3.3. Density of states
In order to clearly understand the optical absorption properties, Fig. 3 shows the total density of states (TDOS) and partial density of states (PDOS) near the Fermi level of pure and 4d TM atom doped TiOS with spin-up (spin-down) states plotted on the positive (negative) y-axes. In view of the presence of unpaired electrons, it is necessary to take spin into account for the dopings of Y, Zr, Nb, Mo, Tc, Ru, and Rh atoms, while it is not for the dopings of Pd, Ag, and Cd atoms. For the pure TiOS, as shown in Fig. 3a, both the valence band (VB) and the conduction band (CB) are formed by the mixing of O 2p and Ti 3d states. However, the VB is mainly contributed by O 2p states, while the CB is mainly contributed by Ti 3d states. This composition of the VB and CB will not be qualitively changed by the dopings of 4d TM atoms. However, both VB and CB of all the doped TiOS are seriously shifted to the low energy region in comparison with those of pure TiOS, which should stem from the upward shift of the Fermi energy level. For the dopings of Y, Zr, Nb, Mo, and Ag atoms, the Fermi energy levels move into the CB as shown in Figs. 3b-3f, and they can be viewed as n-type conductors. So we think the dopings can induce the semiconductor-metal phase transition. Therefore, lower energy photons can be absorbed by electron to induce the intra-band transition. Thus, the light absorption response in the entire visible light region or even longer wavelength range may be strengthened, which clearly explains the increase of the optical absorption in Figs. 2a-2e. However, the Fermi energy levels for the dopings of Tc, Ru, Rh, Pd, and Cd atoms seem to stay in the original band gaps in Figs. 3g-3k, implying that only the inter-band transition can occur, sharply different from those of the dopings of Y, Zr, Nb, Mo, and Ag atoms in Figs. 3b-3f. By a close look at Figs. 3g-3k, we can see that the new bands are formed by the coupling of the 4d states of the TM atoms and the O 2p or Ti 3d states. Obviously, this kind of inter-band transition will contribute to the visible-light absorption. Intuitively and reasonably, the relatively small amount of dopants will induce relatively weak light absorption. This is the reason why only the weak improvement can appear in Figs. 2g-2k. Although the doping-induced new bands can also be observed for Y, Zr, Nb, and Mo in Figs. 3b-3e, the Fermi level is deeply immersed into the original CB. In this case it is the intra-band transition in the original CB that dominates the light absorption, which induces the appearing of the strong improvement of the visible-light absorption.
Fig. 3 (Color online) The TDOS and PDOS of pure and 4d TM doped TiOS. For clarity, the Fermi energy level is shown by the vertical dotted lines at zero energy.
3.4. Band structure
In order to explain more intuitively the optical absorption, we further show the energy bands of the 4d TMs doped TiOS in Fig. 4. For pure TiOS in Fig. 4a, the VBM and the CBM are located at G point, indicating the nature of the direct band gap. For 4d TM doped TiOS, the VBM and CBM are still located at G point. However, most of dopings except Ag will introduce the impurity energy levels (IELs) in the band gap of pure TiOS. As shown in Figs. 4b-4e, the IELs of Ti24YO48, Ti24ZrO48, Ti24NbO48, and Ti24MoO48 are located slightly below the CBM, which can reduce the energy required for the electron transition to the CB and be beneficial for extending the light absorption to visible region and eventually enhancing the visible-light absorption efficiency. Besides, the Fermi energy levels of Ti24YO48, Ti24ZrO48, Ti24NbO48, Ti24MoO48, and Ti24AgO48 enter the CB in Figs. 4b-4f, resulting in the intra-band transition, which effectively induces stronger light absorption. For the weak improvement case, the IELs of Ti24TcO48 and Ti24RuO48 in Figs. 4g and 4h are located near CBM, while the IELs of Ti24RhO48and Ti24PdO48 in Figs. 4i and 4j are located near VBM. In the same way, the existence of IELs can reduce the energy required for the electron transition, and hence enhance the optical absorption in the visible-light region.
Fig. 4 (Color online) The band structure of pure and 4d TM doped TiOS. In (b, c, d, e, g, h, i) the solid (dotted) curve represents the spin-up (spin-down) state. The horizontal dashed lines at the energy zero represent the Fermi energy levels.
Next, in Fig. 5 we present the Mulliken charge of the 4d TM doped TiOS. From Fig. 5a we can see that all 4d TM atoms will carry positive charges and there exist equivalent negative charges appearing in TiOS, indicating the electron transferring from 4d TM atoms to TiOS. Clearly Y, Zr, Nb and Mo can carry much more positive charges than Ru, Rh, Pd and Cd. Large positive charges on doping atoms indicate more electrons on the doping atoms will move from doping atoms to TiOS, further leading to the positive charge centers and making the original CB are filled by electrons. This clearly expounds why the Fermi energy levels are shifted into the CB. Small positive charges on the doping atoms may indicate the electric polarization of the doping atoms and their surroundings. In this case no obvious electron transfer will occur. Also, we present in Fig. 5b-5k the charge density differences of all doped models which vividly depict the redistribution of the electrons in the 4d TM doped TiOS.