This however does not take place An insignificant

This, however, does not take place. An insignificant decrease in the and ΔEv values in n-PbS : O+ compared to the data for the initial sample is within the margin of experimental error and could be regarded merely as a tendency in value decrease of the energy parameters discussed when passing from p-PbS to n-PbS : O+. This, in turn, allows us to assume that the volume concentration of oxygen in n-PbS : O+ must not be higher than 0.5 at. %, or 1 × 1020 cm–3. On one hand, this could be a consequence of the dispersion of the matrix material, and hence of the oxygen implanted into it during ion doping. This phenomenon is discussed in detail in [19,20]. On the other hand, the low N0/d* values could be caused by the relatively high d* values. The d* value can be obtained by comparing the intersubband histone demethylase amplitudes in the initial and the ion-doped lead sulfide (values listed in Table 1). It should be taken into account that intersubband electron transitions in the lead chalcogenide valence band are a three-particle process where a third particle, i.e. a phonon or a lattice defect, ensures the quasi-impulse conservation. This means that the αΣL intersubband coefficients must depend not only on the Hall concentration of holes, but on the number of phonons and crystal lattice defects as well. It also follows from the above that the αΣ values could be different for all three samples listed in Table 1. This makes it impossible to determine the d* value precisely. A rough estimate of d* can be obtained only if we assume the imperfection and the size of regions whose properties have been modified through ion doping are the same for p-PbS : O+ and n-PbS : O+, while the electrophysical parameters of these regions are homogeneous within their bulk. Cross-sections of the studied samples explaining the assumptions made are shown in Fig. 5. Accepting these simplifications, d* value can be estimated using the following simple formula: where , and are the αΣL band amplitudes in the initial p-PbS, p-PbS : O+ and n-PbS : O+, respectively. In accordance with the results of Ref. [21], the error of the d* parameter (derived from formula (6)) can be estimated using
The calculations showed that for studied samples d* = (0.96 ± 0.62) µm with a reliability of 0.90. This proves that the not only sample scattering during ion implantation but also the significant depth of the oxygen penetration into the material may contribute to a decrease in the volume concentration of oxygen in an ion-doped lead sulfide. Let us further discuss the experimental data in Fig. 3а. Comparing these data allows to identify the marked differences in the optical absorption spectra of the initial and the ion-implanted lead sulfides, thus providing insight into the mechanism of the doping effect of oxygen in PbS. Firstly, as a result of ion implantation and annealing, a new quasilocal level EO, located deep in the valence band, appears in the energy spectrum of lead sulfide that may be bound to oxygen. No other energy level that could be attributed to either oxygen or to oxygen-containing complexes was found in the energy spectrum of PbS. Moreover, as a result of ion-implanting of the oxygen impurity and the post-implantation annealing of the samples, centers forming the energy level in the band gap of the original p-PbS : Na, Pbex were destroyed, which the authors of Refs. [11–13] attribute to complexes composed of an acceptor impurity atom (Na or Tl) and a chalcogen vacancy. The elimination of these energy levels as a result of ion doping and annealing of lead sulfide indicates that oxygen atoms occupy positions in the chalcogen sublattice, thus ‘healing’ the anion vacancies. This, however, does not lead to the elimination of sulfur vacancies in annealed p-PbS : Na, Pbex doped with oxygen ions. What is more, their number grows, as evidenced by the increase in integral cross-sections of the sulfur vacancy absorption: [formula (8)], transferring from p-PbS to p-PbS:O+ (A is proportional coefficient)