Surface excitation parameter for rough surfaces

•Instead of providing a general mathematical model of roughness, we directly use a finite element triangle mesh method to build a fully 3D rough surface from the practical sample.•The surface plasmon excitation can be introduced to the realistic sample surface by dielectric response theory and finite element method.•We found that SEP calculated based on ideal plane surface model are still reliable for real sample surface with common roughness. In order to assess quantitatively the importance of surface excitation effect in surface electron spectroscopy measurement, surface excitation parameter (SEP) has been introduced to describe the surface excitation probability as an average number of surface excitations that electrons can undergo when they move through solid surface either in incoming or outgoing directions. Meanwhile, surface roughness is an inevitable issue in experiments particularly when the sample surface is cleaned with ion beam bombardment. Surface roughness alters not only the electron elastic peak intensity but also the surface excitation intensity. However, almost all of the popular theoretical models for determining SEP are based on ideal plane surface approximation. In order to figure out whether this approximation is efficient or not for SEP calculation and the scope of this assumption, we proposed a new way to determine the SEP for a rough surface by a Monte Carlo simulation of electron scattering process near to a realistic rough surface, which is modeled by a finite element analysis method according to AFM image. The elastic peak intensity is calculated for different electron incident and emission angles. Assuming surface excitations obey the Poisson distribution the SEPs corrected for surface roughness are then obtained by analyzing the elastic peak intensity for several materials and for different incident and emission angles. It is found that the surface roughness only plays an important role to SEP only for large interaction angle cases (larger than 60°) and large surface roughness (root-mean-square value lager than 15nm). This result is a clear evidence that the SEP database calculated based on ideal plane surface model are still efficient for realistic sample surface with common surface roughness.