Band structure of transition metal oxides plays a critical role in many applications such as photo-catalysis, photovoltaics, and electroluminescent devices. In this work we report findings that the band structure of MoO3 can be significantly altered by a distortion in the octahedral coordination structure. We discovered that, in addition to epitaxial type of structural strain, chemical force such as hydrogen inclusion can also cause extended lattice distortion. The lattice distortion in hydrogenated MoO3 led to a significant reduction of the energy gap, overshadowing the Moss-Burstein effect of band filling. Charge doping simulations revealed that filling of conduction band drives the lattice distortion. This suggests that any charge transfer or n-type electron doping could lead to lattice distortion and consequentially a reduction in energy gap.
Room-temperature molybdenum trioxide (α-MoO3) has a unique orthorhombic structure (space group: Pbnm, a = 3.697 Å, b = 13.864 Å, and c = 3.963 Å)1,2 which consists of layers of corner sharing and edge sharing MoO6 octahedra. For its unique crystal and related properties, this oxide has showed potential applications in a variety of fields such as solid catalyst3, electrochromism4,5, battery electrode6, charge injection or extraction layer in organic photovoltaics (OPVs) and organic light emitting diodes (OLEDs)7,8. For some applications, MoO3 is generally in contact with metals or with electron donors, such as hydrogen and alkali atoms. These physical contacts usually create interesting effects that have not been fully understood. For example, Greiner et al. reported that the work function and band structure of MoO3 were significantly altered when it was deposited on metals9. According to their UPS valence band spectra, two gap states were observed for the metal deposited MoO3 films. As they proposed, these states resemble the features of defect states found in oxygen-deficient MoO3. Another example is a band gap reduction of MoO3 caused by hydrogen diffusion. Many experiments have been reported that physical appearance of MoO3 becomes blue when being exposed to H210,11,12. From the optical transmission spectral measurements, Balendhran et al. observed a reduction of the optical gap of the MoO3 flake, from 3.2 eV to 2.6 eV, with increasing H2 exposure11. Based on Raman shift of the structure, they stated that this optical gap change is related to a structural change of MoO3 and can be observed in a wide range of processes such as themal treatment, Uv-irradiation and photochemical deposition followed by annealing. To gain a deeper insight into these phenomena, it is of great importance to systematically investigate the relationship between geometric and electronic structures in MoO3.
Previous theoretical studies on MoO3 are mainly focused on its structural, electronic and catalytic properties13,14,15,16,17,18. There is no report on how the lattice distortion and the electron doping affect its band structure. Besides, since the traditional DFT functionals do not accurately describe the van der Waals (vdW) interaction; a repulsive force is found between adjacent layers of MoO3 despite the interlayer distance. To overcome the problem, previous studies on the bulk phase of this oxide were conducted by assuming the unit cell lattice constant b to an experimental value. This assumption is problematic in the calculation of lattice structure upon inclusion of impurities. Ding et al. examined several vdW corrected density functionals on the structural and vibrational properties of MoO313. According to this report, the optB88 functional method produced the most accurate results on the lattice parameters and bond lengths of MoO3. This method made it possible to investigate lattice-deformed MoO3 in a direct and reasonable way.
In this paper, we used the vdW corrected density functional theory calculations to investigate the band structure evolution as a function of lattice distortions and electron doping. By examining the band gaps from various distorted lattice along the a-, b-, and c-axis, we observed an anisotropic behavior. Analysis based on symmetry-resolved density of states (DOS) revealed detailed information about the orbital interaction and the nature of the anisotropic behavior in this oxide. We next considered the effects of electron doping on the crystal, band structure and optical properties of MoO3 by intercalating H atoms. The results indicate that band gap reduction is accompanied by structural reconstruction. This is in agreement with experimental observations. To prove that this phenemena is not restricted to H intercalation, simulations of electron doping into the system were presented. Based on our results, a physical picture can be drawn to describe the relationship between geometric and electronic structures in MoO3.
Our DFT calculations were performed using the Vienna ab initio simulation package (VASP) with the projector augmented wave (PAW) pseudopotentials19,20,21,22,23. Considering the dispersion interaction in the layered structure, the van der Waals functional approach was used, and the exchange-correlation energy of interacting electrons was treated by the optB88 functional developed by Klimeš and coworkers24,25,26. The energy cut off for the plane-wave basis set was 500 eV. A (7 × 3 × 7) Monkhorst-Pack k-point grid was used for geometry optimization and a much denser k-point grid was used for DOS calculations. All considered structures were fully optimized with the force on each atom less than 0.01 eV/Å.
The unit cell we used to calculate the MoO3 crystal is shown in Figure 1a. It keeps the Pbnm space group symmetry with optimized lattice constants a = 3.944 Å, b = 13.982 Å, and c = 3.737 Å. The crystal is based on two nonequivalent bilayers stacked along the b-axis. Each bilayer consists of two sublayers of distorted octahedra that are corner-connected along the a-axis and edge-shared along the c-axis (Figure 1b, c). There are three symmetry distinct oxygen sites: the terminal oxygen O1 is singly coordinated, the bridging oxygen O2 is asymmetrically bonded with the two neighboring Mo atoms, and the symmetric O3 is triply coordinated with two Mo atoms oriented along the c-axis and one sublayer Mo atom.
To investigate the effect of lattice distortion on the band structure of MoO3, we performed calculations for uni-directional change in the cell constant in order to identify the major contribution from various lattice directions. The percentage of the cell length change was used to quantify the magnitude of distortion, i.e. a positive value means expansion while a negative one contraction. This method can serve as an approximation to the simulation of the strain effect. Furthermore, it enables us to isolate the effect of strain induced lattice distortion into individual directions, which is desired for theoretical analysis of the structural-electronic correlation. The computations of optical properties were carried out through the perturbation theory method that implemented in the VASP code. Herein, the imaginary part of the dielectric function ε1 was computed by summing over the occupied and unoccupied single-particle Kohn-Sham (KS) states, and the real part of the dielectric tensor was obtained by the usual Kramers-Kronig transformation. The absorption coefficient was derived from the imaginary and real parts of the dielectric function through the formula
Results and Discussion
Band structure modification under lattice distortion
The calculated band gaps of MoO3 as a function of uniaxial lattice distortion along the a-, b-, and c- axis, respectively, are plotted in Figure 2, which shows an anisotropic behavior. The calculated band gap for the equilibrium structure is 1.62 eV and indirect in nature. This value is smaller than the experimental measurement (~3 eV) owing to the well known underestimation of the band gap in DFT calculations. However, this does not affect our discussion since we are mainly interested in its relative value. As the lattice was stretched or compressed along the a-axis, the band gap decreased or increased remarkably, almost 0.2 eV per 1% distortion around the equilibrium value. However, distortions along the b- or c- axis changes the band gap moderately and oppositely. Our results agree with a previous report of Li et al. who studied the effect of strain on the MoO3 sheets27. However, in the paper Li et al provided no interpretation for this type of behavior. Here we explore the underlining physics.
The π-zx orbital determined the band gap of MoO3. In the octahedral coordination of transition metal oxides, the d orbitals of metal center are split into t2g (xy, yz, zx) and eg (x2 − y2, 3z2 − r2) manifolds when coupling with p orbitals of oxygen atoms according to symmetry considerations. Generally, t2g states contribute bands near the band gap and eg states locate further away in energy due to the crystal-field splitting. In this case, the t2g states determine the band structure modification near the band gap when external interactions were applied. In the MoO6 coordination of MoO3 crystal, t2g further splits into xy, yz, and zx states due to the octahedral distortion, as shown in Figure 3a. For our presentations, the orbital indexes x, y, and z coincide with the crystallographic axes a, b, and c, respectively. In details, the dxy orbital of Mo center overlaps mainly with the py orbital of bridging oxygen O2 and the px orbital of terminal oxygen O1 to form π type bonding in the xy plane (π-xy). Similarly, the dyz orbital mainly hybrids with the pz of O1 and the py of O3 to form π-yz, and the dzx orbital of Mo hybrids with the pz of O2 and the px of O3 to form π-zx. The relative strength of these three pd-π type hybridizations can be easily distinguished from the widths of their unoccupied bands showed in Figure 3b, and the order is π-zx > π-yz > π-xy for the equilibrium structure. Bear in mind that the π-zx hybridization is in the layer plane while the other two are out of it. This order can be understood by the comparison of their MoO4 tetragonal geometries in the three planes, as shown in Figure 4. Examining the bonding along the three axes, the O3-Mo-O3 chain along the c-axis is symmetric having a both bond length of 1.97 Å; the O2-Mo-O2 chain along the a-axis is asymmetric having a short bond of 1.78 Å and a long one of 2.19 Å, respectively; the O1-Mo-O3 coordination orientated in the c-axis is the most asymmetric since it involves the terminated Mo-O1 bond of 1.71 Å and the inter-sublayer Mo-O3 bond of 2.40 Å (Table 1). Since a regular coordination is more favorable for orbital overlap than a distorted one, the Mo center has the largest orbital overlap with the four neighboring oxygen ions in the zx plane in which the symmetric O3-Mo-O3 bonding and the less asymmetric O2-Mo-O2 bonding are involved. The MoO4 interaction in the bc plane is the weakest since the Mo atom is off-centered both along the a- and c-axes (Figure 4). It is the π-zx orbital that contributes the band edges at the VBM and CBM and determines the band gap of the equilibrium structure. As can be seen in Figure 3b, the band width of the π-zx orbital increased or decreased significantly as contraction or expansion was applied along the a-axis, and the band gap was changed accordingly. The band gap modification upon the b- or c-axis distortion was also governed by the expansion or shrink of the π-zx band, and we do not intend to repeat their DOS evidences here.
The distorted octahedral coordination was the origin of the anisotropic band gap modification upon lattice distortion for MoO3. Owing to the asymmetric O2-Mo-O2 bonding along the a-axis and the O1-Mo-O3 coordination oriented along the b-axis, the MoO6 octahedron is distorted in a manner that the Mo cation is off-centered along both the a- and b-axis (Figure 4). Lattice distortion had the effect of driving the Mo cation toward or further off the octahedral center depending on the direction. Then, the structural deformation changed the system band gap through the modification of orbital overlap. Consider, firstly, the case that the a constant was reduced by 5%, the long Mo-O2 bond was shortened by 0.18 Å while, interestingly, the short one was slightly elongated by 0.03 Å. This reduced the asymmetry of the O2-Mo-O2 coordination and moved the off-centered octahedral cation along the a-axis toward the center of the ac plane MoO4 tetragonon, resulting in a larger orbital overlap of the π-zx hybridization. Then the system band gap was reduced because of the expansion of the π-zx bands. Contraction along the b- or c-axis, however, deformed the crystal in an opposite manner compared to that along the a-axis. For contraction along the c-axis, the O3-Mo-O3 coordination was bended to be of smaller angle, from 143.10°to 134.78°, in the case of 5% distrotion. The bending slightly pushed the Mo cation along the a-axis away from the tetragonal center in ac plane by shortening the short Mo-O2 bond while stretching the long one. The deformation reduced the overlap of Mo 3dzx with O2 2pz and O3 2px, resulting in the increase of the band gap. Similarly, the b-axis contraction further distorted the ac plane tetragon by bending the O1-Mo-O3 coordination. The opposite effects of the expansion along these three directions can be expected. Notice that the a-axis distortion directly deformed the asymmetric O2-Mo-O2 coordination while distortion along the b- or c-axis changed it in an indirect way, the band gap modification caused by distortion along the a-axis was larger than that along the other two directions at the same percentage of cell length change.
Mechanical strain is possibly the most direct way to introduce lattice distortion which could effectively tune the physical properties of materials by the structure-electronics correlation27,28,29. In our calculations we isolated the strain induced lattice distortions in individual directions. The results, with appropriate consideration among these directions, are applicable to practical strains27. To understand exact strains in MoO3, the correlation of distortions in different axes must be addressed. The crystal of the MoO3 is characterized by the two dimensional covalent bonding network in the ac plane and the vdW stacking along the b axis. Thus, the a and c constants are correlated with each other strongly by the in plane covalent bonding. The b constants, however, is governed not only by the covalent bonding but also the vdW gap separating the covalent network. According to our study, when MoO3 is strained along the a-axis, it distorts along the c- and b- axes by some small ratios (as expected from the Poisson's ratios). As shown in Figure 2, distortion of the b and c lattice constants follows the same trend, but in opposite direction, in modifying the band gap. This is also the situation for c-axis strain except for the negative Poisson's ratio between b- and c- axes. For the b-axis strain, compression resultes in a small expansion of the a-axis constant and a small contraction of the c-axis constant. However, expansion of the b-axis constant hardly affect the cell constants of the other two axes owing to the exist of the vdW gap between layers.
The effect of electron doping
Hydrogen intercalation in MoO3 were computed to investigate the effect of electron doping on the structural and electronic properties of MoO3. The material system studied in this paper was constructed by bonding one hydrogen atom to a terminated oxygen in a 2 × 1 × 2 supercell (Figure 1d), which can be represented as H0.0625MoO3. Our calculations shown that the Mo-O1 bond was elongated by 0.16 Å as the terminated oxygen binded with the H atom. In addition, the longer Mo-O2 bonds were shortened by 0.05–0.17 Å while the short ones were elongated by 0.01–0.04 Å. As a result, the lattice constant along the a-axis was reduced by 1.5% (Table 1). These results suggest that the impurity-lattice interaction for hydrogenated MoO3 is extensive along the a-axis owing to the asymmetric O2-Mo-O2 chain. Consequently, the resulting band structure is metallic as shown in Figure 5a. According to Bader atomic charge analysis30, each hydrogen atom donated 0.6 electron to the host oxide, slightly changing the atomic charge of the neighboring Mo atoms from their stoichiometric value. The doping electrons occupied the electronic states at the bottom of the conduction band. Most importantly, the separation between the CBM and VBM was substantially reduced by ~0.5 eV. According to discussion in the previous section, the reduction of band gap is attributed to the deformation of the octahedral coordination. As could be seen from the octahedral structrure shown in Figure 4, the bonding of H remarkably reduced the distortion of the MoO6 octahedron. The bands near the gap, espectially the π-zx band, were expanded owing to the enhanced orbital overlap (Figure 5b).
The narrowing of the fundamental band gap has a direct effect on the optical properties of the system. Figure 6a shows the real (ε1) and imaginary (ε2) parts of the polarized dielectric function for MoO3. The dielectric functions show anisotropic responses to polarized light with the electric vector parallel to the a-axis (E|| a) and the c-axis (E|| c) owing to the distinct coordination along these two directions, in agreement with experimental measurements on MoO3 single crystals31. The low energy peaks of the imaginary dielectric function arose principally from the O 2p to Mo 4d transitions. The absorption spectra derived from the dielectric functions also show distinct features for polarized light parallel to the a- and c-axis (Figure 6b). From the spectra, the optical band gap for the pristine MoO3 was ~2 eV, which is about 1 eV under estimated as compared with experimental value but is in agreement with previous DFT calculations32. For the H intercalated MoO3, the absorption spectra were significantly modified. Firstly, new absorption bands emerged in the original gap due to the intraband transition in the partially filled conduction bands. Most interestingly, instead of having a blue-shift caused by the Moss-Burstein effect of band filling, the absorption band arose from the interband transition expanded and moved the absorption onset toward lower energy. The red-shift must result from the reducing band gap caused by the structural deformation. The narrowing of the fundamental band gap, suppressing the filling of the conduction band, reduced the optical band gap.
Our calculated results of the band gap narrowing are supported by experimental observations. Balendhran et al. recently studied the reduction process for MoO3 flakes through controlled H2 exposure11. Their measured (αhν)2-hν curves showed that the optical gap of MoO3 reduced gradually with increasing H2 exposure. Meanwhile, in their Raman spectra, the sharp peak at 820 cm−1 gradually disappeared and a broad peak at 780 cm−1 emerged. Since the peak at 820 cm−1 is assigned to the stretching mode of the Mo-O2 bonding, the Raman shift was obviously attributed to the deformation of the O2-Mo-O2 coordination. According to our calculations, the short Mo-O2 bonds were stretched by the hydrogen inclusion. Consequently, the force constant between Mo and O2 and hence the vibration frequency of the Mo-O2 bonding was reduced by the intercalation of H atoms.
To further the investigation, we simulated the electron doping by adding extra electrons into the unit cell of MoO3 and neutralizing the system via a homogenous positively charged background. As shown in Figure 7, the system band gap reduced monotonically with increasing extra charge and finally converged as the electron concentration reached one electron per Mo atom. Accompanied by the reduction of the band gap was the decrease of the asymmetry of the O2-Mo-O2 coordination. In the pristine MoO3, the bond length difference between the two Mo-O2 bonds was 0.5 Å. The difference was gradually reduced and finally eliminated as the doping concentration reached one electron per Mo. From this observation, the band gap narrowing was connected to the deformation of the O2-Mo-O2 coordination. Most importantly, since our simulations rule out the influence of the atomic size and other chemical parameters, the driving force was obviously the filling of the conduction band by the extra electrons. Thus, the band structure modification and the octahedral deformation in MoO3 is correlated and could be triggered by any process involving the electron doping. Indeed, in a previous report, a lithium insertion was also found to modify the crystal and band structure of MoO3 significantly32.
A physical picture can be established for the the structure-electronics correlation in MoO3. (i) For the asymmetric O2-Mo-O2 chain in MoO3 is easily deformed, the distorted octahedral coordination can be significantly reconstructed to be close to that of a regular octahedron. (ii) The octahedral deformation increases the pd-π type hybridization of Mo 3d and O 2p, resulting in the extension of the band edges and the narrowing of the fundamental band gap. (iii) The driving force for the structural reconstruction could be an epitaxial type structural strain or any n-type electron doping.
The above theoretical results also provide insights into the observed gap states for MoO3 deposited on metals9. Either the epitaxial-type of lattice strain effect or the electron doping by charge transfer at the metal/oxide interface could lead to the distortion of MoO3 lattice, resulting in additional peaks near the band gap. These electronic states are essentially the extension of the zx-π orbitals.
In summary, a systematic study on the effect of lattice distortion and electron doping in MoO3 was carried out. We found that the VBM and CBM of MoO3 were determined by the pd orbital interaction of the Mo with the bridging O2 and the symmetric O3. For the asymmetric bridging coordination, the O2-Mo-O2 chain was easily deformed by external interaction, and its deformation was closely connected to the band gap modification in MoO3. Distortion along this chain effectively modified the system band gap, while distortion along the b- or c-axis modified the system band gap less effectively. The intercalation of hydrogen atoms was also found to significantly deform the O2-Mo-O2 chain, resulting in the emergence of band tail states and band gap narrowing. Simulations confirmed that the driving force of the lattice distortion was the filling of the conduction band. The results observed in hydrogenated MoO3 could be anticipated in any process involving electron doping. Our results explain the optical gap reduction and the Raman shift in H2 exposed MoO3, and the gap states emerged in the MoO3 deposited on metals. This work shows that understanding the relationship between geometric and electronic structures is essential to understand the physical properties of metal oxides.
This work was supported by National Natural Science Foundation of China (Grant No. 61366007 and No. 11164032 and No. 61066005 and No. U1037604), Program for New Century Excellent Talents in University (Grant No. NCET-12-1080), Chinese Ministry of Science and Technology(973 program, Grant No.2012CB326400), Applied Basic Research Foundation of Yunnan Province (Grant No. 2011CI003 and No. 2013FB007), Program for Excellent Young Talents in Yunnan University, and Scholarship Award for Excellent Doctoral Student in Yunnan Province (2013). Computational resources are provided by High Performance Computing Center of Yunnan University.
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Advanced Energy Materials (2019)