The impact of surface and retardation losses on valence electron energy-loss spectroscopy

Unveiling Variations in Electronic and Atomic Structures Due to Nanoscale Wurtzite and Zinc Blende Phase Separation in GaAs Nanowires

Phase separation is an intriguing phenomenon often found in III-V nanostructures, but its effect on the atomic and electronic structures of III-V nanomaterials is still not fully understood. Here we study the variations in atomic arrangement and band structure due to the coexistence of wurtzite (WZ) and zinc blende (ZB) phases in single GaAs nanowires by using scanning transmission electron microscopy and monochromated electron energy loss spectroscopy. The WZ lattice distances are found to be larger (by ∼1%), along both the nanowire length direction and the perpendicular direction, than the ZB lattice. The band gap of the WZ phase is ∼20 meV smaller than that of the ZB phase. A shift of ∼70 meV in the conduction band edge between the two phases is also found. The direct and local measurements in single GaAs nanowires reveal important effects of phase separation on the properties of individual III-V nanostructures.

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 non-destructive and efficient transfer method for preparing 2D materials samples for transmission electron microscopy study

Studying two-dimensional (2D) materials using transmission electron microscopy (TEM) is necessary and very important in many aspects. However, some 2D materials are not resistant to acids or alkalis, which are widely used in normal wet transfer techniques to transfer the exfoliated 2D nanosheets onto the TEM grids. On the other hand, dry stamping method can damage the holey carbon film on the TEM grids. In this article, we present a non-destructive, efficient, and widely applicable transfer method for preparing the TEM samples of the exfoliated 2D materials. Our method only uses the heat-release tape, PMMA, and blue Nitto tape. Neither acid nor alkali is involved in our method, therefore, impurities and damage can be avoided to the greatest extent. The method is also very efficient and can be accomplished in less than 30 min after the exfoliation of the 2D materials. This method is particularly useful for preparing the TEM samples of the 2D materials that are not resistant to acids and alkalis. The present method is also applicable to various 2D materials and various substrates.

Nature of optical excitations and bandgap of RexMo1-xS2alloy at nanoscale probed from high resolution low loss electron energy loss spectroscopy

The two-dimensional (2D) transitional metal dichalcogenides (TMDS) have become an intensive research topic recently. The alloys of these TMDs have offered continuous tunability of the bandstructure and carrier concentration, providing a new opportunity for various device applications. Here the rich variations in optical excitations in Re_xMo_1-xS₂alloy at the nanoscale region are shown. The alloy bandgap and charge response are probed by low-loss high-resolution transmission electron energy loss spectroscopy (HR-EELS). Concurrent density functional theory calculations revealed many electronic structures from n-type semiconductors to metallic and p-type semiconducting nature with band bowing effect. The alloying-induced Peierls distortion leads to a change in crystal symmetry and decreased interlayer coupling. These alloys undergo indirect to direct bandgap transition with the function of Re concentration. These unique correlated structural and electronic properties of these 2D alloys can be potentially applicable for various electronic and optoelectronic devices.

Complex dielectric function and opto-electronic characterization using VEELS for the lead-free BCZT electro-ceramic perovskite

The current work presents the complex dielectric function and the opto-electronic properties of lead-free Ba_0.8Ca_0.2Ti_0.9Zr_0.1O₃ (BCZT) electro-ceramic, derived from valence electron energy loss spectroscopy, in transmission electron microscopy (VEELS-TEM). A single tetragonal perovskite phase, with P4mm space group, was determined by Rietveld refinement of the x-ray diffraction pattern. The VEELS-TEM experiment scanned the energy interval from 0-50 eV. The spectroscopic analysis started with the chemical identification of the atoms that conforms the BCZT solid-solution. Bulk and surface plasmons were located at 27.2 eV and 12.9 eV, respectively in the energy loss function. Complex dielectric function was obtained using Kramers-Kronig analysis from the Gatan Microscopy Suite software. Dielectric constant was calculated from the real part of the complex dielectric function, while the inter-band transitions were identified in the joint density of states function. The refraction index n and the extinction coefficient k, as a function of energy, were obtained from the complex dielectric function. The bandgap energy was determined using a polynomial fit in the optical absorption coefficient plot with an E_g = 3.2 eV.

Site-specific angular dependent determination of inelastic mean free path of 300 keV electrons in GaN nanorods

Inelastic mean free path (IMFP) of the electron is a very important parameter for quantitative analysis of several electron spectroscopies and transport properties. In spite of being a fundamental material property, its experimental determination is not trivial due to complexity of the various electron scattering processes in matter. In this report, we demonstrate a procedure to determine the IMFP of 300 keV electrons in GaN, using the log-ratio technique where the local specimen thickness needs to be accurately known. The GaN nanorod morphology of the sample used here allows the accurate measurement of thickness by 'thickness map' under EFTEM measurements which enable the site specific determination of IMFP. IMFP for different collection semi angles have also been measured to validate the angular dependence. Our experimental results estimates the IMFP of GaN for 300 keV electrons to be 143 ± 11 nm at no-aperture condition and exhibit a strong inverse angular dependence at smaller collection semi angles (β < 20 mrad) and a near angular independence at larger collection semi angles (β > 30 mrad). We discuss these results in the light of three different theoretical models prevalent in the literature.

Properties of Dipole-Mode Vibrational Energy Losses Recorded From a TEM Specimen

The authors discuss the dipole vibrational modes that predominate in the energy-loss spectra of ionic materials below 1 eV, concentrating on thin-film specimens of typical transmission electron microscopy (TEM) thickness. The thickness dependence of the intensity is shown to be a useful guide to the bulk or surface character of vibrational peaks. The lateral and depth resolution of the energy-loss signal is investigated with the aid of finite-element calculations.

Bandgap determination from individual orthorhombic thin cesium lead bromide nanosheets by electron energy-loss spectroscopy

Inorganic lead halide perovskites are promising candidates for optoelectronic applications, due to their high photoluminescence quantum yield and narrow emission line widths. Particularly attractive is the possibility to vary the bandgap as a function of the halide composition and the size or shape of the crystals at the nanoscale. Here we present an aberration-corrected scanning transmission electron microscopy (STEM) and monochromated electron energy-loss spectroscopy (EELS) study of extended nanosheets of CsPbBr3. We demonstrate their orthorhombic crystal structure and their lateral termination with Cs-Br planes. The bandgaps are measured from individual nanosheets, avoiding the effect of the size distribution which is present in standard optical spectroscopy techniques. We find an increase of the bandgap starting at thicknesses below 10 nm, confirming the less marked effect of 1D confinement in nanosheets compared to the 3D confinement observed in quantum dots, as predicted by density functional theory calculations and optical spectroscopy data from ensemble measurements.

Thickness-dependent band gap of α-In2Se3: from electron energy loss spectroscopy to density functional theory calculations

α-In₂Se₃ has attracted increasing attention in recent years due to its excellent electrical and optical properties. Especially, attention has been paid to its peculiar ferroelectric and piezoelectric properties which most other two-dimensional (2D) materials do not possess. This paper presents the first measurement of the thickness-dependent band gaps of few-layer α-In₂Se₃ by electron energy loss spectroscopy (EELS). The band gap increases with decreasing film thickness which varies from 1.44 eV in a 48 nm thick area to 1.64 eV in an 8 nm thick area of the samples. Further, by combining the improved exchange-correlation potential and proper screening of the internal electric field in an advanced 2D electronic structure technique, we have been able to obtain the structural dependence of the band gap within density functional theory up to hundreds of atoms. This is also the first calculation of a similar type for 2D ferroelectric materials. Both experiment and theory suggest that the variation of the band gap of α-In₂Se₃ fits well with the quantum confinement model for 2D materials.

Conductivity models for electron energy loss spectroscopy of graphene in a scanning transmission electron microscope with high energy resolution

Recent advancements in the energy resolution and probing capabilities of monochromated electron-beam spectroscopy instruments have made this experimental technique increasingly useful for investigating and understanding the plasmonic, photonic, and electronic properties of graphene-enhanced systems. We develop herein an empirical model for the in-plane conductivity of doped monolayer graphene, comparing with ab initio data from the terahertz (THz) to the upper range of frequencies accessible with the valence electron energy loss spectroscopy (VEELS). Along with our ab initio data, this model is employed to calculate the energy loss spectra using a relativistic formulation, allowing us to analyze the effects that different electron beam parameters have on the response of graphene in a monochromated scanning transmission electron microscope setup. In particular, we explore the effects of reducing the collection angle of scattered electrons, thereby deducing a computational procedure for extracting the real and imaginary parts of the optical conductivity of graphene layers from VEELS measurements. Our modeling ultimately provides insight into how the optoelectronic properties of graphene are expected to manifest in the VEELS obtained via monochromated beams, with the effects of graphene doping, the excitation of its plasmon-polaritons, and relativistic contributions included comprehensively.

Design and application of a relativistic Kramers-Kronig analysis algorithm

Low-loss electron energy loss spectroscopy (EELS) in the scanning transmission electron microscope probes the valence electron density and relevant optoelectronic properties such as band gap energies and other band structure transitions. The measured spectra can be formulated in a dielectric theory framework, comparable to optical spectroscopies and ab-initio simulations. Moreover, Kramers-Kronig analysis (KKA), an inverse algorithm based on the same name relations, can be employed for the retrieval of the complex dielectric function. However, spurious contributions traditionally not considered in this framework typically impact low-loss EELS modifying the spectral shapes and precluding the correct measurement and retrieval of the dielectric information. A relativistic KKA algorithm is able to account for the bulk and surface radiative-loss contributions to low-loss EELS, revealing the correct dielectric properties. Using a synthetic low-loss EELS model, we propose some modifications on the naive implementation of this algorithm that broadens its range of application. The robustness of the algorithm is improved by regularization, applying previous knowledge about the shape and smoothness of the correction term. Additionally, our efficient numerical integration methodology allows processing hyperspectral datasets in a reasonable amount of time. Harnessing these abilities, we show how simultaneous relativistic KKA processing of several spectra can share information to produce an improved result.

Quantification of Charge Transfer at the Interfaces of Oxide Thin Films

The interfacial electronic distribution in transition-metal oxide thin films is crucial to their interfacial physical or chemical behaviors. Core-loss electron energy-loss spectroscopy (EELS) may potentially give valuable information of local electronic density of state at high spatial resolution. Here, we studied the electronic properties at the interface of Pb(Zr_0.2Ti_0.8)O₃ (PZT)/4.8 nm La_0.8Sr_0.2MnO₃ (LSMO)/SrTiO₃ (STO) using valance-EELS with a scanning transmission electron microscope. Modeled with dielectric function theory, the charge transfer in the vicinity of the interfaces of PZT/LSMO and LSMO/STO was determined from the shifts of plasma peaks of valence EELS (VEELS), agreeing with theoretical prediction. Our work demonstrates that the VEELS method enables a high-efficient quantification of the charge transfer at interfaces, shedding light on the charge-transfer issues at heterogenous interfaces in physical and chemical devices.

Retrieving the energy-loss function from valence electron energy-loss spectrum: Separation of bulk-, surface-losses and Cherenkov radiation

With recent rapid advancement in electron microscopy instrumentation, in particular, bright electron sources and monochromators, valence electron energy-loss spectroscopy (VEELS) has become attractive for retrieving band structures, optical properties, dielectric functions and phonon information of materials. However, Cherenkov radiation and surface-loss contribution significantly alter fine structures of VEELS, even in simple semiconductors and insulators. This leads to the problem that dielectric function or bandgap structure of these materials cannot be determined correctly if these effects are not removed. In this work we present a solution to this dilemma. We demonstrate that energy-loss function and real part of inverse complex dielectric function can be retrieved from raw data of VEELS. Based on the calculated example of Si, the limitation of our approach is discussed. We believe that our approach represents an improvement over previous procedures and has a broad prospect for applications.

Reply to Comment on 'Nanoscale mapping of optical band gaps using monochromated electron energy loss spectroscopy'

We respond to the comment by Thomas Walther and reaffirm the findings of our original article.

Electronic response of aluminum-bearing minerals

Aluminum-bearing minerals show different hydrogen evolution and dissolution properties when subjected to radiation, but the complicated sequence of events following interaction with high-energy radiation is not understood. To gain insight into the possible mechanisms of hydrogen production in nanoparticulate minerals, we study the electronic response and determine the bandgap energies of three common aluminum-bearing minerals with varying hydrogen content: gibbsite (Al(OH)₃), boehmite (AlOOH), and alumina (Al₂O₃) using electron energy loss spectroscopy, X-ray photoelectron spectroscopy, and first-principles electronic structure calculations employing hybrid density functionals. We find that the amount of hydrogen has only a small effect on the number and spectrum of photoexcitations in this class of materials. Electronic structure calculations demonstrate that low energy electrons are isotropically mobile, while holes in the valence band are likely constrained to move in layers. Furthermore, holes in the valence band of boehmite are found to be significantly more mobile than those in gibbsite, suggesting that the differences in radiolytic and dissolution behavior are related to hole transport.

Exploring possibilities of band gap measurement with off-axis EELS in TEM

A technique to measure the band gap of dielectric materials with high refractive index by means of energy electron loss spectroscopy (EELS) is presented. The technique relies on the use of a circular (Bessel) aperture and suppresses Cherenkov losses and surface-guided light modes by enforcing a momentum transfer selection. The technique also strongly suppresses the elastic zero loss peak, making the acquisition, interpretation and signal to noise ratio of low loss spectra considerably better, especially for excitations in the first few eV of the EELS spectrum. Simulations of the low loss inelastic electron scattering probabilities demonstrate the beneficial influence of the Bessel aperture in this setup even for high accelerating voltages. The importance of selecting the optimal experimental convergence and collection angles is highlighted. The effect of the created off-axis acquisition conditions on the selection of the transitions from valence to conduction bands is discussed in detail on a simplified isotropic two band model. This opens the opportunity for deliberately selecting certain transitions by carefully tuning the microscope parameters. The suggested approach is experimentally demonstrated and provides good signal to noise ratio and interpretable band gap signals on reference samples of diamond, GaN and AlN while offering spatial resolution in the nm range.

Mapping VIS-terahertz (≤17 THz) surface plasmons sustained on native and chemically functionalized percolated gold thin films using EELS

Heterogeneous assemblies of molecules (Rhodamine B) adsorbed onto a nano-corrugated metallic surface (a percolated Au network) are investigated using electron energy loss spectroscopy in the scanning transmission electron microscope (STEM-EELS). Our first measurements target the native metallic substrate, which consists of a commercial Au thin film atop an ultrathin carbon membrane. The Au film displays a percolated morphology with nanostructures of estimated thickness ≤10 nm approximately. We observe a rich plasmonic response from the metallic substrate; one which varies nanometrically and spans the VIS-terahertz region. Multiple localized plasmons are detected at individual nanometric integrated areas, while an analysis of their spatial distribution reveals that for each integrated energy range (50 meV integration window) resonances are simultaneously supported at different locations within the film. We record subsequent EEL spectrum images of the hybrid molecular-metallic construct after deposition of Rhodamine B molecules onto the substrate, where plasmons, molecular vibrations and electronic excitations might all be simultaneously detected. A comparison of average signals for both systems is performed and spectral variations within the three spectral regions where molecular signatures may be observed are discussed. Our measurements and their analysis, if applied to the same location before and after molecular deposition, may be used to rationalize optical microscopic and spectroscopic measurements that take advantage of the interplay between molecules and plasmons.

Band gap maps beyond the delocalization limit: correlation between optical band gaps and plasmon energies at the nanoscale

Recent progresses in nanoscale semiconductor technology have heightened the need for measurements of band gaps with high spatial resolution. Band gap mapping can be performed through a combination of probe-corrected scanning transmission electron microscopy (STEM) and monochromated electron energy-loss spectroscopy (EELS), but are rare owing to the complexity of the experiments and the data analysis. Furthermore, although this method is far superior in terms of spatial resolution to any other techniques, it is still fundamentally resolution-limited due to inelastic delocalization of the EELS signal. In this work we have established a quantitative correlation between optical band gaps and plasmon energies using the Zn_1−xCd_xO/ZnO system as an example, thereby side-stepping the fundamental resolution limits of band gap measurements, and providing a simple and convenient approach to achieve band gap maps with unprecedented spatial resolution.

Bandgap measurement of high refractive index materials by off-axis EELS

In the present work Cs aberration corrected and monochromated scanning transmission electron microscopy electron energy loss spectroscopy (STEM-EELS) has been used to explore experimental set-ups that allow bandgaps of high refractive index materials to be determined. Semi-convergence and -collection angles in the µrad range were combined with off-axis or dark field EELS to avoid relativistic losses and guided light modes in the low loss range to contribute to the acquired EEL spectra. Off-axis EELS further supressed the zero loss peak and the tail of the zero loss peak. The bandgap of several GaAs-based materials were successfully determined by simple regression analyses of the background subtracted EEL spectra. The presented set-up does not require that the acceleration voltage is set to below the Čerenkov limit and can be applied over the entire acceleration voltage range of modern TEMs and for a wide range of specimen thicknesses.

In-Situ Stretching Patterned Graphene Nanoribbons in the Transmission Electron Microscope

The mechanical response of patterned graphene nanoribbons (GNRs) with a width less than 100 nm was studied in-situ using quantitative tensile testing in a transmission electron microscope (TEM). A high degree of crystallinity was confirmed for patterned nanoribbons before and after the in-situ experiment by selected area electron diffraction (SAED) patterns. However, the maximum local true strain of the nanoribbons was determined to be only about 3%. The simultaneously recorded low-loss electron energy loss spectrum (EELS) on the stretched nanoribbons did not reveal any bandgap opening. Density Functional Based Tight Binding (DFTB) simulation was conducted to predict a feasible bandgap opening as a function of width in GNRs at low strain. The bandgap of unstrained armchair graphene nanoribbons (AGNRs) vanished for a width of about 14.75 nm, and this critical width was reduced to 11.21 nm for a strain level of 2.2%. The measured low tensile failure strain may limit the practical capability of tuning the bandgap of patterned graphene nanostructures by strain engineering, and therefore, it should be considered in bandgap design for graphene-based electronic devices by strain engineering.

Nanoscale mapping of optical band gaps using monochromated electron energy loss spectroscopy

Using monochromated electron energy loss spectroscopy in a probe-corrected scanning transmission electron microscope we demonstrate band gap mapping in ZnO/ZnCdO thin films with a spatial resolution below 10 nm and spectral precision of 20 meV.

Quantitative parameters for the examination of InGaN QW multilayers by low-loss EELS

We present a detailed examination of a multiple InxGa1-xN quantum well (QW) structure for optoelectronic applications. The characterization is carried out using scanning transmission electron microscopy (STEM), combining high-angle annular dark field (HAADF) imaging and electron energy loss spectroscopy (EELS). Fluctuations in the QW thickness and composition are observed in atomic resolution images. The impact of these small changes on the electronic properties of the semiconductor material is measured through spatially localized low-loss EELS, obtaining band gap and plasmon energy values. Because of the small size of the InGaN QW layers additional effects hinder the analysis. Hence, additional parameters were explored, which can be assessed using the same EELS data and give further information. For instance, plasmon width was studied using a model-based fit approach to the plasmon peak; observing a broadening of this peak can be related to the chemical and structural inhomogeneity in the InGaN QW layers. Additionally, Kramers-Kronig analysis (KKA) was used to calculate the complex dielectric function (CDF) from the EELS spectrum images (SIs). After this analysis, the electron effective mass and the sample absolute thickness were obtained, and an alternative method for the assessment of plasmon energy was demonstrated. Also after KKA, the normalization of the energy-loss spectrum allows us to analyze the Ga 3d transition, which provides additional chemical information at great spatial resolution. Each one of these methods is presented in this work together with a critical discussion of their advantages and drawbacks.

Measurement of the dielectric function of α-Al2O3 by transmission electron microscopy - Electron energy-loss spectroscopy without Cerenkov radiation effects

The dielectric function of α-Al2O3 was measured by electron energy-loss spectroscopy (EELS) coupled with the difference method. The influence of Cerenkov radiation was significant in measurements using a 200kV transmission electron microscope (TEM) and the correct dielectric function could not be obtained using the conventional EELS procedure. However, a good agreement between the optical data and EELS for the dielectric functions was obtained via a 60kV TEM. Combining EELS and the difference method, however, provided an accurate measurement of the dielectric function for α-Al2O3 even at an accelerating voltage of 200kV. The combination of EELS and the difference method in the nano-beam diffraction mode could derive an accurate dielectric function with superior spatial resolution regardless of the occurrence of Cerenkov radiation.

Electron energy loss spectroscopy on semiconductor heterostructures for optoelectronics and photonics applications

In this work, we present characterization methods for the analysis of nanometer-sized devices, based on silicon and III-V nitride semiconductor materials. These methods are devised in order to take advantage of the aberration corrected scanning transmission electron microscope, equipped with a monochromator. This set-up ensures the necessary high spatial and energy resolution for the characterization of the smallest structures. As with these experiments, we aim to obtain chemical and structural information, we use electron energy loss spectroscopy (EELS). The low-loss region of EELS is exploited, which features fundamental electronic properties of semiconductor materials and facilitates a high data throughput. We show how the detailed analysis of these spectra, using theoretical models and computational tools, can enhance the analytical power of EELS. In this sense, initially, results from the model-based fit of the plasmon peak are presented. Moreover, the application of multivariate analysis algorithms to low-loss EELS is explored. Finally, some physical limitations of the technique, such as spatial delocalization, are mentioned.

Local band gap measurements by VEELS of thin film solar cells

This work presents a systematic study that evaluates the feasibility and reliability of local band gap measurements of Cu(In,Ga)Se2 thin films by valence electron energy-loss spectroscopy (VEELS). The compositional gradients across the Cu(In,Ga)Se2 layer cause variations in the band gap energy, which are experimentally determined using a monochromated scanning transmission electron microscope (STEM). The results reveal the expected band gap variation across the Cu(In,Ga)Se2 layer and therefore confirm the feasibility of local band gap measurements of Cu(In,Ga)Se2 by VEELS. The precision and accuracy of the results are discussed based on the analysis of individual error sources, which leads to the conclusion that the precision of our measurements is most limited by the acquisition reproducibility, if the signal-to-noise ratio of the spectrum is high enough. Furthermore, we simulate the impact of radiation losses on the measured band gap value and propose a thickness-dependent correction. In future work, localized band gap variations will be measured on a more localized length scale to investigate, e.g., the influence of chemical inhomogeneities and dopant accumulations at grain boundaries.

Growth and characterization of CNT-TiO2 heterostructures

A thriving field in nanotechnology is to develop synergetic functions of nanomaterials by taking full advantages of unique properties of each component. In this context, combining TiO2 nanocrystals and carbon nanotubes (CNTs) offers enhanced photosensitivity and improved photocatalytic efficiency, which is key to achieving sustainable energy and preventing environmental pollution. Hence, it has aroused a tremendous research interest. This report surveys recent research on the topic of synthesis and characterization of the CNT-TiO2 interface. In particular, atomic layer deposition (ALD) offers a good control of the size, crystallinity and morphology of TiO2 on CNTs. Analytical transmission electron microscopy (TEM) techniques such as electron energy loss spectroscopy (EELS) in scanning transmission mode provides structural, chemical and electronic information with an unprecedented spatial resolution and increasingly superior energy resolution, and hence is a necessary tool to characterize the CNT-TiO2 interface, as well as other technologically relevant CNT-metal/metal oxide material systems.

Thickness measurements using photonic modes in monochromated electron energy-loss spectroscopy

Characteristic energies of photonic modes are a sensitive function of a nanostructures' geometrical parameters. In the case of translationally invariant planar waveguides, the eigen-energies reside in the infrared to ultraviolet parts of the optical spectrum and they sensitively depend on the thickness of the waveguide. Using swift electrons and the inherent Cherenkov radiation in dielectrics, the energies of such photonic states can be effectively probed via monochromated electron energy-loss spectroscopy (EELS). Here, by exploiting the strong photonic signals in EELS with 200 keV electrons, we correlate the energies of waveguide peaks in the 0.5-3.5 eV range with planar thicknesses of the samples. This procedure enables us to measure the thicknesses of cross-sectional transmission electron microscopy samples over a 1-500 nm range and with best-case accuracies below ± 2%. The measurements are absolute with the only requirement being the optical dielectric function of the material. Furthermore, we provide empirical formulation for rapid and direct thickness estimations for a 50-500 nm range. We demonstrate the methodology for two semiconducting materials, silicon and gallium arsenide, and discuss how it can be applied to other dielectrics that produce strong optical fingerprints in EELS. The asymptotic form of the loss function for two-dimensional materials is also discussed.

Dielectric response of pentagonal defects in multilayer graphene nano-cones

The dielectric response of pentagonal defects in multilayer graphene nano-cones has been studied by electron energy loss spectroscopy and ab initio simulations. At the cone apex, a strong modification of the dielectric response is observed below the energy of the π plasmon resonance. This is attributed to π → π* interband transitions induced by topology-specific resonant π bonding states as well as π*-σ* hybridization. It is concluded that pentagonal defects strongly affect the local electronic structure in such a way that multi-walled graphene nano-cones should show great promise as field emitters.

Optoelectronic properties of InAlN/GaN distributed bragg reflector heterostructure examined by valence electron energy loss spectroscopy

High-resolution monochromated electron energy loss spectroscopy (EELS) at subnanometric spatial resolution and <200 meV energy resolution has been used to assess the valence band properties of a distributed Bragg reflector multilayer heterostructure composed of InAlN lattice matched to GaN. This work thoroughly presents the collection of methods and computational tools put together for this task. Among these are zero-loss-peak subtraction and nonlinear fitting tools, and theoretical modeling of the electron scattering distribution. EELS analysis allows retrieval of a great amount of information: indium concentration in the InAlN layers is monitored through the local plasmon energy position and calculated using a bowing parameter version of Vegard Law. Also a dielectric characterization of the InAlN and GaN layers has been performed through Kramers-Kronig analysis of the Valence-EELS data, allowing band gap energy to be measured and an insight on the polytypism of the GaN layers.

Quantifying the low-energy limit and spectral resolution in valence electron energy loss spectroscopy

While the development of monochromators for scanning transmission electron microscopes (STEM) has improved our ability to resolve spectral features in the 0-5 eV energy range of the electron energy loss spectrum, the overall benefits relative to unfiltered microscopes have been difficult to quantify. Simple curve fitting and reciprocal space models that extrapolate the expected behavior of the zero-loss peak are not enough to fully exploit the optimal spectral limit and can hinder the ease of interpreting the resulting spectra due to processing-induced artifacts. To address this issue, here we present a quantitative comparison of two processing methods for performing ZLP removal and for defining the low-energy spectral limit applied to three microscopes with different intrinsic emission and energy resolutions. Applying the processing techniques to spectroscopic data obtained from each instrument leads in each case to a marked improvement in the spectroscopic limit, regardless of the technique implemented or the microscope setup. The example application chosen to benchmark these processing techniques is the energy limit obtained from a silicon wedge sample as a function of thickness. Based on these results, we conclude on the possibility to resolve statistically significant spectral features to within a hundred meV of the native instrumental energy spread, opening up the future prospect of tracking phonon peaks as new and improved hardware becomes available.

Measuring the dielectric constant of materials from valence EELS

Valence EELS combined with STEM provides an approach to determine the dielectric constant of materials in the optical range of frequencies. The paper describes the experimental procedure and discusses the critical aspects of valence electron energy-loss spectroscopy (VEELS) treatment. In particular, the relativistic losses might affect strongly the results, and therefore they have to be subtracted from the spectra prior the analysis. The normalization of the energy-loss function is performed assuming an uniform thickness of the investigated area, which is reasonably fulfilled for carefully prepared FIB samples. This procedure requires the presence of at least one reference material with known dielectric properties to determine the absolute thickness. Examples of measuring the dielectric constant for several materials and structures are presented.

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.