Identification and design principles of low hole effective mass p-type transparent conducting oxides

Abstract

The development of high-performance transparent conducting oxides is critical to many technologies from transparent electronics to solar cells. Whereas n-type transparent conducting oxides are present in many devices, their p-type counterparts are not largely commercialized, as they exhibit much lower carrier mobilities due to the large hole effective masses of most oxides. Here we conduct a high-throughput computational search on thousands of binary and ternary oxides and identify several highly promising compounds displaying exceptionally low hole effective masses (up to an order of magnitude lower than state-of-the-art p-type transparent conducting oxides), as well as wide band gaps. In addition to the discovery of specific compounds, the chemical rationalization of our findings opens new directions, beyond current Cu-based chemistries, for the design and development of future p-type transparent conducting oxides.

Figure 1. Effective mass distribution for electrons and holes in oxides.

The histogram shows the maximum line effective mass for holes (valence band) in red and electrons (conduction band) in blue in our set of binary and ternary oxides. The effective mass bin size is 0.2 and the figure focuses on the region of low effective mass (lower than 5).

Figure 2. Effective mass versus band gap for the p-type TCO candidates.

We superposed on the band gap axis a colour spectrum corresponding to the wavelength associated with a photon energy. The TCO candidates are marked with red dots. A few known p-type (blue diamonds) and n-type (green square) TCOs can be compared to the new candidates. The best TCOs should lie in the lower right corner. For clarity, we kept only one representative when polymorphs existed for a given stoechiometry (for example, PbTiO₃ and K₂Sn₂O₃) and did not plot Rb₂Sn₂O₃, which is superposed on K₂Sn₂O₃.

Figure 3. Vacancy formation energy versus Fermi energy.

The panels indicate results for Sb₄Cl₂O₅ (a) K₂Sn₂O₃ (b) and K₂Pb₂O₃ (c). The oxygen vacancy formation energy is indicated by a blue line. The cation vacancies are indicated by orange and purple lines. All defects are calculated in oxidizing conditions. The zero of Fermi energy is the valence band maximum.

Figure 4. Projected band structures for low hole effective mass oxides.

The panels refer to K₂Sn₂O₃ rhombohedral (a), Tl₄V₂O₇ (b), PbTiO₃ tetragonal (c), Hg₂SO₄ (d), B₆O (e), ZrOS (f), Ca₄P₂O (g), Sb₄Cl₂O₅ (h). The band structures are computed by GGA with a rigid shift of the conduction band (scissor operator) to fit the band gap to the GW value. The colour indicates the character of the bands by projections of the wave function on the different sites. Each element in the ternary compound has one of the red, green or blue colour associated with it and the resulting colour is obtained by mixing them in proportion equivalent to the projections. The red colour is always associated with oxygen. Equivalent Figures without colour scheme but with markers are available in Supplementary Figs S24–S31.