Abstract
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.
Highlights
For a long time, Tungsten has attracted interest in material science since it has the highest melting point of all metals, excellent corrosion resistance and low sputtering coefficient
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
The DIIMFP and DSEP are retrieved in the energy range 1360–1460 eV
Summary
Tungsten has attracted interest in material science since it has the highest melting point of all metals, excellent corrosion resistance and low sputtering coefficient. For quantitative studies of energy loss processes of probing electrons, the information on differential inverse inelastic mean free path (DIIMFP) and differential surface excitation probability (DSEP) is required. Several techniques have been proposed for computing DIIMFP and DSEP involving linear response theory and density functional theory. Such computations are computationally expensive for real atomic structures since a many-body quantum-mechanical problem has to be solved. An alternative approach to get information on DIIMFP and DSEP is to extract them from electron energy loss spectra [1].
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