Single-deflection model & Continuous slowing down approximation

Fig. 1. Reflected electrons spectra

q₀ – incident angle, q - reflection angle, x_Nb – thickness of the top Nb-layer, x_Al – thickness of the Al-layer, E₀ – energy of incident electrons, R – reflection function, e_Nb - mean energy losses in Nb, e_Al - mean energy losses in Al.

Consistent solution of elastic and inelastic problems

The calculation of electron energy spectra reflected from heterogeneous in depths targets is based on formulas  (7), (9), (10), (14).

Fig.2. Reflected electrons spectra

Solid line shows experimental data, dashed line – calculation for multilayer model. Varying of the top Nb-layer thickness together with thickness of Al-layer for each target returns the Nb-layer thickness the fits experimental data best (fitting-procedure). Nb-layers and Al-layer thicknesses found with a help of fitting-procedure are as following: x₁=45 nm, x₂=26, x₃=12 nm, x_Al=38 nm.

Fitting

Fig.3 Fitting-procedure

There are only thicknesses of the layers which varied in fitting-procedure. The model as such together with all its parameters has been kept constant. Solid line – experiment data, dashed line – calculation.