Introduction

ABO3 perovskite structures have been broadly studied over the last decades, mostly because they constitute a family of oxides widely found in solid-state inorganic chemistry, but also because they fit into numerous technological applications1,2,3. Due to their compositional flexibility, cleaving or growing an ABO3 crystal in different crystallographic directions gives rise to surface planes that have atomic terminations of varying stoichiometry. Accordingly, a whole range of particular electronic structures might be found, which will govern highly sensitive local properties4. As a matter of fact, crystal facet engineering has been essential for the controlled improvement of physical and chemical properties, especially in nanostructures5. In catalytic processes, one of the main fields for perovskite applications, facet selectivity has been greatly investigated as it directly affects the efficiency of nanostructured catalysts6,7.

In an ideal perovskite, a cubic lattice is composed of a corner-sharing BO6 octahedra framework whose dodecahedral interspaces are filled with A-site cations. Breaking such crystal will eventually expose lower coordination BOx=3,4,5 units on the surface, which is the major responsible for the electronic structure of cleaved crystals. Much is known about how BO6 octahedra rotation and tilting affect the material’s properties8,9,10, sometimes inducing particular features as ferroelectricity11. However, accurate information regarding other BOx units is necessary to a complete understanding of physical and electronic properties of perovskites’ surfaces.

Of particular interest, meaningful properties have been attributed to BO4 groups. Molybdates having MoO4 units presented enhanced O2 evolution activity, which means their valence bands (VB) are well-aligned with water oxidation potentials12. Recently, (100) NaTaO3 orthorhombic slabs have also shown similar alignment thanks to localized TaO4 energy states13. Interestingly, there is strong evidence that the excited energy is localized in isolated BO4 tetrahedra inside scheelite structures12. In sillenites, specific transmittance and absorption peaks in the visible region have been observed and associated with discrete BO4 groups14. Furthermore, in mullite-type Bi2B4O9 (B = Al3+, Ga3+) materials, unbalanced Mulliken charges and symmetry breaking related to BO4 tetrahedra assisted the charge separation positively, increasing their photocatalytic reactivity15. Although there are a few records of straight relationships between the BO4 units and electronic structure, further investigation on how its possible configurational geometry might influence the material’s electronic properties is required so that their modulation can be feasible.

Among recurrently synthesized nanostructures, thin and ultrathin films allow fine surface science investigations since they have approaching bulk-like characteristics16. Such nanostructured materials may have their properties tuned and controlled when strain (stress) is induced17,18. The effects of biaxial strain have been frequently explored due to the surprising responses obtained when it comes to properties’ modulation, which ranges from induction of dielectric anomalies19 to bandgap engineering20. To control the amount of induced strain, substrates with different mismatches with the films are usually employed21. The application of an electric field to a piezoelectric substrate has also been used to induce biaxial strain and modulate specific properties22. Additionally, developed synthesis methodologies have granted refined control of surface particle size as well as surface area and morphology in thin films, not to mention the fact that characterization techniques that are usually difficult to be implemented for nanoparticles (scanning probe microscopy, for instance) can be readily used in 2-D materials23,24. Therefore, studying the influence of surface BOx arrangements on ultrathin films should provide clear evidence of their role in controlling electronic properties.

Recently, several experimental reports have driven their attention to the synthesis of ABO3 thin films, such as NaTaO324,25 and KTaO326,27,28, on different substrates and heterostructures. Amazingly, angstroms-thick perovskites ultrathin films have already been achieved29,30,31,32, which supports reliable theoretical and experimental comparisons. Furthermore, the modulation of perovskite properties by means of biaxial strain is also widely reported and highly relevant to various applications. Magnetic, electrical, and transport properties, for example, react significantly to strain and can therefore be tuned33,34. Strain-induced lattice deformation (octahedral tilting)35 as well as photoluminescence features36 have also shown considerable changes upon biaxial strain. Here, through ab initio density functional theory37,38, we have systematically studied the effects of biaxial strain on (110) cubic (Na,K)TaO3 ultrathin films, emphasizing how the geometric arrangement of surface-exposed TaO4 tetrahedra influence their electronic structure. Shallow surface states of Ta eg orbitals are located below the conduction band (CB) and can be pushed either into or out of the bandgap as strain is applied and TaO4 planarity varies. Biaxial tensile strain increases Ta-O bond distances and the unit planarity, stabilizing eg orbitals and shifting surface states into the gap. The opposite movement is produced when biaxial compressive strain reduces Ta-O bond distances and makes TaO4 units less planar. To the best of our knowledge, the aforesaid structural-electronic connection has not been reported hitherto and allows bandgap states engineering, which is desirable in many different fields.

Computational Details

Our calculations have run on Vienna Ab Initio Simulation Package (VASP)39,40, with electron-ion interactions described by projector augmented-wave (PAW)41 pseudopotentials. For electrons exchange-correlation interactions, the generalized gradient approximation (GGA) within the PBE functional42 has been used. To sample the Brillouin zone, k-points meshes were generated following the Monkhorst-Pack43 scheme. During geometry optimizations, plane-wave cutoff energy of 520 eV and electronic energy convergence for self-consistent iterations of 10−8 eV were set, aiming at accurate results.

In order to have a reference from which ultrathin films could be built using a slab approach, we have first optimized KTaO3 (KTO) and NaTaO3 (NTO) cubic Pm\(\bar{3}\)m bulk structures, performing 11 × 11 × 11 k-points integrations. The equilibrium lattice parameters were a0KTO = 4.04 Å and a0NTO = 3.98 Å, which are in agreement with experimentally reported values44,45. Typical semiconductor band structures (Fig. 1S) with a Γ-R indirect bandgap of 2.07 eV (KTO) and 2.26 eV (NTO) have been obtained. Despite being well-known that GGA underestimates the bandgap when compared to experimental data45,46, it agrees with other similar theoretical studies47,48.

Ultrathin KTO and NTO films were constructed by replicating the bulk and cleaving it in the (110) direction. Thus, 12 layers thick (~31 Å) films that expose such a surface were relaxed with a 15 Å vacuum to minimize image self-interactions from periodic boundary conditions. The k-points integration was performed up to a 5 × 1 × 5 grid. To simulate in-plane epitaxial strain, the interplane x-z lattice constants were changed up to −4% and 4% for compressive and tensile strain, respectively. We designated the strain as σ = \([({\alpha }_{KTO,NTO}-{a}_{0})/{a}_{0}]\times 100\), where αKTO,NTO is the strained lattice parameter and a0 is the bulk optimized lattice parameter.

Results and Discussion

According to the equilibrium structure of the films, biaxial strain may induce changes in both structural (bond angles, bond distances, crystallinity, etc.) and electronic properties (bandgap, electronic states, Fermi level, etc.). Strain-free, tensile σ = 4% (αKTO = 4.02 Å, αNTO = 4.14 Å), and compression σ = −4% (αKTO = 3.88 Å, αNTO = 3.82 Å) converged structures are displayed in Fig. 1. For both KTO and NTO, strain-free films are more stable than those under tensile and compressive strain (Fig. 2S). Despite exposing polar terminations with non-zero formal charges, no surface reconstruction has been observed. Therefore, an electronic reconstruction mechanism will compensate the polarity induced by the cleavage. KTO structures retain their cubic lattice and relaxation occurs by changes in the interlayer spacing along the y-axis. NTO films, in turn, relax by similar mechanisms but also allow the rotation of internal TaO6 and surface TaO4 units. Note that under biaxial compression, the film acquires a more orthorhombic character while the bulk cubic group spacing can be partially recovered under tensile. A closer look at surface layers reveals a common feature presented by both films upon relaxation. Under biaxial compression (σ < 0%), Ta-O bond distances decrease and TaO4 tetrahedral units become less planar, whereas under biaxial tensile strain (σ > 0%), Ta-O bond distances increase and so does their planarity. We here call planarity (PL) an average of in-plane O-Ta-O angles so that the upper planarity limit corresponds to both x and z plane angles being 180°.

Figure 1
figure 1

Optimized structures of ultrathin KTO (left panel) and NTO (right panel) films. For each film, the structure having the bulk lattice constant (σ = 0%) is in the center, whereas the maximum compression (σ = −4%) is on the left, and the maximum tensile (σ = 4%) is on the right. In both cases, surface TaO4 tetrahedra become more planar under biaxial tensile and less planar under biaxial compressive strain.

Since surface states are crucial in the electronic structure of low dimension materials, we have plotted the projected density of states on the potassium (K) s, oxygen (O) p, and tantalum (Ta) d orbitals in Fig. 2. As in bulk, the valence band maximum consists of O 2p states and the conduction band minimum is mostly Ta 5d levels with a slight O 2p contribution, which indicates d-p (π) hybridization states. Nevertheless, a metallic character is observed in all films as a consequence of their polarity, which induces electronic reconstruction by filling up conduction states. It is interesting to note that there are spin up well-localized energy states near the CB which appear to be shallow and within the bandgap, especially under tensile. The layer resolved projected density of states (LRPDOS, Fig. 3S) confirms that such states are derived from surface TaO4 units. Under compressive conditions where σ < 0%, these states migrate to higher energy regions, eventually entering the CB energy zones. When tensile acts on the system, σ > 0%, the opposite behavior is observed and they move to lower energy zones within the material’s bandgap.

Figure 2
figure 2

Projected density of states of KTO (a) and NTO (b) ultrathin films. Surface states are clearly seen near the conduction band bottom of the films. When compression is induced, σ < 0%, such levels are pushed towards the conduction band. Oppositely, when tensile is applied, σ > 0%, they move into the bandgap. Black dashed lines represent the Fermi levels, and the plots were aligned according to their electrostatic potential.

The band structure of the films (Fig. 3) helps in describing such TaO4 surface states, pointing out their energy difference (ΔE) regarding the CB. A complete plot of both PL and ΔE as functions of σ can be seen in Fig. 4 (all the related data is in Table 1S). It turns out that for σ = 0% both KTO and NTO surface states are already separated from the CB by a total of ΔE = 0.08 eV for the former and ΔE = 0.21 eV for the latter, which characterizes them as shallow states within the bandgap. The planarity values of TaO4 surface tetrahedra are PL = 77.4% (KTO) and PL = 79.1% (NTO). When the tensile limit of σ = 4% is achieved, such planarity rises to 80.7% and 81.5%, respectively. Accordingly, ΔE increases to 0.33 eV (KTO) and 0.30 eV (NTO), which sets the levels even further into the gap. On the other hand, when the compression limit of σ = −4% is reached, PL of surface TaO4 units reduces to 70.4% for KTO and 71.5% for NTO. This approximates surface states and the CB, resulting in a significant bands overlap for KTO, and reducing ΔE to 0.05 eV for NTO. The above results shall be explained in two different but complementary discussions: (i) the reason why surface Ta d states lie below the CB; (ii) the way biaxial strain changes the position of such states.

Figure 3
figure 3

Band structure of KTO (a) and NTO (b) ultrathin films. In each panel, the strain-free case is in the middle, maximum compression is on the left, and maximum tensile in on the right. Surface up states near the CB are confirmed and their change when σ ≠ 0% is evident. Black dashed lines represent the Fermi levels, and the plots were aligned according to their electrostatic potential.

Figure 4
figure 4

Surface TaO4 planarity (PL) and the energy difference between shallow Ta surface states and the CB (ΔE) as functions of biaxial strain (σ). On the left y-axis, PL (bullets) behaves almost linearly with strain and, intrinsically, NTO has surface TaO4 units more planar than KTO ones. On the right y-axis, ΔE (stars) increases up to a limit around 0.30 eV. Negative values of ΔE indicate surface states/CB overlap.

As for the first, we have to consider the consequences that cleaving atomic bonds triggers on an initially TaO6 octahedral (Oh) symmetry existing in bulk KTO and NTO. As part of a group five transition metal, the five-fold degenerated Ta d orbitals are split by the ligand field of six oxygen atoms approaching along the axes, forming a set of doubly-degenerated eg (\({d}_{{{\rm{z}}}^{2}}\) and \({d}_{{{\rm{x}}}^{2}-{{\rm{y}}}^{2}}\)) and triple-degenerated t2g (dxy, dyz, dzx) orbitals. Being oxygen a π-donor ligand, charge transfer occurs through π bonds due to lateral overlap of ligand O 2p and Ta t2g orbitals, which causes their energy to decrease. On the other hand, eg orbitals rise in energy since their interactions with ligand orbitals are mostly repulsive (σ*)49. Consequently, in the TaO6 bulk arrangement, the CB is composed by Ta t2g-Op (π*) bands followed by a higher lying set of Ta eg-O p (σ*) bands. Cleaving the crystal in order to reduce the unit coordination to TaO4 removes two oxygen ligands. In such cases, the absence of ligands along the axes stabilizes the corresponding eg orbital, reducing their repulsive interactions50. Therefore, eg orbitals shall lower in energy but now with the degeneracy broken since \({d}_{{z}^{2}}\) and \({d}_{{{\rm{x}}}^{2}-{{\rm{y}}}^{2}}\) will not be equally stabilized. For instance, changes in the ligand field as it moves from octahedral to a square planar symmetry are generally described as a consequence of removing two ligands along the z-axis, which stabilizes \({d}_{{z}^{2}}\) orbitals electrostatically and increases the energy of \({d}_{{{\rm{x}}}^{2}-{{\rm{y}}}^{2}}\) orbitals that now suffer the greatest repulsion51 (Fig. 4S). For the proposed thin films, the (110) cleavage removes two cis oxygen atoms, leaving initially ‘butterfly’ TaO4 complexes on the surface. Such a cleavage cut out half of \({d}_{{{\rm{x}}}^{2}-{{\rm{y}}}^{2}}\) interactions, while the main electrostatic repulsion in z remains the same, as illustrated in Fig. 5(a). The O-Ta-O angles may acquire variable values, changing the TaO4 planarity so that tetrahedral (Td), square planar (D4h), and intermediate symmetries are allowed. In the studied structures, relaxation induces intermediate values of planarity to reach the structure equilibrium, balancing electrostatic and steric interactions. Figure 5(b) reveals the eg nature of surface states near the CB, confirming the stabilization of \({d}_{{{\rm{x}}}^{2}-{{\rm{y}}}^{2}}\) orbitals caused by the (110) cleavage. The small contribution of \({d}_{{z}^{2}}\) states result from a slight stabilization of its central lobe that reduces in energy when two weak antibonding interactions are removed.

Figure 5
figure 5

Investigation of individual TaO4 units and their electronic characterization: (a) schematic representation of how the (110) cleavage removes cis oxygen ligands and stabilizes eg orbitals; (b) relaxed strain-free (σ = 0%) KTO film projected density of states on eg and t2g orbitals; (c) from the left to the right, structural changes such as the variation of both Ta-O bond distances and the unit planarity are induced by biaxial strain, which alters d-p repulsive interactions, and shift eg states to lower (tensile, further stabilization) or higher (compression, destabilization) energy zones, as shown by the individual isolated TaO4 pDOS. Red, orange, and pink schematic orbitals refer to O p, Ta \({d}_{{x}^{2}-{y}^{2}}\), and Ta \({d}_{{z}^{2}}\) orbitals, respectively. Black dashed lines within pDOS plots represent the Fermi level.

As for the way that biaxial strain changes the position of surface Ta d states, an individual investigation of isolated TaO4 units is required. We have calculated TaO4 tetrahedral groups with different spatial arrangements in 20 Å vacuum supercells (oxygen atoms were saturated with hydrogen to mimic their coordination in both bulk and films). In addition to the configurational case of the strain-free KTO film, we have also calculated TaO4 units with the coordinates and hence planarity in which they are found on KTO film surfaces when σ = ±4%. In the left panel of Fig. 5(c), starting from the strain-free tetrahedra (σ = 0%, \({d}_{TaO}(xy)\) = 1.85 Å, and \({d}_{TaO}(z)\) = 2.04 Å), it is shown that biaxial tensile (σ = 4%) stretches dTa-O bonds to \({d}_{TaO}(xy)\) = 1.88 Å, and \({d}_{TaO}(z)\) = 2.11 Å, rising the unit planarity, whereas biaxial compression (σ = −4%) diminishes the atomic bond distances to \({d}_{TaO}(xy)\) = 1.82 Å, and \({d}_{TaO}(z)\) = 2.00 Å, decreasing the planarity. All bond distances of the discussed cases can be found in Table 2S. The central panel of Fig. 5(c) illustrates the weakening or strengthening of repulsive interactions between antibonding Ta eg-O p orbitals when tensile or compression is applied, respectively. The consequence in the material’s electronic structure is depicted on the right panel. The projected density of states reveals that as a (110) cleavage is performed in the cubic bulk, \({d}_{{{\rm{x}}}^{2}-{{\rm{y}}}^{2}}\) and \({d}_{{z}^{2}}\) states are stabilized and appear occupied (spin-up) below the Fermi level after structural relaxation. If biaxial tensile strain is applied in the x-z plane, Ta-O bonds will stretch, repulsive d-p interactions along such axes will decrease, and eg orbitals are stabilized. Conversely, biaxial compression along x-z brings atoms close together, repulsive d-p interactions increase, and eg orbitals rise in energy.

Finally, we note the fact that the electronic structure of ultrathin KTO films appears to be more sensitive to changes in surface TaO4 planarity than NTO films. As shown in Fig. 4 (left y-axis), the planarity of superficial TaO4 groups in both films respond very similarly to biaxial strain. Showing an essentially linear variation, the PL increases under tensile and decreases under compression, following basically the same slope. On the other hand, the linear coefficient is smaller for the KTO film than for the NTO one, what indicates that the initial planarity of the former is intrinsically lower than that of the latter. Since potassium has an extra electron shell compared to sodium, and hence a larger atomic radius, the repulsion felt by the superficial K-Ta-O arrangement is greater than in the case of Na-Ta-O, which initially prevents KTO-TaO4 groups from being as planar as NTO-TaO4 ones. As the electrostatic interactions are stronger for KTO, it was expected that its electronic structure would change more sensibly upon strain, as shown in Fig. 2. The exact influence of A-site cation on this type of process is still under investigation, nevertheless.

We also suggest that there are upper and lower limits of planarity that biaxial strain is able to induce. Despite the almost linear behavior of PL as a function of strain, too high tensile values stretch Ta-O to such an extent that the TaO4 coordination might be broken. In turn, too high compressive values maximize electrostatic and steric repulsions. For the KTO film, for instance, the repulsion at σ = −4% is such that potassium atoms start a exsolution-like process and are “expelled” from the surface of the film, TaO4 planarity values decrease drastically, and the electronic structure changes considerably. When the maximum tensile is achieved, in turn, both films tend to the similar planarity values and to the same ΔE maximum of ~0.30 eV from which greater PL is only achieved if more severe strain that irreversibly destabilizes the system is applied.

Conclusions

In conclusion, the (110) cleavage in cubic KTaO3 and NaTaO3 crystals made to obtain ultrathin films modifies the Ta d orbitals degeneracy and local electrostatic interactions to such an extent that shallow surface states can be manipulated by biaxial strain. Cleaving the crystal in such direction naturally induces \({d}_{{{\rm{x}}}^{2}-{{\rm{y}}}^{2}}\) orbitals stabilization and introduces them near the CB. We systematically investigated and showed that biaxial tensile or compression modifies surface TaO4 planarity, and therefore the energy of electronic defect states. Biaxial tensile pushes them further into the material’s bandgap while compression moves them towards the CB. As the behavior is generically the same for both different tantalates, we report a practical way of tuning their electronic properties through biaxial strain. Our results elucidate meaningful structural-electronic relationships that can be readily harnessed to control and engineer bandgap energy states. Although further investigation is required to connect such results with tactile applications, the proposed engineering may be widely desirable. For photocatalysis (the main application of NaTaO3 nanostructures), for instance, the alignment of CB and VB states with the water redox potentials is a major challenge and usually achieved by doping. Such strain-driven modulation may be effective and rule out the use of foreign materials. Concerning less explored applications, as spintronics, the magnetic characteristics of the system can be useful for building spin filters or similar devices.