Z_eff -method

Fig. 1. Reflected electrons spectra

Z-effective-method is based on the Single-deflection model together with continuous slowing down approximation. Let’s consider a point on a spectrum of electrons reflected from Nb+N target. Energy losses at this point are proportional to electron path in the target and effective mean energy losses e(Z_eff), and the height of the point on spectra depends on effective atomic number Z_eff:

where Z_Nb – niobium atomic number, Z_N – nitrogen atomic number, c_N – nitrogen concentration in niobium. Interpreting the same way every data point of spectrum one can recover profile of nitrogen distribution in niobium.

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. Target has been represented as consisted of 12 layers. Concentration of nitrogen in each layer assumed to be constant. With a help of Z_eff-method we got a first approach of nitrogen distribution in niobium. Later on, we varied the thicknesses layers and concentrations of nitrogen in niobium for each layer until the best fit of experimental spectrum has been achieved (fitting-procedure). Profile of nitrogen distribution in niobium recovered from experimental spectrum is depicted on Fig.2.

Fitting

Fig.3 Fitting-procedure

The model as such together with all its parameters has been kept constant. Solid line – experiment data, dashed line – calculation.