Synthesis conditions and electronic structures of heavily N-doped TiO$_{2}$

TiO$_{2}$ has drawn a lot of attention for its notable photocatalytic properties. Unfortunately, however, only a small portion of solar spectrum is utilized for photocatalytic activities of TiO$_{2}$ because of its wide band gap. To harvest solar energy more efficiently, TiO$_{2}$ must be sensitized under the irradiation of visible light which accounts for nearly 50 {\%} of solar light reaching ground surface. Although N-doped TiO$_{2}$ is a well-known visible-light driven photocatalyst, its photoabsorption cross section is still limited. In order to enhance visible-light absorption, high-concentration doping of N should be a promising solution. Here, we propose the synthesis conditions of heavily N-doped TiO$_{2}$ both for rutile and anatase structures based on the density-functional theory. We use supercell models with several different N concentrations to clarify the concentration dependence of the synthesis conditions. To discuss the synthesis conditions, we enforce a constraint to avoid the precipitation of other compounds, e.g. TiN, TiO, Ti$_{2}$O$_{3}$, TiO$_{2}$, during the synthesis of heavily N-doped TiO$_{2}$, which is described as a set of inequalities with respect to chemical potentials of N and O ($\mu _{\mathrm{N}}$ and $\mu_{\mathrm{O}})$ The results show that $\mu _{\mathrm{N}}$ must be larger than zero, which should be the upper limit for chemical potentials, in order for heavily N-doped TiO$_{2}$ to deposit stably. This means that high-concentration N doping is energetically difficult to be realized. Also, we will discuss the local arrangement of N atoms in connection with O vacancies and the electronic structures of examined models.