Large electron mass anisotropy in a $d$-electron-based transparent conducting oxide: Nb-doped anatase ${\text{TiO}}_2$ epitaxial films

Electron mass anisotropy in the Nb-doped anatase ${\text{TiO}}_2$ (TNO) was determined by polarized infrared spectroscopy measurements for (012)-oriented TNO epitaxial films. The electron mass along the $c$ axis, $m_{⟨001⟩}^{\ast }$, derived by Drude analyses, was found to be $0.5–3.3m_0$, which was 3–6 times larger than that along the $a$ axis, $m_{⟨100⟩}^{\ast }$, $0.2–0.6m_0$. This large anisotropy was attributed to not only the anisotropic crystal structure but also the $d$-orbital-dominated conduction band. These results indicate that control of crystallographic orientation is of crucial importance for realizing high conductivity in polycrystalline TNO films.

Figure 1

(Color online) (a) $\theta -2\theta$ XRD pattern of a typical (012)-oriented TNO film grown on LAO (011) substrate. (b) Pole figure of the diffractions from anatase {004} and {112} planes (labeled with I or II) and LAO {100} and {111} planes (labeled with L). The labels I and II, respectively, indicate the epitaxial domains shown in Fig. 2. Dotted lines represent the tilt angles of $30°$ and $60°$.

Figure 2

(Color online) (a) Schematic of two epitaxial domains for TNO (012) film on LAO (011) substrate. Dashed arrows indicate the crystallographic directions of the LAO substrate. Configuration of the polarized IR measurements in experimental coordinate is also shown. (b) The models of atomic arrangements for anatase ${\text{TiO}}_2$ (012) and ${\text{LaAlO}}_3$ (011) surfaces.

Figure 3

(Color online) Polarized IR reflection (left panels) and transmission (right panels) spectra of the TNO (102) films with different Nb concentrations (${\mathbf{E}}_{\parallel }$: circle, ${\mathbf{E}}_{\perp }$: triangle). The results of least-squares fitting using the Drude model were shown as solid lines.

Figure 4

(Color online) Electron mass $m^{\ast }$ of the TNO films along the $⟨100⟩$ (circle) and $⟨001⟩$ (square) directions as functions of carrier concentration. The error bars denote experimental uncertainty in $m^{\ast }$, which originates from light absorption by the substrate, light scattering, and experimental errors in $n_e$. Equation (5) was solved by iterative procedure, and the numerical uncertainty is smaller than the experimental one. The $m_{⟨100⟩}^{\ast }$ values obtained from (001)-oriented TNO films were plotted for comparison (cross: this study, diamond: Ref. 3).