Inelastic Mean Free Path Research Articles

Faraday rotation in a disordered medium

The Faraday rotation angle $\ensuremath{\Theta}$ is calculated in a diffusive regime on a three-dimensional disordered slab. It is shown that $\mathrm{tan}\phantom{\rule{0.16em}{0ex}}\ensuremath{\Theta}$ is (i) an oscillating function of the magnetic field or the medium's internal properties, and (ii) proportional to the ratio of the inelastic mean-free path ${l}_{\mathrm{in}}$ to the mean-free path $l$, that is, to the average number of photon scatterings. The maximum rotation is achieved at frequencies when the photon's elastic mean-free path is minimal. We have obtained the rotation angle of backscattered light taking into account the maximally crossed diagrams. The latter leads to an ellipticity in the backscattered wave that can serve as a precursor of weak localization. The critical strength of the magnetic field is ${B}_{c}\ensuremath{\sim}{g}_{c}\ensuremath{\sim}\ensuremath{\lambda}/l$ beyond which rotation in the backscattered wave disappears. The traversal time of an electromagnetic wave through the slab is estimated in a diffusive regime. The disorder enhanced the traversal time by an additional factor ${l}_{\mathrm{in}}/l$ in comparison with a free light propagation time. Comparison with the experimental data is carried out.

Reflection electron energy loss spectroscopy in Mn x Si1 − x composite structures

The dependences of the product of the electron inelastic mean free path λ and the differential cross section for inelastic electron scattering K on energy loss are determined from the experimental energy-loss spectra of the reflected electrons of MnxSi1 − x (0 ≤ x ≤ 1) composite structures. It is shown that the minimum values for the dependences of the product λK on the electron-energy loss can be used for the quantitative determination of element concentrations in this composite structure.

Validity of automated x-ray photoelectron spectroscopy algorithm to determine the amount of substance and the depth distribution of atoms

The author reports a systematic study of the range of validity of a previously developed algorithm for automated x-ray photoelectron spectroscopy analysis, which takes into account the variation in both peak intensity and the intensity in the background of inelastically scattered electrons. This test was done by first simulating spectra for the Au4d peak with gold atoms distributed in the form of a wide range of nanostructures, which includes overlayers with varying thickness, a 5 Å layer of atoms buried at varying depths and a substrate covered with an overlayer of varying thickness. Next, the algorithm was applied to analyze these spectra. The algorithm determines the number of atoms within the outermost 3 λ of the surface. This amount of substance is denoted AOS3λ (where λ is the electron inelastic mean free path). In general the determined AOS3λ is found to be accurate to within ∼10–20% depending on the depth distribution of the atoms. The algorithm also determines a characteristic length L, which was found to give unambiguous information on the depth distribution of the atoms for practically all studied cases. A set of rules for this parameter, which relates the value of L to the depths where the atoms are distributed, was tested, and these rules were found to be generally valid with only a few exceptions. The results were found to be rather independent of the spectral energy range (from 20 to 40 eV below the peak energy) used in the analysis.

Inelastic mean free path from reflectivity of slow electrons

The inelastic mean free path (IMFP) of electrons is derived using a new approach based on the low-energy electron reflectivity from ultrathin films. The thickness-dependent quantum size oscillations as a function of electron energy observed in the reflectivity of slow electrons are modeled using an absorbing Fabry-P\'erot interferometer consisting of vacuum, film, and substrate. The absorbing properties of the film are represented by the imaginary part of the complex refractive index associated with the IMFP which determines the amplitude of the electron reflectivity oscillations. Using this formalism for an Fe film on W(110), the IMFP in Fe is found in the energy range from 4 to 18 eV above the vacuum level. In contrast to the common notion, the IMFP in Fe is shown to have a very weak energy dependence at low energy. The results are in good agreement with independent IMFP measurements found in thickness-dependent photoemission experiments.

Stopping Powers and Inelastic Mean Free Path of 100 eV to 30 keV Electrons in Zirconium Silicates

We have determined the electron stopping power (SP) and inelastic mean free path (IMFP) of (ZrO 2 ) x (SiO 2 ) 1-x (x=1, 0.75, 0.5, 0.25, 0) for electron energies from 100 eV to 30 keV by means of modified Born–Ochkur equations. The energy loss function (ELF) is required in the calculation of SP and IMFP. We used the electron energy losses from 0 to 80 eV obtained by quantitative analysis of reflection electron energy-loss spectroscopy (REELS) spectra. The values of SP and IMFP for high contents of ZrO 2 (x=50% and x=75%) in Zr-silicates are similar to those of ZrO 2 , and similar to those of SiO 2 for low contents of ZrO 2 (x=25%) in Zr-silicates. There are small differences in the values of SP and IMFP for ZrO 2 and SiO 2 .We found that the SP decreases while the IMFP increases with increasing electron energy. We have demonstrated that the ELF obtained from the quantitative analysis of REELS spectra provide us with a straightforward way to determine SP and IMFP for alloy materials by using modified Born-Ochkur equations. Received: 04 December 2012; Revised: 18 December 2012; Accepted: 19 December 2012

Finite temperature inelastic mean free path and quasiparticle lifetime in graphene

We adopt the GW approximation and random phase approximation to study finite temperature effects on the inelastic mean free path and quasiparticle lifetime by directly calculating the imaginary part of the finite temperature self-energy induced by electron-electron interaction in extrinsic and intrinsic graphene. In particular, we provide the density-dependent leading order temperature correction to the inelastic scattering rate for both single-layer and double-layer graphene systems. We find that the inelastic mean free path is strongly influenced by finite-temperature effects. We present the similarity and the difference between graphene with linear chiral band dispersion and conventional two dimensional electron systems with parabolic band dispersion. We also compare the calculated finite temperature inelastic scattering length with the elastic scattering length due to Coulomb disorder, and comment on the prospects for quantum interference effects showing up in low density graphene transport. We also carry out inelastic scattering calculation for electron-phonon interaction, which by itself gives rather long carrier mean free paths and lifetimes since the deformation potential coupling is weak in graphene, and therefore electron-phonon interaction contributes significantly to the inelastic scattering only at relatively high temperatures.

Sample-morphology effects on x-ray photoelectron peak intensities

The authors have used the National Institute of Standards and Technology Database for the Simulation of Electron Spectra for Surface Analysis to simulate photoelectron spectra from the four sample morphologies considered by Tougaard [J. Vac. Sci. Technol. A 14, 1415 (1996)]. These simulations were performed for two classes of materials, two instrument configurations, and two conditions, one in which elastic scattering is neglected (corresponding to the Tougaard results) and the other in which it is included. The authors considered the Cu/Au morphologies analyzed by Tougaard and similar SiO2/Si morphologies since elastic-scattering effects are expected to be smaller in the latter materials than the former materials. Film thicknesses in the simulations were adjusted in each case to give essentially the same chosen Cu 2p3/2 or O 1s peak intensity. Film thicknesses with elastic scattering switched on were systematically less than those with elastic scattering switched off by up to about 25% for the Cu/Au morphologies and up to about 14% for the SiO2/Si morphologies. For the two morphologies in which the Cu 2p3/2 or O 1s peak intensity was attenuated by an overlayer, the ratios of film thicknesses with elastic scattering switched on to those with elastic scattering switched off varied approximately linearly with the single-scattering albedo, a convenient measure of the strength of elastic scattering. This variation was similar to that of the ratio of the effective attenuation length to the inelastic mean free path for the photoelectrons in the overlayer film. For the two morphologies in which the Cu 2p3/2 or O 1s photoelectrons originated from an overlayer film, the ratios of film thicknesses with elastic scattering switched on to those with elastic scattering switched off varied more weakly with the single-scattering albedo. This weaker variation was attributed to the weaker effects of elastic scattering for photoelectrons originating predominantly from near-surface atoms than for photoelectrons that travel through an overlayer film.

Surface excitations in electron spectroscopy. Part I: dielectric formalism and Monte Carlo algorithm

The theory describing energy losses of charged non-relativistic projectiles crossing a planar interface is derived on the basis of the Maxwell equations, outlining the physical assumptions of the model in great detail. The employed approach is very general in that various common models for surface excitations (such as the specular reflection model) can be obtained by an appropriate choice of parameter values. The dynamics of charged projectiles near surfaces is examined by calculations of the induced surface charge and the depth- and direction-dependent differential inelastic inverse mean free path (DIIMFP) and stopping power. The effect of several simplifications frequently encountered in the literature is investigated: differences of up to 100% are found in heights, widths, and positions of peaks in the DIIMFP. The presented model is implemented in a Monte Carlo algorithm for the simulation of the electron transport relevant for surface electron spectroscopy. Simulated reflection electron energy loss spectra are in good agreement with experiment on an absolute scale. Copyright © 2012 John Wiley & Sons, Ltd.

Energy Level Shifts in Spiro-OMeTAD Molecular Thin Films When Adding Li-TFSI

Hard X-ray photoelectron spectroscopy (HAXPES) has been used to study the effects of adding Li-TFSI to hole conducting molecular thin films of 2,2′,7,7′-tetrakis(N,N′-di-p-methoxyphenylamine)-9,9′-spirobifluorene (spiro-OMeTAD). The work shows that a procedure of mixing a Li-TFSI solution into a spiro-OMeTAD solution, and subsequent spin-coating this mixture into a solid thin film causes the Fermi level of the molecular film to move closer to the HOMO level. Hence, adding the Li-TFSI gives similar effects to spiro-OMeTAD as a p-dopant. Specific effects from doping on the valence levels were also characterized. Absorbance measurements also showed that the spiro-OMeTAD film was partially oxidized when Li-TFSI was added before spin-coating. By varying the photon energy in the photoelectron spectroscopy measurements, the probe depth varies between being surface sensitive (<1 nm) and bulk sensitive (inelastic mean free path ≥10 nm). This property was used to follow differences in the composition at different depth of the spiro-OMeTAD/Li-TFSI film. It could be concluded that there was a concentration gradient in the molecular film and that the concentration of Li-TFSI was dominating at the interface between the spiro-OMeTAD/Li-TFSI film and vacuum.

Theoretical and experimental developments in the determination of electron energy loss functions and inelastic mean free paths in elemental solids and binary compounds

We present a new theoretical representation of the electron energy loss function in terms of partial plasmon poles. This representation allows the determination of electron inelastic mean free paths from a known optical spectrum without empirical fitting, and for the first time, with consistent fulfilment of optical sum rules. We compare the new theory to recent experimental determinations of the inelastic mean free path and demonstrate improved agreement.

The X-ray Extended Range Technique a model for investigating X-ray and electron collision processes at a synchrotron

New techniques at synchrotrons can not only drive higher accuracy, structural information and insight in photoabsorption and inelastic scattering of the photon, but also inelastic scattering of the electron. This is important for fields such as XAFS, XANES and powder diffraction, but has also initiated new fields of nanoroughness measurement, measurement of electron inelastic mean free paths, bonding information at an accuracy of crystallographic determination, and similar advances for fluorescence and scattering investigations. We summarise and present some key opportunities for research and development.

Electron inelastic mean free paths in Ti, TiC, TiN and TiO2: A Theoretical Approach

Electron mean free paths are calculated as functions of incident energy for Ti, TiC, TiN and TiO2 in solid. Microscopic calculations are done in each case with the atomic-molecular scattering models.

Structural and electronic characterization of self-assembled molecular nanoarchitectures by X-ray photoelectron spectroscopy

Molecular monolayers and similar nanoarchitectures are indicative of the promising future of nanotechnology. Therefore, many scientists recently devoted their efforts to the synthesis, characterization, and properties of mono- and multilayer-based systems. In this context, X-ray photoelectron spectroscopy is an important technique for the in-depth chemical and structural characterization of nanoscopic systems. In fact, it is a surface technique suitable for probing thicknesses of the same order of the photoelectron inelastic mean free paths (a few tens of ångströms) and allows one to immediately obtain qualitative and quantitative data, film thickness, surface coverage, molecule footprint, oxidation states, and presence of functional groups. Nevertheless, other techniques are important in obtaining a complete spectroscopic characterization of the investigated systems. Therefore, in the present review we report on X-ray photoelectron spectroscopy of self-assembled molecular mono- and multilayer materials including some examples on which other characterization techniques produced important results.

Penetration range and backscattering ratio of low-energy electrons in metals

The accuracy of the Ashley's optical-data model [J.C. Ashley, J. Electron Spectrosc. Relat. Phenom. 50 (1990) 323] for describing the energy loss rate and inelastic mean free path of low-energy electrons in Al and Cu has been examined through the use of Ashley's model for calculating the electron penetration range. The latter has also been calculated using the empirical expressions reported by Iskef et al. [Phys. Med. Biol. 28 (1983) 535] and Gryzinski excitation function. The resulting range of penetration is used for determining the electron backscattering coefficients via the use of Vicanek and Urbassek theory [Phys. Rev. B 44 (1991) 7234] where the transport cross-sections are obtained from Rouabah et al. [Appl. Surf. Sci. 255 (2009) 6217] approximation. Besides the electron backscattering coefficients have been calculated from Monte Carlo simulation in which the inelastic scattering processes are handled using Ashley dielectric approach. It is found that the use of Ashley's optical model via Monte-Carlo method gives backscattering coefficients more accurate than those obtained via Vicanek and Urbassek theory. This confirms the accuracy of Ashley's optical model and shows that the Monte-Carlo method is much more accurate and precise than the Vicanek and Urbassek semi-empirical approach.

Electron inelastic mean free paths in solids: A theoretical approach

In the present paper, the inelastic mean free path (IMFP) of incident electrons is calculated as a function of energy for silicon (Si), oxides of silicon (SiO2), SiO, and Al2O3 in bulk form by employing atomic/molecular inelastic cross sections derived by using a semi-empirical quantum mechanical method developed earlier. A general agreement of the present results is found with most of the available data. It is of great importance that we have been able to estimate the minimum IMFP, which corresponds to the peak of inelastic interactions of incident electrons in each solid investigated. New results are presented for SiO, for which no comparison is available. The present work is important in view of the lack of experimental data on the IMFP in solids.

Looking Deeper: Angle-Resolved Photoemission with Soft and Hard X-rays

Traditional angle-resolved photoemission (ARPES) with excitation in the ca. 20 to 150 eV range has clearly evolved to be the technique of choice for studying the electronic structure of surfaces and complex new strongly correlated and magnetic materials. However, it is clear that ARPES with excitation only up to 150 eV or so remains a very surface-sensitive probe, thus necessitating careful in-situ sample treatment, cleaving, or even synthesis to avoid the measurement of surface-associated artifacts. A key measure of this surface sensitivity is the electron inelastic mean free path (IMFP orΛe), which measures the mean depth of electron emission without inelastic scattering, and both experimental [1, 2] and theoretical [3] IMFP studies showing that the only reliable way to increase bulk or buried layer/interface sensitivity for all material types is to go to higher photon energies in the soft X-ray (ca. 0.5–2 keV) or hard X-ray (ca. 2–10 keV) regime.

Studies of the hot-pressed TiN material by electron spectroscopies

We analyzed chemical composition and electron transport phenomena in surface and sub-surface region of hot-pressed TiN specimens using a combination of X-ray photoelectron spectroscopy (XPS) and elastic-peak electron spectroscopy (EPES) techniques. Both the surface chemical composition and the elements distribution in the bulk of TiN specimens were determined using XPS and XPS depth profiling analysis. In addition to TiN, a mixture of Ti oxynitride (TiOxNy) and TiO2 compounds as well as carbon contaminants have been detected in the surface region of the TiN specimens. The elemental depth-profiles disclosed uniform chemical bulk composition formed mainly by titanium and nitrogen as well as carbon and oxygen contaminants. Surface enrichment of Ti was evidenced as result of Ar ion-induced preferential sputtering of nitrogen. The inelastic mean free path (IMFP) data evaluated from the relative EPES for electron energies 0.5–2keV were uncorrected for surface excitations and compared with those calculated from the predictive TPP-2M formula for the measured surface composition. Except to the electron energy of 0.5keV, a good agreement was found between the measured and predicted IMFPs in the TiN specimen. The higher discrepancies in the measured IMFPs at the lowest energy can be explained by the surface excitation effect. The smallest root-mean-square-deviation and the mean percentage deviation of 2.8Å and 14.8%, respectively, were found between EPES IMFP data and those predicted for TiN with respect to the Ni standard.

Inelastic and elastic mean free paths from FIB samples of metallic glasses

We have used focused ion beam (FIB) milling and scanning electron microscopy (SEM) to prepare samples of known thickness for measurement of the electron scattering elastic and inelastic mean free paths (EMFP and IMFP respectively) of three metallic glasses, Cu(64.5)Zr(35.5), Zr(50)Cu(45)Al(5), and Al(87)Y(7)Fe(5)Cu. After measuring the EMFP and IMFP in a scanning transmission electron microscope, we used the FIB to coat the lamellae with carbon on the top and bottom surfaces, which eliminated secondary electron emission from those surfaces and made SEM measurements of their thickness more reliable. At 200 kV, we find IMFP/ EMFP values of 146±2/43±1, 163±1/41±1, and 149±1/85±1 nm, respectively for the three glass compositions. Our results differ from available models for the IMFP by as much as 50%.

Image simulation for atomic resolution secondary electron image

It has been demonstrated recently that an atomic resolution secondary electron (SE) image can be achieved with a scanning transmission electron microscope (STEM) equipped with a probe-aberration corrector. Its high sensitivity to the surface structure provides a powerful tool to simultaneously study both surface and bulk structure in the STEM, in the combination with the annular dark field (ADF) image. To quantitatively explain the atomic resolution SE image and retrieve surface-structure information, an image simulation is required. Here, we develop a method to simultaneously calculate, for the first time, the atomic resolution SE and ADF-STEM images, based on the multislice method with a frozen-phonon approximation. An object function for secondary electrons, derived from the inelastic scattering, is used to calculate the intensity distribution of the secondary electrons emitted from each slice. The simulations show that the SE image contrast is sensitive to the surface structure and the electron inelastic mean free path, but insensitive to specimen thickness when the thickness is more than 5 nm. The simulated SE images for SrTiO(3) crystal show good agreement with the experimental observations.

Chemical and Elemental Depth Profiling of Very Thin Organic Layers by Constant Kinetic Energy XPS: A New Synchrotron XPS Analysis Strategy

We present a new synchrotron X-ray photoelectron spectroscopy strategy for surface chemical analysis of materials. Our approach is based on the acquisition of photoelectron spectra at constant kinetic energies with the help of a tunable synchrotron X-radiation source. This ensures both constant and tunable information depth for all elements in a very thin organic layer. Many of the problems known to XPS depth profiling using laboratory equipment are thereby avoided. Using our methodology, the 95% information depth, z(95%), can be tuned down to about 0.7 nm in organic materials. The upper limit in our study at the HE-SGM monochromator dipole magnet beamline at the synchrotron radiation source BESSY II is about 4.3 nm. Elemental quantification is achieved through relative sensitivity factors (RSF) specific to the measurement conditions, determined either with the help of calculated photoionization cross sections and inelastic mean free paths or experimentally. The potential of the technique is demonstrated for the in-depth analysis of plasma deposited nitrogen-rich organic thin films used in biomedical applications.