Electronic structure of amorphous indium oxide transparent conductors

Using empirical atomistic simulations and density functional theory (DFT), we examine the atomic and electronic structure of pure- and tin-doped indium oxide in various degrees of amorphisation. Atomic structures ranging from maximally amorphous (within fixed periodic boundary conditions) to fully crystalline are prepared using liquid-quench molecular dynamics simulations in which the cooling/quench rate is the governing parameter. The final structures are reoptimized using DFT and the electronic structure (band gaps and carrier effective masses) are compared to the crystalline material. We find that the conduction bands of ${\text{In}}_2{\text{O}}_3$ are quite resilient in several aspects to changes in the atomic structure. This suggests that local coordination geometries around indium and oxygen are less critical to transparent conductivity than previously thought.

Figure 1

Calculated energy (in eV per formula unit) of quenched ${\text{In}}_2{\text{O}}_3$ structures after total quench simulation times $t_{\text{Q}}$ of up to 5000 ps. The upper- and lower-horizontal lines represent the energetic boundaries between an instant-quench structure (relaxation of molten arrangement) and a fully crystalline structure, respectively. (a) Average energies for 80-atom (black) and 320-atom (gray) cells. (b) Data points for all 80-atom structures. Labels indicate structures A–H which are selected for further analysis. The value quoted for 250 ps for the 320-atom cell in (a) is an average over five simulations only, as opposed to an average over 10 simulations for all others.

Figure 2

(Color online) Structure views of selected final structures of ${\text{In}}_2{\text{O}}_3$ quench simulations ranging from fully crystalline (a) to maximally amorphous (e).

Figure 3

Calculated In-O pair-distribution function (PDF) and O-In-O angular distribution function (ADF) for ${\text{In}}_2{\text{O}}_3$ structures A–D.

Figure 4

Energy per formula unit of ${\text{In}}_2{\text{O}}_3$ relative to the initial crystalline structure, for optimized 80-atom structures for various total quench simulation times up to 2500 ps. The upper- and lower-horizontal lines represent the energetic boundaries between an instant-quench structure (relaxation of molten arrangement) and a fully crystalline structure, respectively. (a) The ionically compensated $\left[2{\text{Sn}}_{\text{In}}\cdot {\text{O}}_{\text{i}}\right]$ system. (b) The electronically compensated $\left[2{\text{Sn}}_{\text{In}}\right]$ system.

Figure 5

The calculated band structure for 40-atom primitive unit cells of (a) crystalline bixbyite ${\text{In}}_2{\text{O}}_3$ and (b) Sn-doped ${\text{In}}_2{\text{O}}_3$ with Sn substituting at the Wyckoff $b$ site. Band energies are referenced to the top of the valence band. The Fermi levels at 0.22 and 2.27 eV, respectively, are indicated by a horizontal dotted line.

Figure 6

Calculated band structure in a cubic 80-atom unit cell of (a) crystalline ${\text{In}}_2{\text{O}}_3$ (structure A) and (b) maximally amorphous ${\text{In}}_2{\text{O}}_3$ (structure H). Shown below (c) is a comparison of band structure along one segment $\left(\Gamma \text{-X}\right)$ for six structures of the ${\text{In}}_2{\text{O}}_3$ quench series.

Figure 7

Calculated band structure of (a) interstitial oxygen ${\text{O}}_{\text{i}}^{″}$, and (b) a nearest-neighbor $\left[2{\text{Sn}}_{\text{In}}\cdot {\text{O}}_{\text{i}}\right]$ defect cluster in a 80-atom cubic unit cell of crystalline ${\text{In}}_2{\text{O}}_3$. (c) Partial band structure along $\Gamma$ to X for the five $\left[2{\text{Sn}}_{\text{In}}\cdot {\text{O}}_{\text{i}}\right]$ quench structures A–E.