Inelastic Mean Free Path Research Articles

Combined first-principles-Monte Carlo analysis to evaluate the effect of surface hydrogen on the secondary electron yield of nickel

Secondary electron yield (SEY) modeling of Ni(110) surface has been carried out with and without the inclusion of wavevector-dependent harmonic corrections (which alter both the inelastic mean free path and stopping power) and is compared to available experimental data. The correction is shown to improve predictions of the inelastic electron mean free path in Ni and yield better agreement with experimental SEY data. It is found that the SEY is strongly dependent on the presence of adsorbates on surfaces. An increase of hydrogen on the surface, for example, is predicted to result in a significant enhancement in the secondary electron yield, with the positional placement of hydrogen layers on or near the Ni surface influencing the SEY. Using first-principles calculations, the permittivities work function and adsorption energy of various Ni systems have also been calculated, and have shown to compare favorably with available experimental data, and have been used in the present Monte Carlo calculations of electron transport.

Measurement of the surface excitation parameter of Kapton, polyethylene (PE), polymethyl methacrylate (PMMA), polystyrene (PS) and polytetrafluoroethylene (PTFE)

Reflection electron energy loss spectra (REELS) were measured for five insulating organic compounds: Kapton, polyethylene (PE), poly(methyl methacrylate) (PMMA), polystyrene (PS) and polytetrafluoroethylene (PTFE), as well as for Ni and Si, in the energy range between 200 and 1600 eV. The average number of surface excitations for a single surface crossing were determined from the experimental data and were found to be considerably smaller than for earlier studied materials, which mainly consisted of elemental metals [Surf. Sci. 486(2001)L461]. The surface excitation parameter, a material parameter used to quantify the relative intensity of surface losses in (photo)electron spectroscopy, was extracted from the data and compared with values found in the literature. The results indicate that surface excitations only have a minor influence on quantification of XPS spectra of polymers. On the other hand, a correction for surface excitations turns out to be essential for measurements of the electron inelastic mean free path of polymers when a metal is used as reference material.

Calculations of electron inelastic mean free paths. XIII. Data for 14 organic compounds and water over the 50 eV to 200 keV range with the relativistic full Penn algorithm

We have calculated inelastic mean free paths (IMFPs) for 14 organic compounds (26‐n‐paraffin, adenine, β‐carotene, diphenyl‐hexatriene, guanine, Kapton, polyacetylene, poly (butene‐1‐sulfone), polyethylene, polymethylmethacrylate, polystyrene, poly(2‐vinylpyridine), thymine, and uracil) and liquid water for electron energies from 50 eV to 200 keV with the relativistic full Penn algorithm including the correction of the bandgap effect in insulators. These calculations were made with energy‐loss functions (ELFs) obtained from measured optical constants and from calculated atomic scattering factors for X‐ray energies. Our calculated IMFPs could be fitted to a modified form of the relativistic Bethe equation for inelastic scattering of electrons in matter from 50 eV to 200 keV. The average root‐mean‐square (RMS) deviation in these fits was 0.17%. The IMFPs were also compared with a relativistic version of our predictive Tanuma–Powell–Penn (TPP‐2M) equation. The average RMS deviation in these comparisons was 7.2% for energies between 50 eV and 200 keV. This average RMS deviation is smaller than that found in a similar comparison for our group of 41 elemental solids (11.9%) and for our group of 42 inorganic compounds (10.7%) for the same energy range. We found generally satisfactory agreement between our calculated IMFPs and values from other calculations for energies between 200 eV and 10 keV. We also found reasonable agreement between our IMFPs for organic compounds and measured IMFPs for energies between 50 eV and 200 keV. Substantial progress for IMFP measurements for liquid water has been made in recent years through the invention of liquid water microjet photoelectron spectroscopy and droplet photoelectron imaging. We found that the IMFPs from these experiments and the associated analyses were larger than our IMFPs by factors between two and four for energies between about 30 eV and 1000 eV. The energy dependences of the measured IMFPs are, however, similar to that of our IMFPs in the same energy range. Since IMFPs calculated from the same algorithm for a number of inorganic compounds agree reasonably well with measured IMFPs for energies between 100 eV and 200 keV, the large differences between IMFPs for water from recent experiments and our results are surprising and need to be resolved with additional experiments.

Quantification of hard X‐ray photoelectron spectroscopy: Calculating relative sensitivity factors for 1.5‐ to 10‐keV photons in any instrument geometry

A method for the rapid determination of theoretical relative sensitivity factors (RSFs) for hard X‐ray photoelectron spectroscopy (HAXPES) instruments of any type and photon energy has been developed. We develop empirical functions to describe discrete theoretically calculated values for photoemission cross sections and asymmetry parameters across the photon energy range from 1.5 to 10 keV for all elements from lithium to californium. The formulae describing these parameters, in conjunction with similar practical estimates for inelastic mean free paths, allow the calculation of a full set of theoretical sensitivity factors for a given X‐ray photon energy, X‐ray polarisation and instrument geometry. We show that the anticipated errors on these RSFs are less than the typical errors generated by extracting X‐ray photoelectron spectroscopy (XPS) intensities from the spectra and thus enable adequate quantification for any XPS/HAXPES experiment up to 10 keV. A spreadsheet implementation of this method is provided in the supporting information, along with example RSFs for existing commercial instruments.

Low-energy electron distributions from the photoionization of liquid water: a sensitive test of electron mean free paths.

The availability of accurate mean free paths for slow electrons (<50 eV) in water is central to the understanding of many electron-driven processes in aqueous solutions, but their determination poses major challenges to experiment and theory alike. Here, we describe a joint experimental and theoretical study demonstrating a novel approach for testing, and, in the future, refining such mean free paths. We report the development of Monte-Carlo electron-trajectory simulations including elastic and inelastic electron scattering, as well as energy loss and secondary-electron production to predict complete photoelectron spectra of liquid water. These simulations are compared to a new set of photoelectron spectra of a liquid-water microjet recorded over a broad range of photon energies in the extreme ultraviolet (20–57 eV). Several previously published sets of scattering parameters are investigated, providing direct and intuitive insights on how they influence the shape of the low-energy electron spectra. A pronounced sensitivity to the escape barrier is also demonstrated. These simulations considerably advance our understanding of the origin of the prominent low-energy electron distributions in photoelectron spectra of liquid water and clarify the influence of scattering parameters and the escape barrier on their shape. They moreover describe the reshaping and displacement of low-energy photoelectron bands caused by vibrationally inelastic scattering. Our work provides a quantitative basis for the interpretation of the complete photoelectron spectra of liquids and opens the path to fully predictive simulations of low-energy scattering in liquid water.

Electron Inelastic Mean Free Path in UO2 and (U, Pu)O2 Fuels

Electron Inelastic Mean Free Path in UO2 and (U, Pu)O2 Fuels

Benchmarking the ideal sample thickness in cryo-EM

The relationship between sample thickness and quality of data obtained is investigated by microcrystal electron diffraction (MicroED). Several electron microscopy (EM) grids containing proteinase K microcrystals of similar sizes from the same crystallization batch were prepared. Each grid was transferred into a focused ion beam and a scanning electron microscope in which the crystals were then systematically thinned into lamellae between 95- and 1,650-nm thick. MicroED data were collected at either 120-, 200-, or 300-kV accelerating voltages. Lamellae thicknesses were expressed in multiples of the corresponding inelastic mean free path to allow the results from different acceleration voltages to be compared. The quality of the data and subsequently determined structures were assessed using standard crystallographic measures. Structures were reliably determined with similar quality from crystalline lamellae up to twice the inelastic mean free path. Lower resolution diffraction was observed at three times the mean free path for all three accelerating voltages, but the data quality was insufficient to yield structures. Finally, no coherent diffraction was observed from lamellae thicker than four times the calculated inelastic mean free path. This study benchmarks the ideal specimen thickness with implications for all cryo-EM methods.

Interfacial Properties of a PEM Water Electrolysis Pt Electrode Probed by Operando Tender Ambient Pressure X-Ray Photoelectron Spectroscopy

The probe of the chemical, structural, and electronic properties at the electrode-electrolyte interfaces under operational conditions is critical for the mechanistic study and optimization of all the electrochemical systems and has therefore been at the center of numerous studies [1]. Soft X-ray Ambient pressure X-ray photoelectron spectroscopy (APXPS) has been known as a promising in-situ/operando technique, but its applications in the probe of a realistic solid/liquid interface under ambient conditions has been limited by the short inelastic mean free path (IMFP) of photoelectrons in the liquid medium. Here, inspired by prior work [2,3] and taking advantage of the synchrotron tender X-ray source (Beamline 9.3.1) at the Advanced Light Source of the Lawrence Berkeley National Laboratory [4], the IMFP can be significantly increased. A larger IMFP enables interfacial characterization under higher background pressures and through liquid overlayer greater than 30 nm in thickness. We have designed and built a graphene sealed operando electrolysis electrochemical cell that is compatible with an existing tender X-ray APXPS setup for the investigation of electrode-electrolyte interfaces under operational conditions. The present setup will be utilized to probe various systems involving solid/liquid interfaces, including but not limited to the interactions of ions, the solvation of salts, and electrocatalysis.In this work, the utilization of tender X-rays (2000 – 6000 eV) facilitates investigations of the electrode-electrolyte interface with a liquid-layer thickness of tens of nanometers, which can be preserved within the sandwiched region between the topmost graphene and the Pt nanoparticle loaded proton exchange membrane (PEM). In addition, the environmental water vapor pressure within the analysis chamber was kept at the water vapor pressure at 298 K (~15 Torr). The setup allows the study of a water splitting electrolyzer under real working conditions, where the electrocatalytic performance and the operando photoemission spectroscopy can be simultaneous investigated. As a proof-of-concept, Pt nanoparticle-catalyzed oxygen evolution reaction (OER) was investigated under operando conditions. The electrochemistry and detailed analysis of the photoemission spectra demonstrating the evolution of the chemical, structural, and electronic properties at the H2O/Pt interface under the influence of external electrical field will be presented.

Development of Operando Analytical System for Simultaneous Measurements of Electrochemical Reaction Rate and Haxpes

To quantitatively understand the electrochemical reaction, the reaction rate must be measured such as by hydrodynamic voltammetry. At the same time, the electronic states of the electrode surface closely related to the bonding of atoms and molecules, as well as to the reaction mechanisms, must be understood. We have designed and constructed an operando analytical system for the simultaneous measurements of the electrochemical reaction rate and the hard X-ray photoemission spectrum.1) In this system, a solution containing reactants was continuously supplied in a Hagen-Poiseuille flow with a channel flow electrode (CFE) method to a specimen, such as catalyst, under the control of temperature, pressure, concentration, and solution flow rate, so that the electrochemical reaction rate is able to be accurately measured or controlled. Two different environments, solution and ultra-high vacuum, were connected with an ultra-thin Au/SixNy window with a thickness of 20 nm (Fig. 1(a)) to make the operando hard X-ray photoemission spectroscopy (HAXPES) possible during the steady-state electrochemical reaction. In this report, the Au thin film 5 nm in thickness was used as a model electrode.Figure 1(b) shows a schematic illustration of the operando reaction rate-HAXPES measurement system. This system was installed to a UHV chamber at the beamline BL46XU of SPring-8, Japan.2) The energy of the synchrotron X-ray was 14 keV. The analyzer was Focus HV-CSA 300/15. Figure 1(c) shows the chronoamperometry result of the oxygen reduction reaction obtained at 0.4 V vs. Ag/AgCl sat. KCl in 0.1 M HClO4 at room temperature. From the current, the reaction rate was calculated as 0.9 nmol s-1 cm-2.1) Figure 1(d) shows the Au3d5/2 HAXPES spectrum of the Au thin film electrode measured during electrochemical reaction (blue circles for data and solid line for fitting). The horizontal axis indicates the kinetic energy of photoelectrons. The green triangles and solid line are of the spectrum of the reference metal Au. When the kinetic energy of the photoelectrons of Au3d5/2 was 11,809 eV, the inelastic mean free path estimated from the TPP-2M equation was 8.7 nm.3) Therefore, the HAXPES signal was from the entire Au film electrode.With this high energy of X-ray, HAXPES of the specimens located on this Au electrode can be measured as expected. Separately, a Pt film was deposited onto the Au thin film electrode. After the measurement of the Au peak, only the scanning energy was changed to observe clearly the Pt3d5/2 peak from the Pt film through the underlying Au thin film. In the future, specimens, such as fuel cell catalysts, can be located on the Au thin film electrode for the operando measurements. References 1) K. Suda et al., J. Electrochem. Soc., (2021) https://doi.org/10.1149/1945-7111/abf9712) H. Oji et al., J. Phys. Conf. Ser., 502, 012006 (2014).3) S. Tanuma et al., Surf. Interface Anal., 21, 165 (1994). Figure 1

Cryo-TEM simulations of amorphous radiation-sensitive samples using multislice wave propagation.

Image simulation plays a central role in the development and practice of high-resolution electron microscopy, including transmission electron microscopy of frozen-hydrated specimens (cryo-EM). Simulating images with contrast that matches the contrast observed in experimental images remains challenging, especially for amorphous samples. Current state-of-the-art simulators apply post hoc scaling to approximate empirical solvent contrast, attenuated image intensity due to specimen thickness and amplitude contrast. This practice fails for images that require spatially variable scaling, e.g. simulations of a crowded or cellular environment. Modeling both the signal and the noise accurately is necessary to simulate images of biological specimens with contrast that is correct on an absolute scale. The 'frozen plasmon' method is introduced to explicitly model spatially variable inelastic scattering processes in cryo-EM specimens. This approach produces amplitude contrast that depends on the atomic composition of the specimen, reproduces the total inelastic mean free path as observed experimentally and allows for the incorporation of radiation damage in the simulation. These improvements are quantified using the matched filter concept to compare simulation and experiment. The frozen plasmon method, in combination with a new mathematical formulation for accurately sampling the tabulated atomic scattering potentials onto a Cartesian grid, is implemented in the open-source software package cisTEM.

Improved depth information from routine analysis of the inelastic background of XPS and HAXPES spectra using optimized two‐ and three‐parameter cross‐sections

Determination of the depth distribution of complex nanostructures by X‐ray photoelectron spectroscopy (XPS) inelastic background analysis may be complicated if the sample materials have widely different inelastic scattering cross‐sections. It was recently demonstrated that this may be solved by using a mixture of cross‐sections. This permits retrieval of depth distributions of complex stacks and deeply buried layers with a typical 5% accuracy. This requires however that the cross‐sections of the individual sample materials are known which is often not the case and this can complicate practical use for routine analysis. In this paper, we explore to what extent a suitable two‐ or three‐parameter cross‐section can be defined independent of prior knowledge of the cross‐sections involved but simply defined by fitting the cross‐section parameters to the spectrum being analyzed. This paper presents a theoretical study following our recent paper that explored how to make the best choice of inelastic mean free path and inelastic scattering cross‐section for the inelastic background analysis with the Quases‐Tougaard software. It was previously shown that a rough analysis of the inelastic background could give a good idea of the depth distribution. Here, we demonstrate with model spectra from buried layers created with Quases‐Tougaard Generate software that a rather accurate analysis can be performed for very different cases with an average ~5% error. This analysis is easy to apply as it only needs the two‐ or three‐parameter cross‐sections generated with the Quases‐Tougaard software. This study is aimed to improve routine analysis of the inelastic background of XPS and hard X‐ray photoelectron spectroscopy (HAXPES) spectra.

Low-Energy Electron Inelastic Mean Free Path of Graphene Measured by a Time-of-Flight Spectrometer.

The detailed examination of electron scattering in solids is of crucial importance for the theory of solid-state physics, as well as for the development and diagnostics of novel materials, particularly those for micro- and nanoelectronics. Among others, an important parameter of electron scattering is the inelastic mean free path (IMFP) of electrons both in bulk materials and in thin films, including 2D crystals. The amount of IMFP data available is still not sufficient, especially for very slow electrons and for 2D crystals. This situation motivated the present study, which summarizes pilot experiments for graphene on a new device intended to acquire electron energy-loss spectra (EELS) for low landing energies. Thanks to its unique properties, such as electrical conductivity and transparency, graphene is an ideal candidate for study at very low energies in the transmission mode of an electron microscope. The EELS are acquired by means of the very low-energy electron microspectroscopy of 2D crystals, using a dedicated ultra-high vacuum scanning low-energy electron microscope equipped with a time-of-flight (ToF) velocity analyzer. In order to verify our pilot results, we also simulate the EELS by means of density functional theory (DFT) and the many-body perturbation theory. Additional DFT calculations, providing both the total density of states and the band structure, illustrate the graphene loss features. We utilize the experimental EELS data to derive IMFP values using the so-called log-ratio method.

Properties of Au film on Ru(0001) revealed by AES, LEED, and DEPES

In this work the application of the surface sensitive experimental methods such as Auger electron spectroscopy, low energy electron diffraction, and directional elastic peak electron spectroscopy is shown to characterize the growth mode, the long and short range order of Au layers on the Ru(0001) surface. The adsorption was carried out at different substrate temperatures from room temperature till 460 °C. Auger signal from the substrate and the adsorbate recorded during the continuous Au adsorption indicates the formation of the first and then the second gold wetting layer at elevated substrate temperatures. At room temperature the formation of the second layer just before the completion of the first monolayer occurs. Further adsorption leads to the growth of three dimensional gold islands on 2 ML of Au on Ru(0001). At elevated temperatures the reduction of the Auger signal drop rate from the substrate and the signal rise rate from the adsorbate after the formation of 2 ML of Au can be rationalized by the coalescence of three dimensional Au islands and/or the decrease of the sticking coefficient of gold. Above 460 °C the saturation of Auger signals corresponding to 2 ML of Au is observed. The LEED pattern observations reveal the long range order within the clean and covered by about 5 ML of gold Ru(0001). The diffraction spots of the adsorbate reflect the Au(111) arrangement. The application of the DEPES method to the clean and covered by gold Ru(0001) surface reveals the presence of A and B type terraces on the Ru(0001) surface, as well as mutually rotated by 180° adsorbate domains, which exhibit the 12¯1111Au//01¯100001Ru and 1¯21¯111Au//01¯100001Ru orientations with respect to the crystalline substrate. The detailed R-factor analysis of experimental and theoretical DEPES distributions, the latter obtained with the use of the multiple scattering calculations, reveals equal population of A and B type Ru(0001) terraces, as well as unrotated and rotated Au(111) domains, which results in the six-fold symmetry DEPES intensity distributions for clean and covered substrate. The discussion of DEPES results concerns the adsorbate and substrate structures, inelastic mean free paths, and scattering properties of individual Au and Ru atoms described by the scattering factors and differential scattering cross sections.

Analytical Formula for the Electron Inelastic Mean Free Path

The electron inelastic mean free path (IMFP) is the average distance between successive inelastic collisions of an electron moving in a medium with a given energy. Within the dielectric formalism, the IMFP is defined by an integral. The problem is that the integration is rather complicated. In 2015, an analytical formula for IMFPs was derived from this definition (J. Phys. Chem. C 2015, 119, 23627–23631). However, the derived formula is restricted to energies above 500 eV. This limitation is overcome in this work. The lower limit of the present analytical formula for IMFPs is about 50 eV.

Vertical position of Sr dopants in the SrxBi2Se3 superconductor

The discovery of topological superconductivity in doped ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ made this class of materials highly important for the field of condensed matter physics. However, the structural origin of the superconducting state remained elusive, despite being investigated intensively in recent years. We use scanning tunneling microscopy and the normal incidence x-ray standing wave (NIXSW) technique in order to determine the vertical position of the dopants---one of the key parameters for understanding topological superconductivity in this material--- for the case of ${\mathrm{Sr}}_{x}{\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$. In particular, we analyze the NIXSW data in consideration of the inelastic mean free path of the photoemitted electrons, which allows us to distinguish between symmetry-equivalent sites. We find that Sr atoms are not situated inside the van der Waals gap between the ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ quintuple layers but rather in the quintuple layer close to the outer Se planes.

Understanding the Exposure Process in the Extreme Ultra Violet Lithography.

Although being the optical lithography, the extreme ultraviolet (EUV) lithography with 13.5-nm wavelength is very different from the deep ultraviolet (DUV) lithography with 193-nm wavelength. Hence, the understanding of the complex detailed EUV mechanisms to cause a chemical reaction in chemically amplified resists (CARs) is required to develop EUV resists and exposure process. In this paper, for organic, metal-organic and metal-oxide resists, the electron-scattering model of exposure mechanisms needs to include the elastic and inelastic mean free paths. On top of that, Dill's parameters of DUV and EUV resisters from the photo-generated reaction are discussed to indicate the physical and chemical characteristics. For CAR and EUV resists, Dill B parameter is large than Dill A and B parameters.

Probing the Spin State of Spin-Crossover Complexes on Surfaces with Vacuum Ultraviolet Angle-Resolved Photoemission Spectroscopy

Spin-crossover complexes in direct contact with substrates have sparked considerable interest, in particular, in view of their potential applications in molecular electronics. While a huge number of spin-crossover complexes is available, many of them are not robust enough to withstand the sample preparation and/or the interaction with the substrate. The techniques usually employed for these investigations, namely, near-edge X-ray absorption fine structure spectroscopy and low-temperature scanning tunneling microscopy, are not adapted for systematic studies because of the limited access to synchrotron-radiation facilities and complexity of the (indirect) spin determination, respectively. Here, we detail a methodology using a (more) commonly available technique, namely, vacuum ultraviolet (angle-resolved) photoemission spectroscopy, to determine the spin state of layers of three different spin-crossover complexes with thicknesses down to the submonolayer regime. We present an approach to determine the thicknesses of the investigated layers, relying on the inelastic mean free path of electrons determined from combined photoemission and X-ray absorption measurements. We report on the high-spin to low-spin relaxation dynamics of spin-crossover (SCO) layers and the influence of the ultraviolet light on these dynamics. While the observed relaxation processes occur on a timescale on the order of minutes, probing spin-state dynamics on the picosecond timescale is foreseeable with pump–probe photoemission spectroscopy.

Influence of Defects on the Schottky Barrier Height at BaTiO3/RuO2 Interfaces

The Schottky barrier formation between polycrystalline acceptor‐doped BaTiO3 and high work function RuO2 is studied using photoelectron spectroscopy. Schottky barrier heights for electrons of ≈1.4 eV are determined, independent of doping level and oxygen vacancy concentration of the substrates. The insensitivity of the barrier height is related to the high permittivity of BaTiO3, which results in space‐charge regions (SCRs) being considerably wider than the inelastic mean free path of the photoelectrons. SCRs at any kind of interface should, therefore, be more important for the electronic and ionic conductivities in BaTiO3 than in materials with lower permittivity. A Ba‐rich phase at the surface of reduced acceptor‐doped BaTiO3 is also identified, which is explained by the formation of Ti vacancies in the 2D electron gas region at the surface.

First principles inelastic mean free paths coupled with Monte Carlo simulation of secondary electron yield of Cu-Ni, Cu-Zn, and Mo-Li

Secondary electron yield (SEY) is relevant for widely used characterization methods (e.g., secondary electron spectroscopy and electron microscopy) and materials applications (e.g., multipactor effect). Key quantities necessary for understanding the physics of electron transport in materials and simulation of SEY are electron mean free paths (MFPs). This paper explores the impact of alloying on MFPs and SEY for Cu-Ni, Cu-Zn, and Mo-Li alloys relative to their component metals Cu, Ni, Zn, Mo, and Li. Density functional theory calculations yield density of states, Fermi energy, work function, and frequency- and momentum-dependent energy loss function. These material properties were used to calculate MFPs and Monte Carlo simulations were performed to obtain energy dependent SEY for the alloys as well for the component metals. The results show that MFPs and SEYs of the studied alloys lie between those of component pure elements but are not a simple composition weighted average. Detailed analysis of the secondary electron generation and emission process shows that the changes in the SEY of alloys relative to the SEY of their component metals depend on the changes in both electronic structure and dielectric properties of the material.

Machine learning approach for the prediction of electron inelastic mean free paths

The prediction of electron inelastic mean free paths (IMFPs) from simple material parameters is a challenging problem in studies using electron spectroscopy and microscopy. Herein, we propose a machine learning (ML) approach to predict IMFPs from some basic material property data. The ML model showed excellent performance based on the calculated IMFPs for a group of 41 elemental materials [Li, Be, C (graphite), C (diamond), C (glassy), Na, Mg, Al, Si, K, Sc, Ti, V, Cr, Fe, Co, Ni, Cu, Ge, Y, Nb, Mo, Ru, Rh, Pd, Ag, In, Sn, Cs, Gd, Tb, Dy, Hf, Ta, W, Re, Os, Ir, Pt, Au, and Bi] from a previous paper [Shinotsuka et al., Surf. Interface Anal. 47, 871 (2015); Surf. Interface Anal. 47, 1132 (2015)]. which was comparable with that of the robust Tanuma-Powell-Penn (TPP-2M) formula. The developed ML model was then extended to materials that do not have reported IMFPs in the database. The IMFPs for 18 transition and lanthanide metals (Mn, Zn, Zr, Tc, Cd, La, Ce, Pr, Nd, Pm, Sm, Eu, Ho, Er, Tm, Yb, Lu, and Hg) were predicted by the ML model. In the comparison with full-Penn algorithm-calculated IMFPs through two newly found experimental energy loss functions (ELFs), i.e., Mn and Zr, the Gaussian process regression-predicted IMFPs not only agreed well with those calculated using the TPP-2M formula in the energy range &gt;50 eV but were also consistent with the trend of IMFPs calculated through experimental ELFs in the range of 2.7--50 eV, where the TPP-2M formula cannot be used. Our findings suggest that ML is very powerful and efficient and has great potential to complete a database of IMFPs for materials that can prove solutions closer to reality than empirical models on materials with similar physical and chemical properties and can be applied to other different situations for correlated information prediction.