron arrangements is also demonstrated.

Treating retardation effects in valence EELS spectra for Kramers–Kronig analysis

Retardation effects such as Cerenkov losses and waveguide modes alter the valence electron energy-loss spectrum of semiconductors and insulators as soon as the speed of the probing electron exceeds the speed of light inside the probed medium. This leads to the dilemma, that optical properties from these media cannot be determined correctly using electron energy-loss spectrometry (EELS) if no corrections are applied. In this work we present two ways out of this dilemma: a reduction of the beam energy and the application of an off-line correction. We demonstrate the accuracy of these two methods by using two similar layers of Si x : H having slightly different refractive indices and discuss the impact of the normalization parameter during Kramers–Kronig analysis (KKA) on the obtained dielectric properties. We further demonstrate that KKA can be applied without the use of standard specimens, if thickness determination using transmission electron microscopy and EELS is accurate enough.

The microstructure of SiO thin films: from nanoclusters to nanocrystals

The microstructure and electronic structure of silicon-rich oxide (SRO) films were investigated using transmission electron microscopy and electron energy loss spectroscopy as the main analytical techniques. The as-deposited SRO film was found to be a single phase SiO1.0, as suggested by its electronic structure characteristics determined by the valence electron energy loss spectrum. This single phase undergoes a continuous but incomplete phase decomposition to Si and SiO2 for films annealed between 300 and 1100°C. The resulting Si phase first appears as ∼2 nm-diameter amorphous clusters which grow to larger sizes at higher annealing temperatures, but only crystallize at a critical temperature between 800 and 900°C. This cluster/matrix configuration of the SRO films is consistent with the appearance of the interface plasmon and its oscillator strength as a function of the nanoparticle size. Three separate stages were identified in the sequence of annealed films that were characterized by the presence of single-phase SiO, amorphous silicon nanoclusters, and silicon nanocrystals, respectively. The presence of amorphous silicon nanoclusters in the intermediate stage, the mean size of which can be controlled via annealing, may offer an alternative to silicon nanocrystal composites for optical applications.

Investigation of Local Coordination and Electronic Structure of Dielectric Thin Films from Theoretical Energy-Loss Spectra

AbstractQuantum mechanical simulations were performed to calculate the valence electron energy-loss spectra (VEELS) for hafnium oxide, hafnium silicate, silicon oxide and silicon systems using the full potential Linearized Augmented Plane Wave (LAPW) formalism within the Density Functional Theory (DFT) framework. The needed energy-loss function (ELF) was derived from the calculation of the complex dielectric tensor within the random phase approximation (RPA). The calculated spectra were compared with experimental scanning transmission electron microscopy (STEM)/EELS of atomic layer deposited (ALD) HfO2 on Si(100) to evaluate their use as a “fingerprint” method that can be used to distinguish among various polymorphs of HfO2 thin films and relate the fine structure to the electronic structure and local bonding environment. Calculated low-loss spectra are found to be in satisfactory agreement with experimental data. Also, the combination of such theoretical calculations and experimental data could be of key importance in our understanding of fundamental issues of these systems. Compared to energy-loss near edge structure (ELNES) or core energy-loss spectra, the ELF calculated for low-loss spectra is computationally less expensive and can prove useful for prompt analysis.

Local Optical Properties, Electron Densities, and London Dispersion Energies of Atomically Structured Grain Boundaries

Quantitative analysis of spatially resolved valence electron energy-loss spectra shows strong physical property contrasts for Sigma5 and near Sigma13 grain boundaries in Fe-doped SrTiO3, resulting in London dispersion interaction energies of 14 to 50 mJ/m(2) between the adjacent grains. The determination of local physical properties of grain boundary cores and the appreciable contribution of long-range London dispersion to interface energies provides new information on formation and control of interfaces in materials.

Electron energy-loss spectroscopy study of thin film hafnium aluminates for novel gate dielectrics.

We have used conventional high-resolution transmission electron microscopy and electron energy-loss spectroscopy (EELS) in scanning transmission electron microscopy to investigate the microstructure and electronic structure of hafnia-based thin films doped with small amounts (6.8 at.%) of Al grown on (001) Si. The as-deposited film is amorphous with a very thin (approximately 0.5 nm) interfacial SiOx layer. The film partially crystallizes after annealing at 700 degrees C and the interfacial SiO2-like layer increases in thickness by oxygen diffusion through the Hf-aluminate layer and oxidation of the silicon substrate. Oxygen K-edge EELS fine-structures are analysed for both films and interpreted in the context of the films' microstructure. We also discuss valence electron energy-loss spectra of these ultrathin films.