The recent experimental work shows that perovskite BaSnO3 can be heavily doped by K to become a stable p-type semiconductor. Here, we find that p-type perovskite BaSnO3 retains transparency for visible light while absorbing strongly in the infrared below 1.5 eV. The origin of the remarkable optical transparency even with heavy doping is that the interband transitions that are enabled by empty states at the top of the valence band are concentrated mainly in the energy range from 0.5 to 1.5 eV, i.e., not extending past the near IR. In contrast to n-type, the Burstein-Moss shift is slightly negative, but very small reflecting the heavier valence bands relative to the conduction bands.

Transparent conducting oxides (TCOs) are oxides that combine low visible light absorption with good high electrical conductivity.1,2 They are used in the opto-electrical devices such as solar cells, displays, opto-electrical interfaces and other optoelectronic devices.3–7 For solar cells, high transparency and high carrier mobility are needed for transmitting light and conducting photogenerated carriers. For displays, high DC conductivity, low haze, and high transparency for the operating wavelength and viewing angle ranges are needed. The most commonly used TCO material is Sn doped In2O3, known as ITO. This is a stable n-type material that can be readily deposited in thin films and has excellent TCO performance.8,9 Compared with n-type TCO materials, the best p-type TCOs have lower performance in terms of conductivity while remaining reasonably transparent.10–12 For example, the n-type ITO has a conductivity of 103 Scm−1,13 whereas the best p-type TCO, Mg-doped CuCrO2 in delafossite, only achieves a one order of magnitude lower conductivity of 220 Scm−1.14 The p-type TCO materials with good conductivity have been long sought after to achieve high performance all-oxide optoelectronic devices and transparent electronics.

Perovskite oxides possess various unique functionalities, including the transparent conductivity of n-type BaSnO3.15–28 Other functionalities include superconductivity,29 magnetism,30 ferroelectricity,31 and multiferroicity.32 This diversity reflects that stability and flexibility of the perovskite structure. The high binding energy of the O 2p states in perovskite structure, which is associated with the stability of the structure, and the fact that in addition to the Sn(IV) state in BaSnO3, Sn also has a relatively common lower valence Sn(II) state in oxides, suggest that BaSnO3 can be readily doped into an n-type semiconductor, as is in fact the case. However, recently, Kim et al. reported p-doping of BaSnO3 thin films by K substitution using pulsed laser deposition and found that the p-n junctions based on BaSnO3 are very stable after several thermal cycling sequences.33 They ascribed this to the highly stable perovskite structure.

The band structure of BaSnO3 shows valence bands derived from O 2p states and conduction bands from Sn 5s states, with a semiconducting gap.34–36 The Sn 5s states of Sn are very spatially extended, and this combined with the single 5s state per unit cell leads to a single non-degenerate conduction band with light mass and no nearby higher lying bands. These two features underlie the high performance transparent conductivity of n-type BaSnO3. In contrast, there are nine O 2p orbitals per unit cell, and furthermore the O 2p states are more localized that the Sn 5s state. Therefore, the efficacy of p-type BaSnO3 as a TCO may be quite different than n-type. Specifically, n-type BaSnO3 doped with La for example, is a high performance TCO. This is a consequence of the very dispersive conduction bands, which provide no final states for direct optical transitions in the visible from carriers near the conduction band minimum to higher lying states. The valence bands are less dispersive, and there are more bands within 3 eV of the valence band maximum. This leads to an expectation that there may be interband transitions from lower valence bands to unoccupied states near the valence band maximum in p-type material. This would then be expected to lead to reduced transparency in heavily p-type doped BaSnO3.

Here, we report the detailed calculations that show remarkably that such interband transitions are concentrated in the infrared and that contrary to the above expectation p-type BaSnO3 can have high transparency in the visible part of the spectrum even when heavily doped to obtain conduction. We also find a band structure consistent with reasonable conduction based on the calculated transport functions. As such, p-type BaSnO3 is a good candidate material for transparent electronic devices.

Our first-principles calculations were performed using the augmented planewave plus local orbital (APW+lo) method,37 as implemented in the WIEN2k code.38 We used the sphere radii of 2.5 Bohr, 2.08 Bohr, and 1.79 Bohr for Ba, Sn, and O in BaSnO3, respectively, and 1.87 Bohr for Cu, 1.61 Bohr for O in Cu2O and 2.05 Bohr for Cu, 1.72 Bohr for Al and 1.72 Bohr for O in CuAlO2. A basis set cut-off, kmax, determined by the criterion Rminkmax = 9.0 was used. Here, Rmin is the O sphere radius.

The experimental lattice parameters and spacegroups are a = 4.116 Å for BaSnO3, Pm3m,39–41a = 4.267 Å for Pn3¯m-Cu2O,42,43 and a = 2.8604 Å, c = 16.9530 Å for R3¯m-CuAlO2.44 We fixed the lattice parameters to the experimental values and relaxed the internal atomic coordinates of the layered compounds using the Perdew, Burke, and Ernzerhof generalized gradient approximation (PBE-GGA). Following the structure optimization, we did electronic structure and optical calculations using the modified Becke-Johnson type potential functional of Tran and Blaha, denoted as TB-mBJ in the following.45 This potential gives band gaps in remarkably good accord with the experiment for a wide variety of simple semiconductors and insulators,45–49 including perovskite stannates. Spin-orbit coupling (SOC) is included in all electronic structure and optical calculations.

We treated p-type doping by K on the Ba site using the virtual crystal approximation. The virtual crystal approximation is an average potential approximation. It goes beyond rigid bands and specifically includes composition dependent distortions of the band structure. The use of the virtual crystal approximation is supported by the fact that in these compounds the highly electropositive elements, Ba and K, are fully ionized and serve only to stabilize the structure and donate charge.

We begin with the optical properties of p-type BaSnO3. Fig. 1 shows the absorption spectra as a function of p-type doping. Undoped BaSnO3 is a semiconductor with an indirect band gap and onset of absorption at ∼3.2 eV. We find substantial absorption for infrared (<1.5 eV) light with p-type doping. This is in contrast to n-type BaSnO317 and reflects the higher density of valence bands. So, p-type BaSnO3 is not transparent for infrared light. The absorption comes from a Drude peak at low energy, whose width will depend on scattering, and additional peaks due to interband transitions. The key present finding is that there are no significant interband transitions in the visible part of the spectrum.

FIG. 1.

Calculated absorption spectra for p-type BaSnO3 as a function of doping level in carriers per Sn atom. In terms of carrier concentration, 0.1 holes per Sn correspond to p = 1.434x1021 cm−3.

FIG. 1.

Calculated absorption spectra for p-type BaSnO3 as a function of doping level in carriers per Sn atom. In terms of carrier concentration, 0.1 holes per Sn correspond to p = 1.434x1021 cm−3.

Close modal

Fig. 2 shows the band structure with p-type doping of 0.05 holes per Sn (p = 7.17 × 1020 cm−3). The solid vertical arrows indicate the main transitions in the infrared, which are between bands below the valence band maximum and the flat top band running along the Brillouin zone edges (the R-M directions). A dashed arrow indicates a potential transition in the visible from a band at M. However, this transition is suppressed by the matrix element, as shown by the detailed calculations.

FIG. 2.

The valence band structure of BaSnO3 with 0.05 holes per Sn (see text). Optical transitions are marked with arrows. The dashed arrow indicates a very weak optical transition due to matrix elements.

FIG. 2.

The valence band structure of BaSnO3 with 0.05 holes per Sn (see text). Optical transitions are marked with arrows. The dashed arrow indicates a very weak optical transition due to matrix elements.

Close modal

It is of interest to note that in contrast to n-type, which shows a large positive Burstein-Moss shift with doping,16,17,50p-type BaSnO3 shows a much smaller, and slightly negative shift, reflecting both the relatively heavier valence bands and the expected fact that replacement of divalent Ba by monovalent K reduces the binding of the O 2p states.

The other key property of a good TCO is high conductivity. The conductivity of a TCO can in general be tuned via the doping level, i.e., the carrier concentration. This also affects the transparency. In practice, doping and defects are essential for increasing the conductivity of TCO thin films, but usually heavy carrier concentration reduces the transparency. So, reasonable carrier mobility is needed. Here, we use the quantities σ/τ to characterize the transport properties of p-type and n-type BaSnO3. Experimentally, the mobility of BaSnO3 reaches a level of 320 cm2 V−1 s−1 at a doping level of 8 × 1019 cm−3.27 We plot σ/τ for p-type and n-type BaSnO3 in Fig. 3. As seen, p-type is inferior to n-type but only by a factor of less than 10.

FIG. 3.

σ/τ of n-type BaSnO3 (red line) and p-type BaSnO3 (black line) as a function of carrier concentration. These results are obtained with rigid band calculations using the BoltzTraP code and the band structure of undoped BaSnO3 in order to facilitate the comparison of p-type and n-type.

FIG. 3.

σ/τ of n-type BaSnO3 (red line) and p-type BaSnO3 (black line) as a function of carrier concentration. These results are obtained with rigid band calculations using the BoltzTraP code and the band structure of undoped BaSnO3 in order to facilitate the comparison of p-type and n-type.

Close modal

This assumes that p-type and n-type have similar inverse scattering rates τ. At present, it is likely that τ for p-type samples is limited by sample perfection, e.g., various defects, and that it can be improved, similar to n-type. Further experimental study will be needed to determine to what extent conductivity can be improved in p-type material via improvement in sample quality. This ultimately will govern the performance that can be achieved as a transparent conductor. A materials figure of merit for transparent conductors is the ratio of the DC conductivity to the optical conductivity in the visible. The present results show that p-type BaSnO3 has good transparency in the visible even with very heavy doping that would be consistent with a high conductivity and that the band structure is favorable for good conductivity. However, we are not able to quantify the ultimate limit for the conductivity that can be achieved in p-type BaSnO3 and therefore the figure of merit.

To further understand the transport properties of p-type BaSnO3, we calculated its plasma frequencies, Ωp, as a function of doping concentration. As a comparison, we calculated this property for the known p-type materials: CuAlO2 and Cu2O. Conductivity in metals and degenerately doped semiconductors depends on the plasma frequency, σΩp2τ, where τ is an effective inverse scattering rate. As shown in Fig. 4, the conductivity of p-type BaSnO3 is comparably even larger than CuAlO2 and Cu2O under some carrier concentrations. Thus, while inferior to n-type, p-type BaSnO3 has TCO properties comparable to or better than other known p-type TCO materials and additionally has the advantage of being an isotropic cubic material.

FIG. 4.

Square plasma frequency of p-type BaSnO3 (black line), CuAlO2 (red line) and Cu2O (blue line) as a function of carrier concentration, which are obtained from virtual crystal calculations for (K,Ba)SnO3 and for CuAlO2 and Cu2O with virtual crystal p-type doping on the O site.

FIG. 4.

Square plasma frequency of p-type BaSnO3 (black line), CuAlO2 (red line) and Cu2O (blue line) as a function of carrier concentration, which are obtained from virtual crystal calculations for (K,Ba)SnO3 and for CuAlO2 and Cu2O with virtual crystal p-type doping on the O site.

Close modal

One may also note that unlike n-type there is a significant infrared absorption due to interband transitions. Such absorption in the infrared in a transparent material may have some possible utility in thermal management, e.g., in building windows or in reducing heating of displays that are in direct sunlight. The main result is that p-type BaSnO3 can have a favorable combination of conductivity and visible light transparency to be a good p-type transparent conductor.

p-type BaSnO3 has a remarkably good σ/τ for a material with narrow upper valence bands. The narrowness is important in concentrating the optical absorption in the infrared. However, as can be seen from the parabolic band expression σ/τn/m, where n is the carrier concentration and m is the effective mass, narrow bands lead to low σ/τ. The origin of the good σ/τ for BaSnO3 can be understood in terms of the detailed band structure. The valence band maximum at R comes from three bands that are degenerate without spin orbit and have a tiny spin orbit splitting due to the low atomic number of O. This band comes from a combination of O p orbitals directed perpendicular to the Sn-O bonds and is flat along the R-M lines. This leads to Fermi surfaces even at relatively low carrier concentrations that consist of interconnected cylindrical pipes running along the zone edges, as depicted in Fig. 5. This is very far from the spherical carrier pockets that would be expected for a non-degenerate band at R with cubic symmetry. This type of isosurface structure, consisting of interconnected cylinders or near cylinders, is also present in cubic p-type PbTe and n-type SrTiO3, which are also materials that show remarkably good conductivity. As discussed for those materials, the origin of this property is that the conductivity and density of states have different average effective masses in this case, with light mass dominated by the dispersion transverse to the cylinders entering the conductivity and a heavy mass entering the density of states.51–53 In other words, the top valence band is highly dispersive across the cylinder directions, contributing strongly to the conductivity, and weakly dispersive along the cylinders, contributing to a high density of states.

FIG. 5.

Fermi surface for 0.05 holes per Sn, as shown in Fig. 2. This corresponds to a carrier concentration, p = 7.17 × 1020 cm−3. Note the cage formed from interconnected cylinders along the Brillouin zone edges.

FIG. 5.

Fermi surface for 0.05 holes per Sn, as shown in Fig. 2. This corresponds to a carrier concentration, p = 7.17 × 1020 cm−3. Note the cage formed from interconnected cylinders along the Brillouin zone edges.

Close modal

In conclusion, we used the first-principles calculations to study the optical and electronic properties of doped p-type perovskite BaSnO3. The results show that the absorption of visible light for p-type BaSnO3 is very weak even with heavy doping. Besides, based on the results, p-type BaSnO3 is expected to have comparable conductivity with CuAlO2 and Cu2O. So, it has useful p-type optoelectronic properties and is a p-type transparent conducting oxide enabling for transparent perovskite oxide electronics.

This work was supported by the Department of Energy, Basic Energy Sciences, through the MAGICS Center, Award No. DE-SC0014607.

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