Differential Surface Excitation Probability Research Articles

Quantitative Interpretation of Electron Spectroscopy Signals. Extracting the Differential Inverse Inelastic Mean Free Path and Differential Surface Excitation Probability in Solids

A method for extracting the differential inelastic scattering cross sections of electrons xin(Δ) from the energy spectra of electron spectroscopy is developed. The derived cross sections are verified by interpreting experimental data on electron-energy-loss spectra, X-ray photoelectron spectroscopy, and Auger spectroscopy. The paper highlights existing methods for determining the cross sections xin(Δ) using electron-energy-loss spectra. Inconsistency in analytical solution of the inverse problem (i.e., deconvolution) is shown for calculating the inelastic scattering cross section of electrons xin(Δ). In this paper, the solution of the mathematically ill-posed problem of cross-section retrieval is based on a fitting procedure consisting in multiple direct-problem calculations, i.e., calculations of the electron spectra taking into account both elastic and inelastic multiple scattering events. To implement an efficient fitting algorithm, a high-performance procedure for solving the direct problem of determining the energy spectra of electron spectroscopy is developed. The method for calculating the spectra is based on solution of the boundary problem for the transport equation by using the invariant imbedding method. The procedure developed in this work allows the energy-loss cross sections in the surface layer and in the sample homogeneous bulk layer remote from the surface to be reconstructed. The cross sections xin(Δ) retrieved from experimental data on the electron-energy-loss spectra satisfactorily reproduce the Auger spectroscopy and X-ray photoelectron spectroscopy signals and vice versa: the cross sections xin(Δ) retrieved from the X-ray photoelectron spectroscopy data satisfactorily reproduce the electron-energy loss and Auger spectroscopy spectra. It is shown that for the description of the X-ray photoelectron spectroscopy spectra of Be, Mg, Al, Nb, and W, it is not necessary to use additional mechanisms of energy losses, so-called “intrinsic excitations”.

Determination of the Relative Concentration of Deuterium Implanted into Beryllium by Elastic Peak Electron Spectroscopy

The relative concentration of deuterium implanted into a beryllium sample is determined by elastic peak electron spectroscopy (EPES). The method of partial intensities based on solution of the boundary value problem for the transport equation by the invariant embedding method is used for subsequent determination of the energy spectra of reflected electrons. The differential inverse inelastic mean free paths (DIIMFPs) and the differential surface excitation probability (DSEP) are retrieved using a fitting procedure based on numerous solutions of the direct problem with fitting parameters. The high efficiency of the fitting procedure is based on the technique of numerical solution of equations for the partial intensities, which combines precision and a record-high calculation speed. In the work DIIMFP and DSEP are obtained for both the surface region and for a homogeneous array in the bulk. Calculations of DIIMFP and DSEP are carried out for pure beryllium and for beryllium samples implanted with deuterium. The relative concentrations of deuterium into beryllium were determined at a different fluence. The obtained values of the relative deuterium concentrations are nD/nBe = 0.12 ± 0.02 and 0.15 ± 0.03 for an irradiation dose of 5.5 × 1021 and 20.1 × 1021 m–2, respectively. The results indicate that, in comparison with the methods used earlier, the developed method allows an order of magnitude in of the sensitivity of determining the relative hydrogen-isotope concentration in compounds to be attained.

Extracting the differential inverse inelastic mean free path and differential surface excitation probability of Tungsten from X-ray photoelectron spectra and electron energy loss spectra

Precise knowledge of the differential inverse inelastic mean free path (DIIMFP) and differential surface excitation probability (DSEP) of Tungsten is essential for many fields of material science. In this paper, a fitting algorithm is applied for extracting DIIMFP and DSEP from X-ray photoelectron spectra and electron energy loss spectra. The algorithm uses the partial intensity approach as a forward model, in which a spectrum is given as a weighted sum of cross-convolved DIIMFPs and DSEPs. The weights are obtained as solutions of the Riccati and Lyapunov equations derived from the invariant imbedding principle. The inversion algorithm utilizes the parametrization of DIIMFPs and DSEPs on the base of a classical Lorentz oscillator. Unknown parameters of the model are found by using the fitting procedure, which minimizes the residual between measured spectra and forward simulations. It is found that the surface layer of Tungsten contains several sublayers with corresponding Langmuir resonances. The thicknesses of these sublayers are proportional to the periods of corresponding Langmuir oscillations, as predicted by the theory of R.H. Ritchie.

Differential inverse inelastic mean free paths and differential surface excitation probability in aluminium in the energy range of 0.5–120 keV

Electron energy loss and photoelectron spectra are obtained on the basis of transfer equation solution. The boundary problem is solved using invariant imbedding approach. The partial intensity method is used to calculate electron energy loss and photoelectron spectra. Differential inelastic electron scattering cross sections in bulk aluminium and in a surface layer are extracted by fitting procedure in an energy range 0.5–120 keV. The method of spectra computation is tested by comparison of results with the experimental data of five foreign scientific laboratories. The physical meaning of the surface-excitation parameter is discussed.

Differential inverse inelastic mean free path and differential surface excitation probability retrieval from electron energy loss spectra

Quantitative interpretation of the electron spectroscopy data requires the information on differential inverse inelastic mean free paths (DIIMFP) and differential surface excitation probabilities (DSEP). In this paper, we test an algorithm of extracting DIIMFP and DSEP from reflected electron energy loss spectra (REELS) and photo-electron spectra (PES) in which the desired functions are parametrized on the base of a classical Lorentz oscillator. Unknown parameters are found by using the fitting procedure. To account for surface excitations, the investigated samples are considered as multi-layer systems. Simulations of REELS and PES are performed by making use of the partial intensity approach. The partial intensities for the reflection function and the photo-electron density flux are computed on the base of the invariant imbedding method. Extracted DIIMFPs and DSEPs are compared with those obtained by other authors. Finally, REELS and PES spectra for Be, Mg, Al, Si, Nb and W are computed using the retrieved DIIMFPs and DSEPs, and compared with the experimental spectra. All comparisons show good agreement.

Extracting detailed information from reflection electron energy loss spectra

We use REELS (reflection electron energy loss spectroscopy) measurements at relatively large energies (up to 40keV) and good energy resolution (0.3eV) to extract the bulk and surface loss function for Au, Mo and Ta. For these cases there are small, but significant deviations between the electron-based estimates of the dielectric function as published by Werner et al. (J. Phys. Chem. Ref. Data 38 (2009) 1013), and the corresponding photon absorption/reflection based estimates. The present, higher-resolution electron-based measurements reveal more of the fine structure in the differential inverse inelastic mean free path (DIIMFP) and the differential surface excitation probability (DSEP). The same fine-structure is visible in the photon-derived estimates of the bulk and surface loss function, quantities closely related to the DIIMFP and DSEP. Thus we demonstrate that it is indeed possible to derive these fine details of the surface and bulk loss function with REELS, underlining its potential for extracting information on the dielectric function of materials.

Analysis of reflection electron energy loss spectra (REELS) for determination of the dielectric function of solids: Fe, Co, Ni

A simple procedure is developed to simultaneously eliminate multiple scattering contributions from two reflection electron energy-loss spectra (REELS) measured at different energies or for different experimental geometrical configurations. The procedure provides the differential inverse inelastic mean free path (DIIMFP) and the differential surface excitation probability (DSEP). The only required input parameters are the differential cross section for elastic scattering and a reasonable estimate for the inelastic mean free path (IMFP). No prior information on surface excitations is required for the deconvolution. The retrieved DIIMFP and DSEP can be used to determine the dielectric function of a solid by fitting the DSEP and DIIMFP to theory. Eventually, the optical data can be used to calculate the (differential and total) inelastic mean free path and the surface excitation probability. The procedure is applied to Fe, Co and Ni and the retrieved optical data as well as the inelastic mean free paths and surface excitation parameters derived from it are compared to values reported earlier in the literature. In all cases, reasonable agreement is found between the present data and the earlier results, supporting the validity of the procedure.

Differential surface and volume excitation probability of medium-energy electrons in solids

A procedure is developed to rigorously decompose experimental loss spectra of medium-energy electrons reflected from solid surfaces into contributions due to surface and volume electronic excitations. This can be achieved by analysis of two spectra acquired under different experimental conditions, e.g. measured at two different energies and/or geometrical configurations. The input parameters of this procedure comprise the elastic scattering cross section and the inelastic mean free path for volume scattering. The (normalized) differential inelastic mean free path as well as the differential surface excitation probability are retrieved by this procedure. Reflection electron energy loss spectroscopy (REELS) data for Si, Cu and Au are subjected to this procedure and the retrieved differential surface and volume excitation probabilities are compared with data from the literature. The results verify the commonly accepted model for medium energy electron transport in solids with unprecedented detail.

Optical constants of Cu measured with reflection electron energy loss spectroscopy (REELS)

Two energy loss spectra of 1000 and 3000 eV electrons reflected from a Cu surface are analysed to give the normalized distribution of energy losses in a single surface and volume inelastic scattering process. These single scattering loss distributions are subsequently fitted to theoretical expressions for the differential inverse inelastic mean free path (DIIMFP) and differential surface excitation probability (DSEP) providing the real and imaginary part of the dielectric function in terms of a set of Drude–Lorentz oscillators. The optical constants obtained in this way are subjected to several sum rule checks and compared with other experimental data and with density-functional-theory (DFT) calculations. The present optical data agree excellently with the DFT-results, while the earlier optical data deviate significantly from these two data sets for energies below 30 eV. The mean free path for inelastic electron scattering for energies below 2000 eV is derived from the dielectric data and is found to agree satisfactorily with values reported earlier.

Differential probability for surface and volume electronic excitations in Fe, Pd and Pt

The normalized differential mean free path for volume scattering and the differential surface excitation probability for medium energy electrons travelling in Fe, Pd and Pt are extracted from reflection electron energy loss spectra (REELS). This was achieved by means of a recently introduced procedure in which two REELS spectra taken under different experimental conditions are simultaneously deconvoluted. In this way, it is possible to obtain the unique reconstruction for the surface and volume single scattering loss distribution. The employed method is compared with a procedure that is frequently used for this purpose [S. Tougaard, I. Chorkendorff, Phys. Rev. B 35 (1987) 6570]. It is shown, both theoretically and through analysis of model spectra as well as experimental data that the approach by Tougaard and Chorkendorff does not result in a single scattering loss distribution. Rather, it gives a mixture of surface, bulk and mixed scattering of any order.

Measurement of the surface excitation probability of medium energy electrons reflected from Si, Ni, Ge and Ag surfaces

Reflection electron energy loss spectra (REELS) are presented for medium energy (200 eV to 5 keV) electrons backscattered from Si, Ni, Ge and Ag surfaces. Multiple bulk inelastic scattering is eliminated from the experimental spectra and the differential surface excitation probability is retrieved from the resulting spectra. The differential as well as the integral surface excitation probabilities are compared with available theoretical results and experimental data published earlier. A material parameter is derived from the measurements that describes the dependence of the average number of surface excitations experienced in a single surface crossing on the electron energy and direction of surface crossing. While the shape of the distribution of energy losses in a single surface excitation is in reasonable agreement with theory, the integral surface excitation probability, i.e. the number of surface excitations experienced by the probing electron during a single surface crossing, exhibits a significant scatter when comparing results from different sources.