Microscopic Origin of Universal Quasilinear Band Structures of Transparent Conducting Oxides

A tight-binding-based microscopic theory is developed that accounts for quasilinear conduction bands appearing commonly in transparent conducting oxides. It is found that the interaction between oxygen $p$ and metal $s$ orbtials plays a critical role in determining the band structure around the conduction-band minimum. Under certain types of short-range orders, the tight-binding model universally leads to a dispersion relation which corresponds to that of the massive Dirac particle. The impact of the graphenelike band structure is demonstrated by evaluating the electron mobility of highly doped $n$-type ZnO.

Figure 1

Band structures of (a) ZnO, (b) ${\mathrm{In}}_2{\mathrm{O}}_3$, (c) ${\mathrm{Zn}}_2{\mathrm{SnO}}_4$ (inverse-spinel), and (d) ${\mathrm{In}}_2{\mathrm{ZnO}}_4$ (amorphous). The energy zero is set to the valence top. The color code in the lowest conduction bands indicate the weight of oxygen $p$ orbitals ($P$) normalized by that of metal $s$ orbitals ($M_S$). The inset spheres are Fermi surfaces at the nominal carrier density of ${10}^{21}$ (crystalline) or ${10}^{20}$ (amorphous) ${\mathrm{cm}}^{-3}$.

Figure 2

Schematic pictures of the local geometry around metal and oxygen atoms in TCOs and TASOs. (a) Tetrahedral and (b) octahedral geometries.

Figure 3

(a) Conduction bands of cubic ZnO along various $\overrightarrow{k}$ directions. The solid line is the fitted dispersion relation. The Fermi levels at 0 K corresponding to various (electron) carrier densities (${\mathrm{cm}}^{-3}$) are indicated by dashed horizontal lines. The consideration of finite-temperature Fermi-Dirac distributions shifts down the Fermi level slightly ($\sim 0.01\mathrm{eV}$ at 300 K). (b) The relative ratio of oxygen $p$ orbitals parallel or perpendicular to $\overrightarrow{k}$ ($|P_{\parallel }/M_s|$ and $|P_{\perp }/M_s|$, respectively). The solid line indicates the result with parameters fitted in (a). (c) and (d) show the square of wave functions at specific $\overrightarrow{k}$ points. The black dots indicate oxygen atoms.

Figure 4

(a) The overlap integral between the lattice-periodic parts of eigenfunctions with respect to the scattering angle and electron energy. The elastic scattering is assumed. (b) The computed total drift mobility of electrons in ZnO with respect to carrier densities. The circles are experimental data in Ref. 18. The apparent divergence of individual mobility at ${10}^{18}{\mathrm{cm}}^{-3}$ is due to the linear scale; the mobility is always finite.