Influence of electron refraction effects at surfaces and interfaces in quantitative surface analysis with XPS and AES

Highlights: •The refraction effects experienced by Auger and X-ray photoelectrons are calculated when they cross the sample/vacuum surface and other interfaces. •Are evaluated the errors induced by a straight propagation model when it is used for the determination of the surface composition or of over-layers thicknesses. •The consequence in metrology (e.g. in semiconductor technology) at the nanoscale are outlined. -- Abstract: The influence of the refraction effects in quantitative surface analysis is evaluated when Auger electrons or X-ray photoelectrons cross the sample/vacuum surface and other interfaces. Based on elementary quantum mechanical arguments, this evaluation concerns the determination of surface concentrations of homogeneous samples, as well as the determination of thicknesses of over layers or subsurface layers of stratified samples. From various numerical applications, such as the thickness determination of a graphene monolayer in X-ray Photoelectrons Spectroscopy (XPS), it is established that the refraction effects may lead deviations – with respect to the so-called straight-line approximation –, which may reach tenths of a percent for photoelectrons induced by soft X-rays when they are issued from metals and detected at decreasing take-off angles. The consequence in XPS – including Angle-Resolved XPS – and in Auger Electron Spectroscopy (AES) is discussed and some aspects of the discussion may also concern LEED (Low Energy Electron Diffraction) via the fact that the refraction effects results from the difference between the inner and the outer energy of the electrons of interest, a difference equals to the sum of the Fermi energy and the work function and often referred in the LEED literature as inner potential U