Optical Properties of Zn2Mo3O8: Combination of Theoretical and

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Optical Properties of ZnMoO: Combination of Theoretical and Experimental Study Tathagata Biswas, Pramod Ravindra, Eashwer Athresh, Rajeev Ranjan, Sushobhan Avasthi, and Manish Jain J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b07473 • Publication Date (Web): 11 Oct 2017 Downloaded from http://pubs.acs.org on October 16, 2017

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The Journal of Physical Chemistry

Optical Properties of Zn2Mo3O8: Combination of Theoretical and Experimental Study Tathagata Biswas,† Pramod Ravindra,‡ Eashwer Athresh,¶ Rajeev Ranjan,¶ Sushobhan Avasthi,‡ and Manish Jain∗,† †Center for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore, 560012 ‡Centre for Nano Science and Engineering (CeNSE), Indian Institute of Science , Bangalore, 560012 ¶Department of Materials Engineering, Indian Institute of Science, Bangalore, 560012 E-mail: [email protected]

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Abstract We have investigated the electronic structure and optical properties of Zinc Molybdenum Oxide (Zn2 Mo3 O8 ) by using both first principle calculations and experiments. Optical properties of this material is very similar to other ternary oxides of tetravalent Molybdenum (A2 Mo3 O8 : A=Mg, Fe, Cd), therefore this study provides meaningful insight into optical properties and possible phtotovoltaic applicability of these class of metal oxide cluster compounds. We use state-of-the-art methods, based on density functional theory and the GW approximation to the self energy, to obtain the quasiparticle bandstructure and absorption spectra of the material. Our calculations shows that Zn2 Mo3 O8 is a near indirect gap semiconductor with an indirect gap of 3.14 eV. The direct gap of the material is 3.16 eV. We also calculate the optical absorption in the material. Calculated results compare well with UV-visible spectroscopy and spectroscopic ellipsometry measurements done on polycrystalline thin-films of Zn2 Mo3 O8 . We show the material has a large excitonic binding energy of 0.78 eV.

Introduction Oxides have attracted attention recently as absorbers in solar cells. Several oxides are earth abundant, chemically stable, non-toxic, and can be deposited at low cost. Therefore oxides hold the promise of inexpensive, environmentally safe and potentially high-efficiency solar cells. Unfortunately, oxide solar cells have seen limited success mostly because the large band gap (in most cases in the UV regime). The carrier recombination lifetimes and mobilities in these materials also tends to be low. Due to the limitations, oxides have been predominantly explored for photocatalysis, seldom as absorbers in photovoltaic devices. 1,2 So there is a need to explore oxides to identify promising solar absorbers. Zinc Molybdenum Oxide (Zn2 Mo3 O8 ) is one of the first metal oxide clusters to be synthesized, 3,4 along with few other ternary oxides of tetravalent Molybdenum (A2 Mo3 O8 : A=Mg, Fe, Cd, Mn, Co, Ni). Zn2 Mo3 O8 (ZMO) has been recently used as an anode in batteries 5 2


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as well as a photoanode for photoassisted electrolysis (PAE) of water. 6 For a material to be suitable photoabsorber, it has to satisfy several criteria. 7 First, the phototransition should not split the chemical bonds, which restricts the search space to covalently bonded semiconductors with d–d transitions. Second, the band gap of the material has to be in the range of ∼ 1.5-2.5 eV so that it absorbs a significant portion of the solar energy radiation. This can be achieved by a strong crystal field that creates a large splitting of the d orbitals. Third, the materials has to exhibit moderately high electron and hole mobility. The last criteria is the most restrictive because oxides typically are poor hole conductors. Fortunately, materials with strong metal–metal interaction (small distance) and materials with 4d or 5d bands, can exhibit high carrier mobilities. According to previous experimental studies 6 all the ternary oxides of tetravalent Molybdenum (A2 Mo3 O8 : A=Zn, Mg, Fe was studied only) show very similar photoelectrochemical properties and have been found to satisfy all the aforementioned criteria. The Mo–Mo distance in ZMO is 2.53 Å which is smaller than that in Molybdenum metal (∼ 2.7 Å). This indicates a strong metal–metal hybridization. The valence band edge and conduction band edge both have Mo(4d) character. This ensures that most of the transitions in the visible region of the spectrum have a d–d character. Finally, ZMO has been reported to have a indirect band gap of 1.55 eV and a direct gap of 1.9 eV. 6 However, this report 6 was not very conclusive about the band gap, as the quantum efficiency verses wavelength did not show any abrupt change in slope. Also, band gaps extracted from the Tauc plots – (Φhν)0.5 vs hν for indirect bandgap and (Φhν)2 vs hν for direct bandgap – were unconvincing because a straight line fit couldnot be obtained in two different non-overlapping spectral regions. Usually for materials whose absorption spectra show both direct and indirect band gaps, such as CdO 8 this is not the case. Performing first principles calculation on ZMO can clarify these issues by providing a better understanding of the electronic structure and optical properties of not only ZMO but this group of metal oxide cluster compounds. Our calculations can also explain why the optical properties of these materials (A2 Mo3 O8 ) do not depend on the

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divalent cation (A2+ ). In this study we use a combination of first principle calculations and UV-visible spectroscopy and spectroscopic ellipsometry to study electronic structure and optical properties of ZMO. Our first principles calculations are performed at density functional theory (DFT) level to understand the ground-state properties of the material. We construct maximally localized Wannier functions (MLWF) to get a deeper understanding of the electronic structure as well as the metal ligand hybridization in this metal oxide cluster compound. Next, we compute the quasiparticle band structure of ZMO by using the GW approximation to the self-energy. We also compute the optical spectra of ZMO using the Bethe-Salpeter equation (BSE). To compare the calculations with experiments, polycrystalline ZMO thin-films were experimentally synthesized using pulse-laser deposition. UV-visible spectroscopy and spectroscopic ellipsometry were used to determine the optical bandgap and the real and imaginary parts of the dielectric function of polycrystalline samples of ZMO. We show that the experimentally determined optical gap is in good agreement with the absorption onset, as seen from the imaginary part of the dielectric function, after averaging along all three directions of polarization of light.

Computational Methods The first principle DFT calculations in this work were performed using the pseudopotential plane wave method as implemented in Quantum Espresso 9 package. We used recently developed Optimized Norm-Conserving Vanderbilt (ONCV) pseudopotentials 10,11 and the generalized gradient approximation (GGA) 12 proposed by Perdew, Burke and Ernzerhof (PBE) for the exchange-correlation potential. The pseudopotentials used in the calculations include semi-core states (3s, 3p in case of Zn and 4s, 4p in case of Mo), to capture the strong exchange-interaction resulting from those states. The unit cell of ZMO has 26 atoms containing two formula units of ZMO. The Brillouin zone was sampled using a 3 × 3 × 2

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k-grid and the wavefunctions were expanded using plane waves with energy upto 70 Ry. In case of structural relaxation we used a higher number of plane waves upto 100 Ry to ensure convergence of the results. In order to obtain the lattice parameter values from DFT calculation we relaxed the lattice constants as well as the atomic positions using BFGS quasi-newton algorithm, 9 such that the pressure on the unit cell is less than 0.5 Kbar and force on each atom is less than 0.025 eV/Å. Once we obtained DFT Kohn-Sham (KS) wavefunctions by solving KS equation, we constructed MLWFs 13,14 using methods implemented in Wannier90 15 package. We have included 200 bands in the wannierisation procedure. The outer window for wannierisation extends from 130 eV below VBM to ∼19 eV above VBM. For the disentanglement procedure, 14 the inner window was selected to include all the bands in the energy range 21 eV below VBM to ∼7 eV above VBM. We used d states on Zn and Mo sites and s, p states on O sites as initial guesses of the Wannier projections. With this procedure, we obtain well localized Wannier functions (see Table S1 in supplementary material for details). In order to find the energy levels of the objective orbitals without the effects of hybridization with other states, 16–18 we follow the following procedure. We first rewrite the Hamiltonian of the system in MLWF basis. In this basis, the Hamiltonian will consist of four blocks – one objective orbital block (Ho (k)), some other block of states (Ho′ (k)) that hybridizes with objective orbital block and offdiagonal blocks (V (k)) which account for the amount of hybridization between those two groups of states. Schematically the Hamiltonian in the MLWF basis can be written as: 



Ho (k) V (k)  H(k) =   V † (k) Ho′ (k)

(1)

We set the orbitals of interest as the objective block. To exclude the effect of hybridization, we diagonalize just the objective block of the Hamiltonian (Ho (k)). This method enables us to find energies of the unhybridized orbitals of interest. We calculated the quasiparticle band structure of ZMO within the GW approximation 5



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to the self energy. 19,20 To calculate the optical response of the material, we solve the BetheSalpeter equation (BSE) 21–23 where we explicitly take electron-hole interaction into account. The solution to the BSE can be used to compute the imaginary part of the dielectric function, which contains all the essential information about optical response of a material. We used the BerkeleyGW 24 package to perform one-shot G0 W0 and BSE calculations. There are several other GW schemes available, such as partial self-consistent GW and self consistent GW, 25–29 but due to computational expense we restrict ourselves to the one-shot G0 W0 level of calculation. The dielectric matrix was expanded in plane waves with energy upto 35 Ry and extended to finite frequencies within the generalized plasmon pole model 20 proposed by Hybertsen and Louie. We have used 1000 bands for both dielectric matrix and self-energy operator (Σ) calculations. We added a static remainder 30 term to the self energy, to ensure the convergence of our results with the number of bands (see Fig. S3 in supplementary materials for details). Overall, our quasiparticle energies were converged to ∼ 0.1 eV. For the BSE calculation, the kernel was interpolated from 3×3×2 coarse k-grid to a 9×9×6 fine k-grid. We included 20 valence and 6 conduction bands to construct the electron-hole interaction kernel. These calculation parameters were sufficient to ensure the convergence of the absorption spectrum up to ∼ 3 eV from the absorption-edge (see Fig. S4 in supplementary materials for details). To obtain the absorption spectrum at finite temperature we follow recently proposed “one shot calculation” procedure. 31 In this methodology one displaces the atoms in a m×m×m supercell by ∆τκα , ∆τκα = (

Mp 1 X )2 (−1)ν−1 eκα,ν σν,T Mκ ν

(2)

where σν,T is defined as, 2 σν,T = (2nν,T + 1)

h ¯ 2Mp Ων

(3)

and Mκ is the mass of the κth nucleus, and Mp is the proton mass. Ων and eκα,ν are the vibrational eigenfrequency and eigenmodes respectively, obtained by diagonalizing the

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dynamical matrix. nν,T is the Bose-Einstein occupation function at temperature T . We then compute the imaginary part of the dielectric function without taking into account any electron-hole interaction. We follow this procedure to estimate the effect of electron-hole coupling to the band gap of ZMO at 300 K. We have done the calculation with 2×2×1 supercell. To obtain the RPA dielectric function we use a 4×4×4 k-point sampling of the Brillouin zone.

Experimental Methods Thin films of ZMO were deposited using Pulsed Laser Deposition. Stoichiometric pellets were prepared by mixing appropriate amounts of ZnO and MoO3 and elemental Mo. 32 The mixture was cold pressed, sealed in a quartz ampule at low pressure (10-4 mbar) and heated to 1223 K for 8 h so that the components can react. The pellet was then sintered, also at low pressure, to 1253 K for 10 h. This pellet was ablated using a KrF excimer laser (248 nm, Coherent CompEX Pro) to deposit polycrystalline thin films of ZMO. UV-visible spectroscopy was performed using Shimadzu MPC3600 spectrometer, using an integrating sphere attachment. Spectroscopic ellipsometry was done using J.A. Woollam M2000U ellipsometer. The bandgap was calculated from UV-visible spectroscopy. Transmittance and reflectance (diffuse + specular) of thin films of ZMO were measured individually. Absorption coefficient α is calculated using, α=

−1 T ln d 1−R

(4)

Where d is the thickness of the film, T the total transmittance and R the total reflectance. Using the absorption coefficient, the bandgap can be extracted using the Tauc equation, 1

αhν = A(hν − Eg ) r where r = 2 for indirect bandgap and

1 2

(5)

for direct bandgap. The plot of (αhν)2 vs hν, when

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number. Alternating layers of Mo and Zn atoms are separated by layers of oxygen atoms arranged in distorted hexagonal-close-packed structure. The stacking of the O layers follow abac sequence along [001] direction. Our calculated lattice parameters and atomic positions are listed in Table . 1. Table. 1 also shows the experimental values of the lattice parameters as obtained from neutron diffraction experiments. 33 We can see from the table that our results are in excellent agreement with the experiment. 33 The slight overestimation of the calculated lattice parameters (< 2 %) compared to the experiment is expected due to the underbinding of GGA exchange-correlation functional. 34,35 Table 1: Comparison between atomic positions from the calculation and experimental data obtained from total neutron diffraction. Lattice parameters (in Å) a c unit cell volume Atom Wyckoff x Zn(1) 2(b) 0.3333 Zn(2) 2(b) 0.3333 Mo 6(c) 0.1475 O(1) 2(a) 0.0000 O(2) 2(b) 0.3333 O(3) 6(c) 0.4881 O(4) 6(c) 0.1662

y 0.6667 0.6667 0.8525 0.0000 0.6667 0.5119 0.8338

Experimental 33 5.77 9.91 286.11 z 0.5155 0.9491 0.2500 0.8921 0.1450 0.3658 0.6334

x 0.3336 0.3335 0.1455 0.0000 0.3333 0.4882 0.1659

y 0.6671 0.6670 0.8543 0.0002 0.6669 0.5116 0.8343

Theoretical 5.78 10.06 294.05 z 0.5167 0.9492 0.2503 0.8915 0.1447 0.3643 0.6344

Fig. 2(a) shows the electronic band structure of ZMO obtained from DFT calculations. Our DFT level calculation suggests that ZMO is an indirect-gap material with a band gap of 1.67 eV. The valence band maxima (VBM) occurs along the Γ-K direction and conduction band minima(CBM) is near M point of the Brillouin zone, giving the material indirect band gap. The direct-gap of the material is also very close (1.7 eV) and occurs very close to M point. In Fig. 2(b) we show orbital resolved density of states (DOS) for Zn(3d), Mo(4d) and O(2p) states. The bands around the band gap are mostly flat. This is because these bands have a large localized Mo(4d) character with some hybridization with O(2p) states. The flatness of these bands suggests that both electron and hole mobilty in ZMO is expected to 9




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calculated optical gap is ∼ 0.3 eV larger than experimental value and lowest energy excitons in our calculations being dark, can both be attributed to finite temperature and polar 43 effects, both of which have not been included in our calculations. At finite temperature phonons can renormalize the band gap in two ways. Firstly the electron-phonon coupling, leads to the Fan and Debye-Waller 44,45 terms in the GW self energy which can effect the quasiparticle energies. Secondly in case of polar materials long range electric fields contribution to the frequencydependent dielectric function becomes important and has to be included separately. 43 Both these effects can not only renormalize the quasiparticle and optical band gap, but can also change the oscillator strengths of the bound excitons. 46 We have estimated the magnitude of band gap renormalization due to the effects discussed above. To check if the electron-phonon interaction is important, we calculated the imaginary part of the dielectric function within the random phase approximation (RPA) at room temperature (300 K) using recently developed “one shot calculation” method. 31 The result shows that at 300 K the absorption edge red-shifts by ∼0.3 eV, when compared to zero temperature value (see Fig. S2 in supplementary material for details). To predict the experimental optical gap at finite temperature, one needs to include both the electron-hole interaction as well as electron-phonon interaction in the calculation. The electron-phonon coupling will not only have an effect on the quasiparticle gap but also on the exciton binding energy. As a result the optical gap can differ from the zero temperature value (2.38 eV) in a completely non-trivial way (and not just by the shift in the quasiparticle gap). However our calculation shows that in case of ZMO the electron-phonon interaction is important to obtain optical properties accurately and it is possible that the band gap can get renormalized by ∼0.3 eV. In recent years ‘polar’ materials with two atoms in the unit cell have been studied to understand the effect of lattice screening on GW quasiparticle gap. 43 We have computed the LO-TO splittings using density functional perturbation theory to estimate these effects in case of ZMO (see Table. S2 in the supplementary material for details) and we believe that

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this effect can also lead to a renormalization of the gap. We base this is on the trend we see for materials studied by Botti et al. 43 The largest LO-TO splitting ZMO is ∼0.15 mHartree. For materials studied in Reference [43], the LO-TO splitting of this order renormalizes the gap by ∼0.05 eV. We also find few optical modes (∼5) that split by ∼0.1 mHartree. All of these modes together can lower the quasiparticle band gap further and effect the optical gap as well. Fig. 6(a) shows a large aniostropy in absorption for low energy transitions. The absorption peak at ∼ 2.7 eV is present in case of light polarization perpendicular to c-axis but not there when polarization of light is parallel to c-axis. Now if we compare the absorption onset with the quasiparticle gap and the difference can be considered as the exciton binding energy. For ZMO we get a large exciton binding energy (0.78 eV), which is expected as the low energy transitions are between Mo(4d) levels which are very localized and form almost flat bands throughout the Brillouin zone. The lowest energy exciton in this material is a Frenkel exciton, which is almost completely localized within a unit cell. As a result, the coulombic interaction between the electron and hole makes the exciton binding energy large. 47–49 In Fig. 6(b) we show the exciton wavefunction corresponding to lowest energy exciton (2.38 eV). The plots are isosurface of modulus squared of the real-space exciton wavefunction. The isosurface of the exciton wavefunction was plotted by choosing 2% of the maximum value. We fixed the hole position to be near the Mo atom along the bond between Mo and one of the O atom. Fig. 6(b) shows that the excitons in this system are Frenkel like, as it is localized within a single unit cell in c direction and has a slightly larger spread in a-b plane.

Conclusion We have used state-of-the-art GW-BSE methodology to understand the electronic structure ZMO starting from DFT mean field. Our calculation shows that the valence and conduction bands in this material arises due to hybridization between Mo(4d) and O(2p,2s) orbitals.

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Our calculated GW band structure shows a indirect band gap of 3.14 eV. Furthermore, our optical band gap (2.38 eV) is in agreement with experimental value of 2.07 eV, considering we have not included any finite temperature effects in our calculation. The exciton binding energy in this material is quite large (0.78 eV) for it to be used in photovoltaic applications. In addition, the GW band structure of ZMO indicates that mobilty of both electron and hole is going to be very low. This along with the anisotropic absorption below 3 eV will make this material difficult to use for photovoltaic applications.

Acknowledgement The authors thank Prof. S. Raghavan and Prof. P. Ramamurthy for useful discussions This work is supported under the US-India Partnership to Advance Clean Energy-Research (PACE-R) for the Solar Energy Research Institute for India and the United States (SERIIUS), funded jointly by the U.S. Department of Energy (Office of Science, Office of Basic Energy Sciences, and Energy Efficiency and Renewable Energy, Solar Energy Technology Program, under Subcontract DE-AC36-08GO28308 to the National Renewable Energy Laboratory, Golden, Colorado) and the Government of India, through the Department of Science and Technology under Subcontract IUSSTF/JCERDC-SERIIUS/2012 dated 22nd Nov. 2012. We thank Super Computer Research and Education Centre (SERC) at IISc for the computational facilities.

Supporting Information Available Spread of different MLWFs, absorption spectra plotted on logarithmic scale, effect of finite temperature on absorption spectrum, LO-TO splittings for ZMO, convergence of quasiparticle energies with number of bands and convergence of absorption spectrum with number of k-points in the Brillouin zone. This material is available free of charge via the Internet at http://pubs.acs.org/. 17



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Optical Properties of Zn2Mo3O8: Combination of Theoretical and

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