Inelastic Mean Research Articles

Hard X-ray photoelectron spectra (HXPES) of bulk non-conductor vitreous SiO2: Minimum linewidths and surface chemical shifts

Hard X-ray photoelectron spectra (2200eV to 5000eV photon energies) have been obtained for the first time on a bulk non-conductor, vitreous SiO2, on a high resolution (E/ΔE of 10,000) synchrotron beamline at the Canadian Light Source (CLS). To minimize charging and differential charging, the SiO2 was coated with very thin layers (0.5 to 1.5nm) of Cr metal. The O 1s linewidth obtained at 2500eV photon energy was 1.26eV—the minimum linewidth for SiO2—and in good agreement with that obtained at 1486eV on a Kratos Axis Ultra spectrometer equipped with a magnetic charge compensation system. The Si 1s linewidth of 1.5eV, somewhat broader than that previously obtained at 1486eV on the Si 2p3/2 line of 1.16eV, is mainly due to the much larger inherent Si 1s linewidth (0.5eV) compared to the inherent Si 2p linewidth (<0.1eV). Both linewidths are dominated by the large final state vibrational broadening previously described.The Cr coating produces surface monolayers of interfacial Cr “suboxide” (Cr-subox), Cr metal, and a surface Cr oxide (Cr-surfox). Cr-subox (SiOCr) gives rise to the weak near-surface Si 1s peak, while both oxides give rise to both the weak surface O 1s peak and the Cr 2p oxide peak. Both the O 1s and Si 1s surface peaks are shifted by ∼2eV relative to the large bulk Si 1s and O 1s peaks. The weak Si 1s and O 1s surface peaks along with the Cr 2p oxide peak decrease in intensity greatly as the photon energy increases, due to an increase in inelastic mean free path (IMFP) in SiO2 from 27Å at 1486eV to 90Å at 5000eV. The decrease in intensity of these surface peaks is consistent with the theoretical IMFP's in the literature. The intensity of the weak O 1s and Si 1s peaks, along with the Cr 2p oxide peak, shows that the surface structure gives close to monolayer amounts of Cr-subox, Cr metal, and Cr-surfox. These high-energy spectra should be very useful in the future for bulk analysis of the O species in non-conducting silicate glasses, or surface analysis on non-conducting silicate surfaces and bulk as a function of photon energy.

(Invited) Investigation of the Si/TiO2/Electrolyte Interface Using Operando Tender X-ray Photoelectron Spectroscopy

Photoelectrochemical (PEC) cells based on semiconductor-liquid interfaces provide a method of converting solar energy to electricity or fuels 1-3. Recently, we have demonstrated operational systems that involved stabilized semiconductor-liquid junctions 4,5. We have employed operando ambient-pressure X-Ray photoelectron spectroscopy (AP-XPS) on these highly stable semiconductor-liquids junctions to directly characterize the semiconductor-liquid junction at room temperature under real-time electrochemical control 6,7. The escape depth of photoelectrons that originate from tender X-ray synchrotron radiation — 2.3 to 5.2 keV — allows for sampling of the sample simultaneously near the sample surface but through an electrolyte layer as the inelastic mean free path of such photoelectrons is on the order of 5 to 10 nanometers. Accordingly, tender X-ray AP-XPS has enabled simultaneous monitoring of the semiconductor surface, the semiconductor-electrolyte interface, and the bulk electrolyte of a PEC cell as a function of the applied potential, E. Accumulation, depletion and Fermi level pinning were observed. The observed shifts in the core level emission binding energies with respect to the applied potential directly revealed ohmic and rectifying junction behavior on metallized and semiconducting samples, respectively. 1. H. J. Lewerenz et al., Energ. Environ. Sci., 3, 748–760 (2010). 2. H. J. Lewerenz, in Photoelectrochemical Materials and Energy Conversion Processes, R. C. Alkire, D. M. Kolb, J. Lipkowski, and P. N. Ross, Editors, vol. 12, p. 61–181, Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, Germany (2010). 3. Z. Huang, C. Xiang, H. J. Lewerenz, and N. S. Lewis, Energ. Environ. Sci., 7, 1207–1211 (2014). 4. S. Hu et al., Science, 344, 1005–1009 (2014). 5. M. F. Lichterman et al., Energy Environ. Sci., 7, 3334–3337 (2014). 6. S. Axnanda et al., Meet. Abstr., MA2013-02, 921–921 (2013). 7. S. Axnanda et al., (2014), submitted.

Mermin Differential Inverse Inelastic Mean Free Path of Electrons in Polymethylmethacrylate

INTRODUCTION Electrons continually interact with the matter around us. We use electron beams for our purposes, either on the side of production of materials or on that of their characterization. Let us think to the many applications such as the processing of materials with plasma and to the local melting of materials for joining large components. We use electron beams also in the electron lithography, an important technique utilized for the production of the microelectronics devices. Let us consider the importance of the beams of electrons in the characterization of the materials, performed using techniques such as the electron microscopy and all the electron spectroscopies. Electrons interact with the surfaces of the space-crafts. The plasma– wall interaction in the fusion reactors also involves electron–matter interaction. Electrons play a role also in the cancer proton therapy, where cascades of secondary electrons are produced. These electrons of very low energy are toxic for the human body cells, since they produce damage to the biomolecules due to ionizations/excitations and the resulting break of chemical bonds. Also the secondary electrons which have ultra-low energies – and which, for a long time, were thought to be relatively harmless – are dangerous for the biomolecules due to the so-called “dissociative electron attachment.” And, of course, we wish to minimize the effects of the irradiation on the healthy tissues near to the diseased cells. In all the mentioned cases, the modeling of the interaction of the electrons with the matter is very important, as it can be used to provide a solid theoretical interpretation of the experimental evidences. The interpretation of the experimental results is often based on the Monte Carlo method (MC). The doping contrast in secondary-electron emission of pnjunctions was investigated by the use of the MC method (Dapor et al., 2008; Rodenburg et al., 2010). The modeling of electron interaction with polymers, and in particular with the polymethylmethacrylate, has been demonstrated to be very important in nano-metrology. Line-scan of resist materials with given geometrical cross-sections deposited on silicon or silicon dioxide, and the corresponding linewidth measurements, obtained with the secondary electrons in the CriticalDimension Scanning Electron Microscope (CD SEM), require an interpretation that can be performed using MC calculations (Dapor et al., 2010). The MC method, in turn, requires an accurate description of the differential inverse inelastic mean free path (DIIMFP), in order to calculate the inelastic mean free path (IMFP) and the distribution function for inelastic collisions of electrons causing energy losses less than or equal to given values.

Probing complex heterostructures using hard X-ray photoelectron spectroscopy (HAXPES)

X-ray Photoelectron Spectroscopy (XPS) plays a central role in the investigation of electronic properties as well as compositional analysis of almost every conceivable material. However, a very short inelastic mean free path (IMFP) and the limited photon flux in standard laboratory conditions render this technique very much surface sensitive. Thus, the electronic structure buried below several layers of a heterogeneous sample is not accessible with usual photoemission techniques. An obvious way to overcome this limitation is to use a considerably higher energy photon source, as this increases the IMFP of the photo-ejected electron, thereby making the technique more depth and bulk sensitive. Due to this obvious advantage, Hard X-ray Photo Electron Spectroscopy (HAXPES) is rapidly becoming an extremely powerful tool for chemical, elemental, compositional and electronic characterization of bulk systems, more so with reference to systems characterized by the presence of buried interfaces and other types of chemical heterogeneity. The relevance of such an investigative tool becomes evident when we specifically note the ever-increasing importance of heterostructures and interfaces in the context of a wide range of device applications, spanning electronic, magnetic, optical and energy applications. The interest in this nondestructive, element specific HAXPES technique has grown rapidly in the past few years; we discuss critically its extensive use in the study of depth resolved electronic properties of nanocrystals, multilayer superlattices and buried interfaces, revealing their internal structures. We specifically present a comparative discussion, with examples, on two most commonly used methods to determine internal structures of heterostructured systems using XPS.

FORMULA FOR MAXIMUM SECONDARY ELECTRON YIELD FROM METALS

Based on free-electron model, the calculated inelastic mean escape depth of secondary electrons, experimental one, the energy band of metal, the characteristics and processes of secondary electron emission, maximum number of secondary electrons released per primary electron δ(Φ,EF)PEm as a function of parameter Km, work function Φ and Fermi energy EF was deduced, where Km is a constant for a given metal in the energy range 100–800 eV. According to the relationship between maximum secondary electron yield from metal δ(Φ,EF)m and δ(Φ,EF)PEm, the formula for δ(Φ,EF)m as a function of atomic number Z, parameter Km, Φ and EF was deduced. Using the deduced formula for δ(Φ,EF)m, Z, experimental δ(Φ,EF)m, Φ and EF, Km relative to alkali metals, Km relative to earth-alkali metals and the mean value of Km were computed, respectively. And the formulae for maximum secondary electron yield from alkali metals, earth-alkali metals and metals were obtained and proved to be true, respectively. On the basis of the deduced formula for δ(Φ,EF)m and the empirical relation that high Φ are connected with high EF, it can be concluded that high δ(Φ,EF)m are connected with high Φ and vice versa.

Penn Algorithm Including Damping for Calculating the Electron Inelastic Mean Free Path

We present an approach for introducing damping into the Penn algorithm by using the Mermin dielectric function instead of the Lindhard dielectric function. We find that for a damping of 1.5 eV, the electron inelastic mean free path calculated by the present algorithm for Al is in excellent agreement with experimental values in the energy range 5–9 eV. Meanwhile, for a damping of 2.0 eV, our result for Au is consistent with the GW+T ab initio calculation at several electronvolts. In particular, at an energy of 1 eV, our result for Au is 297 A and lies within the range 220–330 A obtained from measurements by ballistic electron emission microscopy.

Study of inelastic mean free path of metal nanostructures using energy filtered transmission electron microscopy imaging.

We report a simple method for measuring the inelastic mean free path of nanostructures of known geometry using energy filtered transmission electron microscopy imaging. The mean free path of inelastic electrons was measured by using systems having known symmetry, such as cylindrical or cubic, combined with Poisson statistics without employing the knowledge of microscope parameters, namely the convergence angle and the collection angle. Having inherent symmetry of such systems, their absolute thickness can be measured from their two-dimensional projection images. We have calculated mean free path of inelastic scattering of electrons in gold, silver and nickel doing case study research by employing gold nanorod, silver nanocube and nickel nanorod lying on a carbon-coated TEM grid at two different electron energies (viz. 200 and 300 keV) following this alternative approach. Results obtained using such alternative approach were verified using microscope parameters.

Angular broadening in core‐electron spectroscopy

The role of angular broadening in quantitative core‐electron spectroscopy is investigated using an analytic approach. It is shown why, practically, this effect remains relatively small for a broad range of parameters. A correction factor is derived, suggesting that the replacement of inelastic mean free path by an effective attenuation‐length parameter is not necessarily an optimal choice. The derived expression further proposes useful insight on the contribution of leading experimental parameters and, in particular, on the sharp increase of elastic‐scattering corrections above a (depth dependent) critical angle. Copyright © 2015 John Wiley &amp; Sons, Ltd.

Electron inelastic mean free paths in cerium dioxide

Electron transport properties in CeO2 powder samples were studied by elastic-peak electron spectroscopy (EPES). Prior to EPES measurements, the CeO2 sample surface was pre-sputtered by 0.5keV Ar ion etching. As a result, an altered layer with thickness of 1.3nm was created. X-ray photoelectron spectroscopy (XPS) analysis revealed two chemical states of cerium Ce4+ (68%) and Ce3+ (32%) at the surface region of CeO2 sample after such treatment. The inelastic mean free path (IMFP), characterizing electron transport, was evaluated as a function of energy within the 0.5–2keV range. Experimental IMFPs were corrected for surface excitations and approximated by the simple function λ=kEp, where λ was the IMFP, E denoted the energy (in eV), and k=0.207 and p=0.6343 were the fitted parameters. The IMFPs measured here were compared with IMFPs resulting from the TPP-2M predictive equation for the measured composition of oxide surface. The measured IMFPs were found to be from 3.1% to 20.3% smaller than the IMFPs obtained from the predictive formula in the energy range of 0.5–2keV. The EPES IMFP value at 500eV was related to the altered layer of sputtered CeO2 samples.

Chemical‐Reaction‐Induced Hot Electron Flows on Platinum Colloid Nanoparticles under Hydrogen Oxidation: Impact of Nanoparticle Size

AbstractGeneration of hot electron flows and the catalytic activity of Pt nanoparticles (NPs) with different sizes were investigated using catalytic nanodiodes. We show that smaller Pt NPs lead to higher chemicurrent yield, which is associated with the shorter travel length for the hot electrons, compared with their inelastic mean free path. We also show the impact of capping on charge carrier transfer between Pt NPs and their support.

Momentum-Dependent Lifetime Broadening of Electron Energy Loss Spectra: A Self-Consistent Coupled-Plasmon Model.

The complex dielectric function and associated energy loss spectrum of a condensed matter system is a fundamental material parameter that determines both the optical and electronic scattering behavior of the medium. The common representation of the electron energy loss function (ELF) is interpreted as the susceptibility of a system to a single- or bulk-electron (plasmon) excitation at a given energy and momentum and is commonly derived as a summation of noninteracting free-electron resonances with forms constrained by adherence to some externally determined optical standard. This work introduces a new causally constrained momentum-dependent broadening theory, permitting a more physical representation of optical and electronic resonances that agrees more closely with both optical attenuation and electron scattering data. We demonstrate how the momentum dependence of excitation resonances may be constrained uniquely by utilizing a coupled-plasmon model, in which high-energy excitations are able to relax into lower-energy excitations within the medium. This enables a robust and fully self-consistent theory with no free or fitted parameters that reveals additional physical insight not present in previous work. The new developments are applied to the scattering behavior of solid molybdenum and aluminum. We find that plasmon and single-electron lifetimes are significantly affected by the presence of alternate excitation channels and show for molybdenum that agreement with high-precision electron inelastic mean free path data is dramatically improved for energies above 20 eV.

Effective attenuation lengths for photoelectrons emitted by high-energy laboratory X-ray sources

We report calculations of effective attenuation lengths (EALs) for Si 2s1/2, Cu 2p3/2, Ag 3d5/2, and Au 4f7/2 photoelectrons excited by Mg Kα, Al Kα, Zr Lα, and Ti Kα X-rays, where the photoelectron energies ranged from 321eV to 4.426keV. These EALs, appropriate for determining overlayer-film thicknesses, were calculated from the transport-approximation formalism and from Monte Carlo simulations using photoionization cross sections from the dipole and non-dipole approximations. Satisfactory consistency was found between EALs determined from the TA formalism and from MC simulations, while differences between EALs for Au 4f7/2 photoelectrons from the dipole and non-dipole approximations were between 1% (for Mg and Al Kα X-rays) and 2.5% (for Ti Kα X-rays) for photoelectron emission angles less than 50°. As in past work for electron energies less than 2keV, we found a simple linear relation between the ratio of the average EAL (for emission angles less than 50°) to the inelastic mean free path (IMFP) and the single-scattering albedo, a function of the IMFP and the transport mean free path. The root-mean-square difference between our average EALs and those from the linear expression was 1.44%. This expression should be useful in determinations of film thicknesses by XPS with unpolarized X-rays for photoelectron energies up to about 5keV.

Energy loss of electrons impinging upon glassy carbon, amorphous carbon, and diamond: Comparison between two different dispersion laws

In this paper, we compare and discuss calculated inelastic mean free path, stopping power, range, and reflection electron energy loss spectra obtained using two different and popular dispersion laws. We will present and discuss the results we obtained investigating the interaction of electron beams impinging upon three allotropic forms of carbon, i.e. solid glassy carbon, amorphous carbon, and diamond. We will compare numerical results with experimental reflection electron energy loss spectra.

Inelastic carrier lifetime in a coupled graphene/electron-phonon system: Role of plasmon-phonon coupling

We calculate the inelastic scattering rates and the hot electron inelastic mean free paths for both monolayer and bilayer graphene on a polar substrate. We study the quasiparticle self-energy by taking into account both electron-electron and electron-surface optical (SO) phonon interactions. In this calculation the leading order dynamic screening approximation (G$_0$W approximation) is used to obtain the quasiparticle self-energy by treating electrons and phonons on an equal footing. We find that the strong coupling between the SO phonon and plasmon leads to a new decay channel for the quasiparticle through the emission of the coupled mode, and gives rise to an abrupt increase in the scattering rate, which is absent in the uncoupled system. In monolayer graphene a single jump in the scattering rate occurs, arising from the emission of the low energy branch of the coupled plasmon-phonon modes. In bilayer graphene the emission of both low and high energy branches of the coupled modes contributes to the scattering rate and gives rise to two abrupt changes in the scattering rate. The jumps in the scattering rate can be potentially used in the hot electron device such as switching devices and oscillators.

Energy loss of fast electrons impinging upon polymethylmethacrylate

This paper deals with the calculation of the differential inverse inelastic mean free path, the inelastic mean free path, the stopping power, the range of penetration, and the distribution function for inelastic collisions causing energy losses less than or equal to given values, for fast electrons impinging upon polymethylmethacrylate. Numerical tables are provided along with the comparison with computations of other investigators.

Reflection Electron Energy Loss Spectra beyond the optical limit

A position-dependent Inverse Inelastic Mean Free Path (IIMFP), calculated according to the Chen–Kwei theory of inelastic scattering, is used to obtain Reflection Electron Energy Loss Spectra (REELS) by a Monte Carlo approach. The basic ingredient of the theory is the energy-loss and momentum-transfer dependent dielectric function, for which we use a plasmon-pole approximation to the Lindhard dielectric function. The dependence on the momentum transfer enters by assuming a proper dispersion relation for the energy loss. Experiments reveal however that, beside energy loss, also plasmon damping disperses with momentum transfer. By comparing measured and calculated REEL spectra, we explore the role of damping dispersion for a quasi-free-electron material like silicon.

Effect of atomic structure on excitation of the electronic subsystem of a solid by a swift heavy ion

An effect of different phase states of a solid on excitation of its electronic subsystem due to penetration of a swift heavy ion (SHI) is examined on example of silicon dioxide (crystalline quartz vs. amorphous glass). The complex dielectric function formalism describing collective response of the electronic and ionic subsystems of a condensed target to excitation is used to calculate scattering cross sections of a penetrating ion and electrons generated due to target ionizations. A Monte Carlo model based on these cross sections is applied for tracing electron kinetics in the nanometric vicinity of the trajectory of a swift heavy ion. It is demonstrated that differences of the maximal values of the SHI energy losses and the electron inelastic mean free paths calculated for two phase states of SiO2 do not exceed 10–15%, whereas the elastic mean free paths differ more significantly.

Electron emission from silicon and germanium after swift heavy ion impact

The presented Monte Carlo model simulates excitation of the electron subsystem of semiconductors by a penetrating swift heavy ion (SHI). The cross sections of interaction of an ion with the electron subsystem of a target are calculated via the complex dielectric function formalism, which accounts for all the collective modes of the electron ensemble of the target. The predicted electron inelastic mean free paths are in a very good agreement with those from the NIST database. The calculated SHI energy losses coincide well with SRIM and CasP codes. The model is used to calculate the spectra of electrons emitted from germanium and silicon targets during SHI irradiation. These spectra agree well with the experimental data.

Nanoscale three-dimensional reconstruction of elastic and inelastic mean free path lengths by electron holographic tomography

Electron holography at medium resolution simultaneously probes projected electrostatic and magnetostatic potentials as well as elastic and inelastic attenuation coefficients with a spatial resolution of a few nanometers. In this work, we derive how the elastic and inelastic attenuation can be disentangled. Using that result, we perform the first three dimensional tomographic reconstruction of potential and (in)elastic attenuation in parallel. The technique can be applied to distinguish between functional potentials and composition changes in nanostructures, as demonstrated using the example of a GaAs—Al0.33Ga0.67As core-shell nanowire.

Stopping powers and inelastic mean free path of 200 eV–50 keV electrons in polymer PMMA, PE, and PVC

The stopping power (SP) and inelastic mean free path (IMFP) of three polymers: polymethyl methacrylate (PMMA), polyethylene (PE), and polyvinyl chloride (PVC) for electron energies from 200eV to 50keV have been determined based on dielectric models. The energy loss function (ELF) is the main input in the calculation of the SP and IMFP for the dielectric models. ELF in this study was determined from a previously published quantitative analysis of reflection electron energy loss spectroscopy (REELS) spectra. The SP of PMMA, PE and PVC decreases and the IMFP increases with increasing electron energies up to 50keV. For comparison, data from the National Institute of Standards and Technology (NIST) database for electron energies from 10 to 50keV were used and show that SP in this study is lowered by 10–15%. The obtained IMFP for PE was compared with those calculated using the TPP2M predictive equations and shows that a reasonable agreement with a root-mean-square (rms) is 7.01Å. The present approach has high potential for the experimental determination of SP and IMFP from the REELS spectra.