Symmetry-induced transparency in conductive metal oxides for optoelectronics

The unification of optical transparency and electronic conductivity in metal oxides produces a special class of rare materials, transparent conductive oxides (TCOs). This combination of physical properties makes them essential components for optoelectronic applications, including photovoltaic and photoelectrochemical devices, LCDs, and LEDs (see Figure 1). Although the unique chemistry of TCOs has been investigated extensively since the mid-20th century, the ultimate question—What factors produce an optimal TCO?—has no certain answer. As we strive for increased light-to-current conversion rates in solar cells and improved efficiencies in electronic devices, complete knowledge and control of these material functionalities is imperative.

Indium sesquioxide (In₂O₃) is the prototypical n-type TCO, exhibiting excellent carrier mobilities (>100cm²/Vs) coupled with an optical band gap outside the visible range (>3.2eV). For the past 40 years, the magnitude and nature of the electronic band gap has been debated. By taking into account the underlying In₂O₃crystal symmetry combined with high-resolution x-ray spectroscopy, we have reached a revised understanding of its electronic structure.¹ This provides new insight into both the essential ingredients for a good TCO and the design strategy needed for maximizing future performance.

Figure 1. Crystal structure of indium sesquioxide (In₂O₃) and a schematic of a typical thin-film solar cell. TCO: Transparent conductive oxide.

To address the underlying electronic structure of In₂O₃, we employ two approaches. First, we conduct first-principles electronic-structure calculations based on density-functional theory. This enables access to the distribution of electrons within a system and, as such, to all ground-state properties. We then perform symmetry analysis on the resulting band structure to understand the nature of the bonding and optical properties. We subsequently investigate the doped and defective electronic-structure behavior.² At the same time, our experimental collaborators have grown high-quality epitaxial In₂O₃samples³ and performed a series of high-resolution synchrotron-based spectroscopic measurements (soft and hard x-ray photoemission and soft x-ray emission).¹

Figure 2. Calculated density-functional theory band structure of In₂O₃and experimental x-ray spectra relative to the Fermi energy, E_F, at the bottom of the conduction band. E_g: Band-gap energy. XPS: X-ray photoemission strength.

From in-depth symmetry analysis of the In₂O₃ band structure we came across a surprising discovery: band-edge transitions are parity forbidden. As both the states at the top of the valence band and bottom of the conduction band are of even parity, dipole transitions cannot occur between them. In fact, comprehensive optical analysis revealed that strong optical transitions occur only from 0.8eV below the top of the valence band. Predictions that the electronic and optical band gaps in In₂O₃ are inequivalent were validated unequivocally when a combination of independent spectroscopic measurements found that the In₂O₃ electronic band gap is indeed less than 3eV (see Figure 2).¹ This is in stark contrast to the previously assumed band gap (3.75eV).

Both the magnitude of the electronic band gap and the absolute band-edge positions are key attributes in determining material performance in optoelectronic devices. The band offsets between two components determine their charge-transport behavior. As most oxides deviate from their formal chemical composition (e.g., In₂O_3−δ), the resulting high intrinsic-carrier concentrations (10²⁰cm⁻³) make it difficult to determine the underlying band gaps. This arises from occupation of the lower conduction band and movement of the band edges on addition of carriers, leading to renormalization (see Figure 3). By simulating n-type In₂O₃, we provided a quantitative estimation of these contributions.² We have demonstrated a direct correspondence between the chemical nature of the donor defects and the magnitude of renormalization. Coupled with the experimental data, this corresponds to a re-evaluation of the In₂O₃ intrinsic band gap to 2.67eV.³

Figure 3. Schematic changes in the conduction band contributing to optical band-gap (E_g^opt) changes on addition of electrons. Δ_BM: Change due to Burstein–Moss occupation. Δ_RN: Deviation caused by renormalization.

The small band-gap energy of In₂O₃ is, somewhat paradoxically, a major factor in determining its excellent TCO performance. The low conduction-band position—driven by relativistic contraction of the In 5s orbital—means that the Fermi-level pinning energy lies above the conduction-band minimum.⁴ This is remarkable and ensures that In₂O₃ can support high electron concentrations without forming compensating acceptor defects, even when heavily doped.⁵ Other TCOs with higher band-gap (conduction-band) energies (e.g., ZnO 3.44eV, SnO₂ 3.60eV) cannot match the low resistivity of In₂O₃.

In conclusion, an optimal TCO should have both a small fundamental electronic band gap (low conduction band for n-type or high valence band for p-type TCOs) and a large optical band gap (to limit visible-light absorption). In₂O₃ maintains optical transparency through dipole forbidden band-edge transitions, despite having a fundamental electronic band gap in the blue range. We are now pursuing more complex multicomponent crystalline TCOs such as InXO₃(ZnO)_n (where X represents In, Ga, or Al).⁶ Our preliminary work indicates that the intrinsic properties of the binary components have a strong role to play in these materials and offer a definite avenue for improving future TCO performance.

We thank John Pern (NREL) for his interest in our work and Russell Egdell (University of Oxford, UK) for coordinating the experimental collaboration on this project. This work is supported by the Department of Energy under contract DE-AC36-99GO10337.