The fitting obtained with the ATLAS code and with the analytical model are remarkably similar in spite of the different starting hypothesis. In the first case, we assume a heterojunction between the TIL and the substrate and in the second one the limitation is due to a generic temperature-dependent resistance. In this second case,
we use a lumped equivalent circuit where the current limitation between both layers is concentrated at the corners, while ATLAS uses a true tri-dimensional grid. In both cases, we preserve the idea that all the Ti atoms contribute to the sheet conductivity of the implanted layer, which means that the IB is formed. The possibility of having a “normal” doping, that is to say, that the Ti atoms behave as donor or acceptor type shallow impurities is non-congruent with the Hall mobility sign change and also the TIL layer would be in parallel or isolated for all the temperatures. Anyway, the electronic configuration of the Ti electrons preclude the possibility of behave as a typical III or V dopant if it is substitutional to Si in the lattice. RBS measurements show that the Ti atoms are interstitially located and ab initio calculations show that in that case we have a half-filled intermediate band. This band is located closer to the conduction band than to the valence band and is fully compatible with the experimental data.
The IB hole mobility used in both models presents some controversial aspects. It is clear that we have not enough precision to determine its value but, anyway, it seems that it increases with the dose. As the dose goes up, TIL layer becomes more damaged and even polycrystalline and it seems that the mobility should go down in contradiction with the experimental data that show an increase from 0.4 to 0.6 cm2 V-1 s-1. This increase could be related to the IB width because as the Ti concentration increases, so should the bandwidth; this implies a reduction in the carrier effective mass, and hence an increase in the mobility [27]. Other very important argument to discuss is the absence of any IB effect in the 10[11] cm-2 sample. This sample has a very high Ti concentration as it is shown in Fig. 13.2 but under the Mott limit except at the maximum where is just reaching this concentration. We assume that the Ti concentration is not enough to develop an IB, and the Ti electrons remain in the atom vicinity without any electrical activity. Finally, another fact that supports our hypothesis of the IB formation is the increase in the carrier lifetime as the doping is increased. In this experiment, which has been previously published [28], we used samples with doses of 1015, 5-1015 and 1016 cm-2 and we measured the carrier lifetime using a quasi-steady-state photoconductance technique. As Ti is a very well-known killer center, the lifetime should diminish when the dose increases. Nevertheless, the result is the opposite and the lifetime increases. This fact supports the theory that the formation of an IB which in turn implies the delocalization of the electrons wavefunctions avoids the non-radiative SRH recombination.
