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Semiconducting Transition Metal Oxides

Introduction

• Semiconductivity is a transformative material property of the 20th century, enabling electronics and optoelectronics.

• The materials base for semiconductor applications is small, with Si being the most used semiconductor.

• III-V compounds dominate optoelectronic applications (LEDs and laser diodes).

• Non-oxide II-VI semiconductors are used in niche applications (infrared detectors and thin-film solar cells).

• Wide-gap oxides serve as secondary device components (gate dielectrics, transparent conducting oxides (TCO), and transparent thin-film transistors (TFT)).

• In conventional semiconductors (group 14, III-V, and II-VI systems), the band gap follows from the octet rule.

• Band gaps generally increase with ionicity due to the increased energy difference between cation and anion orbitals.

• Additional interactions with occupied or unoccupied orbitals (e.g., transition metal d-orbitals) can remove dangling bonds from the band gap, supporting defect tolerance.

*Figure 1 illustrates how valence and conduction bands form from hybridization between cation and anion atomic orbitals, creating a band gap in (a) elemental, (b) III-V, and (c) II-VI semiconductors. Part (d) shows the mixing of additional orbitals (e.g., transition metal d).

• Widening the materials base for semiconductor applications is important for several reasons:

  • Si, despite being widely used in solar cells, has an indirect band gap and is defect-intolerant.

  • Some technologically important elements (In and Te) have low annual production rates.

  • Materials design aims to optimize material properties and discover new materials for desirable functionalities (e.g., p-type TCO).

  • The interface with other components (band-offsets, minimization of interface defects) and device fabrication processes (low thermal budget) are also important considerations.

• For large-area applications like solar energy conversion, chemically stable materials amenable to large-scale low-cost production processes are desirable. Oxides are a class of compounds with such properties.

• However, only a few oxides (Zn, Ga, In, and Sn) are used as transparent n-type conducting layers.

• These oxides are difficult to dope p-type, and other main group oxides (MgO or $Al<em>2O</em>3$) have very large gaps and are insulators.

• Transition metal (TM) oxides are a potential materials class for exploring semiconducting properties.

• Current areas of interest include ternary oxides, transition metal alloys, and non-equilibrium deposition methods to access compositions or disordered configurations outside the thermodynamically accessible phase space.

• The review aims to aid the design and discovery of novel oxides by distilling trends and design principles from available data on the binary 3d oxides.

Electronic Structure of Transition Metal Oxides

Mott and Charge-Transfer Insulators vs. Semiconductivity

• While $TiO<em>2$ and $Cu</em>2O$ are well-known n-type and p-type semiconductors, respectively, oxides with partially occupied d-shells are generally described as Mott insulators.

• Mott insulators are often viewed as distinct from semiconductors because semiconductors are associated with band theory, while Mott insulators are defined by the breakdown thereof.

• The on-site d-d Coulomb and exchange interaction U and the charge transfer energy Δ are used to describe the trends of the band gaps.

• $NiO$ is often used as a prototypical example where the excitation corresponds either to the reaction
  $2Ni^{+II}O^{-II} → Ni^{+I}O^{-II} +Ni^{+III}O^{-II}$ (case of Mott insulator) or to
  $Ni^{+II}O^{-II} → Ni^{+I}O^{-I}$ (case of charge transfer insulator).

• Either description implies a localization of electrons ($Ni^{+I}$) and holes ($Ni^{+III}$ or $O^{-I}$) on an atomic scale, thereby discounting the band picture.

• Nevertheless, $NiO$ can exhibit good p-type conduction, making it attractive as a transparent hole-transport layer.

• A band structure theory that fully accounts for the electron-electron interaction can describe a band gap irrespective of electron number.

• In this case, the s, p, and d orbitals are treated on the same footing, and the band gap is determined both by on-site correlations of the d orbitals and by the band-energies and band-dispersions arising from the interactions between all orbitals.

• Mott and charge transfer insulators have a well-defined valence band maximum (VBM) and conduction band minimum (CBM) with their respective carrier effective masses for band transport.

• As with all semiconductors, additional requirements to be met for useful semiconducting properties include effective masses, dopability, and a low propensity for defect formation.

• TM oxides are prone to localize electron or hole carriers, in which case transport occurs via a small-polaron-hopping instead of a band-conduction mechanism.

Band Structure Calculations

• Band gap and band structure predictions for semiconductors are usually performed by means of quasi-particle energy calculations based on the GW approximation.

• For main group semiconductors, the reliability of such calculations is well established.

• The importance of d-orbitals for the band-structure of transition metal compounds poses additional challenges for such calculations regarding convergence parameters, particularly the number of bands included for the dielectric response functions and basis set completeness.

• Further extensions of the GW approach include vertex corrections in the self-energy and the relevance of ionic contributions to the dielectric screening.

• Band gap predictions for transition metal oxides are currently only emerging, and ad hoc corrections for d-states are sometimes necessary to obtain reliable band gaps.

Quasi-particle energy calculations were performed using the PAW implementation of the GW approximation (VASP version 5.3), with settings slightly modified from Ref. [40].
An initial DFT calculation was performed using the generalized gradient approximation (GGA) with a Coulomb parameter U = 3 eV for all 3d cations except Cu, for which U = 5 eV was used. Self-consistent band energies were obtained via 5 consecutive GW iterations. The response functions were calculated in the random phase approximation.
The energy cutoff was 330 eV for the wavefunctions and 200 eV for response functions. A total number of $64 ar{at}$was used, where $n{at}$ is the number of atoms in the unit cell. The k-point density was set to approximately $4000/n{at}$.
An on-site potential $Vd$ for the 3d orbitals was used to compensate for the tendency of this GW scheme to overestimate the 3d orbital energies compared to the sp bands ($Vd$ = −1.3, −2.8, −4.0, 0, −0.9, −1.2, −0.7, −2.4 eV for the 3d cations Ti, V, Cr, Mn, Fe, Co, Ni, Cu, respectively).
This approach was constructed as a compromise, providing a feasible route for GW calculations for a wide range of materials within a single scheme.
Results for a larger number of materials are included in a database that will be opened to public access.
Table I shows the calculated band gaps in comparison to experimental data.
*To characterize the band dispersion and expected band transport properties, Table I also lists the