Effect of surface roughness on angle‐resolved XPS

Abstract

In the present contribution, the strategy of atomic force microscope mapping of periodical rough surfaces is combined with an extension of the polyhedral model. Atomic force microscope images are numerically interpolated, applying non-uniform rational B-splines, which also have the advantage that simultaneously to the interpolation, they provide the normals at any point on the rough surfaces. Compared with the polyhedral model, in the present scheme, any rough surface is accurately well approximated by a finite set of almost infinitesimal planes, which are all oriented in accordance with the normals obtained, while non-uniform rational B-splines interpolate the surface. In this view, the Beer-Lambert law is straightforwardly applied to compute all local (almost pointwise resolved) contributions to the photoelectron intensity on the analyser site. The proposed numerical scheme is validated in case of Si samples possessing either arbitrary rough, one-or two-dimensional periodic structures on the analysed surfaces. In this manner, it is shown that the computed angle-resolved XPS well agree with the experimental ones.

Numerical approximation of AR-XPS spectra for rough surfaces considering the effect of electron shadowing

“…As a continuation of the work published by Katona et al . and Bianchi et al ., where BLL was combined with a nonuniform rational B‐spline (NURBS) description of a given topography and thus for the spatially resolved surface normals, here, the numerical scheme for the shadowing of the electrons is explicitly described in analogy with Bianchi et al . In contrast with Katona et al .…”

Surface roughness, waviness, and shape induced effects in angle‐resolved XPS

“…As imposed by the prediction and update in Eqns and , level of resolution j = 2 would mean only one wavelet coefficient in a scanning direction. The AR‐XPS spectra are then calculated for each shape , j = 9, 8, …, 3, using the NURBS–Beer‐Lambert scheme by the authors . The layer thicknesses of SiO 2 and C contamination were separately evaluated from the AR‐XPS on the passive (atomically flat) area of the Si sample and found to be 1.3 nm and 0.5 nm, respectively.…”

“…., 3, using the NURBS-Beer-Lambert scheme by the authors. [4] The layer thicknesses of SiO 2 and C contamination were separately evaluated from the AR-XPS on the passive (atomically flat) area of the Si sample and found to be 1.3 nm and 0.5 nm, respectively.…”

“…Motivated by the experimental facts and simplified models of roughness, recently, a NURBS–Beer–Lambert scheme was developed and applied by the authors . In this scheme, one realistically incorporates the topography of the analyzed surfaces using atomic force microscopy (AFM) data as proposed by Olejnik et al .…”

“…[3] Motivated by the experimental facts and simplified models of roughness, recently, a NURBS-Beer-Lambert scheme was developed and applied by the authors. [4] In this scheme, one realistically incorporates the topography of the analyzed surfaces using atomic force microscopy (AFM) data as proposed by Olejnik et al [5] These AFM images are then linearly interpolated by using nonuniform rational B-splines (commonly abbreviated as NURBS) [6] to determine the contribution from each so-resulting planar facets to the intensity of photoelectrons via the Beer-Lambert law. [7,8] Note that this NURBS-Beer-Lambert scheme goes beyond any simplification model of a rough surface.…”