Influence of strain on optical properties of multiferroic EuTiO
3film:
A first-principles investigation
XinyuWang,1SiqiZhen,1YiMin,1PengxiaZhou,1,2YanyanHuang,1,3ChongguiZhong,1,3,a) ZhengchaoDong,1,3,b)and JunmingLiu2
1School of Sciences, Nantong University, Nantong 226019, China
2Laboratory of Solid State Microstructures and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
3College of Physics, Optoelectronics and Energy, Soochow University, Suzhou 215006, China
(Received 2 August 2017; accepted 28 October 2017; published online 16 November 2017) We use first-principles calculations based on the density functional theory to investigate the mag- netic properties, optical properties, and electronic structure of perovskite-type multiferroic EuTiO3 (ETO) thin films with biaxial strain. The calculations indicate that, in ETO films, the magnetic moment of Eu ions and the energy of the direct band gap decrease slowly (increase rapidly) with increasing compressive (tensile) strain. A direct band gap tunable from 1.0 to 1.52 eV is expected in ferroelectric and ferromagnetic ETO thin films upon application of 1%–4% tensile strain, and photogenerated carriers with spin-polarization can be induced from Eu 4f to Ti 3d states. This behavior can be confirmed by monitoring the strain-dependent optical absorption coefficient of ETO thin films and is explained by the shift of the strain-tuned electronic structure. These results suggest the potential applications of ETO thin films in multiferroic photovoltaic cells.Published by AIP Publishing.https://doi.org/10.1063/1.4998665
I. INTRODUCTION
ABO3-type perovskite thin films constitute an important class of functional materials for technological applications such as solid-state refrigeration, solar cells, and sensors because of their promising electrical, magnetic, and optical properties.1,2An interesting case in point is perovskite ferro- electric materials, which have an intrinsic spontaneous polar- ization that leads to an anomalous photovoltaic effect. That is, the photocurrent is a function of the electric-field-induced polarization, so that the photovoltage becomes proportional to the distance along the electric field and can be larger than the band gap.3,4Therefore, a higher photoelectric conversion efficiency can be obtained in perovskite-type ferroelectric materials, which is of great interest for applications in solar cells.
According to reports on perovskite-type materials, most bandgaps exceed 2.4 eV, directly hindering effective absorp- tion of visible light (3.3–1.59 eV).5–7Based on experiment and theory, the main methods to reduce the band gap to the ideal value for photovoltaic applications include impurity doping, the size effect, lattice mismatch, and strain engineering. For instance, in Ba/Ni codoped KNbO3 and Co doped SrTiO3
perovskite materials, smaller band gaps with concomitantly greater absorption in the visible region have been obtained.8,9 In addition, the band gap of the SrTcO3film decreases substan- tially under a compressive or tensile strain, even dropping to zero with 8.75% compressive strain.10Ramakanthet al.used the sol-gel fabrication method to prepare BaTiO3nanoparticles of varying size and reported that the application of strain weak- ens electron-phonon and exchange-correlation interactions
between charge carriers, and that the band gap decreases from 3.2 to 2.53 eV with decreasing average size of BaTiO3nano- particles.11Unfortunately, the band gaps obtained in the afore- mentioned materials remain too large to be of use in photovoltaic solar-cell applications.
A multiferroic EuTiO3 (ETO) thin film is a typical perovskite-type material and has attracted considerable attention because of its interesting physical properties, such as the magnetodielectric effect, quantum fluctuations, and magneto-optical properties.12–15 Although bulk ETO is a quantum paraelectric (PE) with G-type antiferromagnetic (AFM) order below the Neel temperatureTN, both ferroelec- tric (FE) and ferromagnetic (FM) ordering can be induced in ETO films by applying a sufficiently large strain.16 These intriguing phase transitions open the way to applications for multiphase information storage. Moreover, the ETO film with no strain has a small direct band gap of 0.93 eV, which is close to the ideal value of 1.4 eV, making the ETO film a strong candidate for use in multiferroic photovoltaic solar cells.4 Thus, the optical properties of these films have aroused significant interest in recent years.15,17,18 However, the influence of strain on magnetism, the optical band gap, and the electronic structure of ETO films remains poorly understood. Research on this topic includes the work of Jianget al., who investigated the band gap in epitaxial ETO thin films fabricated on (001) LaAlO3substrates and reported that the band gap decreases by about 240 meV because of the 3% lattice mismatch between the film and substrate.19 Unfortunately, this narrowed band gap remains far from ideal for effective absorption in the visible region. In prac- tice, the application of strain or the use of ionic doping is expected to broaden the band gap of the ETO film, allowing it to be tuned to the desired value for device applications.
a)Electronic mail: [email protected]
b)Electronic mail: [email protected]
0021-8979/2017/122(19)/194102/6/$30.00 122, 194102-1 Published by AIP Publishing.
Thus, in the present work, we use first-principles calcu- lations based on the density functional theory to investigate the magnetism, electronic structure, and optical absorption of ETO thin films as a function of compressive and tensile strain. In contrast to previous investigations,19the purpose of this work is to investigate the magnetic moments and band gap of ETO films as a function of strain, obtain the range of strain that gives an ideal band gap for photovoltaic applica- tions, and explain these changes in terms of the strain-tuned shifts in the electronic structure. The results indicate that a direct band gap tunable from about 1.00 to 1.52 eV should occur in FE and FM ETO thin films upon applying 1%–4%
tensile strain. Furthermore, under these conditions, photo- generated spin-polarized carriers with a relatively small elec- tron effective mass can be photoexcited from Eu 4fto Ti 3d states. We hope that these results stimulate experimental investigations into photovoltaic applications involving ETO films deposited on suitable substrates.
II. CRYSTAL STRUCTURE AND COMPUTATIONAL DETAILS
Despite the cubic perovskite structure for AFM-PE bulk ETO (space group Pm3m) with lattice constanta¼3.905 A˚ at room temperature, the epitaxial strain is believed to be responsible for the octahedral distortion and the resulting loss of crystal-structure symmetry in ETO thin films.20 In this work, we consider an isotropous biaxial strain in ETO films to allow for both epitaxial compressive and tensile lat- tice mismatch between the ETO thin film and the substrate.
By full relaxation, we obtain the equilibrium lattice constant cand internal atom positions as a function of biaxial strain from5% to 5% based on the optimized lattice parametera.
For these first-principles calculations to account for the change in the structural symmetry and the varying magnetic interactions of epitaxial ETO films, we construct a ffiffiffi
p2 ffiffiffi
p2
2 tetragonal cell, which contains 4 Eu, 4 Ti, and 12 O, as shown in Fig.1.
The projector-augmented wave method implemented in the Vienna ab initio simulation package21–23is used herein for both structural-relaxation and static calculations, in which Eu (5s25p64f7), Ti (3s23p63d2), and O (2s22p4) are treated as valence states. Because Eu atoms cause strong electronic correlations that cannot be neglected, we use the Perdew–Burke–Ernzerhof-type (PBE) exchange-correlation potential instead of the general GGAþU method. The choice of Uand Jhas been adequately investigated, so we use the reported valuesU¼8.0 eV and J¼0.8 eV (Ref.24) for our calculations. When using the PBEþUmethod, these values produce a stable G-type AFM ground state and a rela- tively suitable band gap that is consistent with the experi- mental results from unstrained ETO films.
For the electronic-structure calculations, the Brillouin zone is integrated by using the Monkhorst–Pack method in 12128. The cutoff energy is 500 eV for the electronic plane-wave functions. The stable, optimized structure of ETO films under various strains is obtained after full relaxa- tion. Finally, the polarization P~of ETO films under various strains is estimated by using the polarization theory based on P~¼ ðRq~rÞ=V, whereqand~rare the Born effective charge and coordinate vector of each ion, respectively, andVis the cell volume.
III. RESULTS AND DISCUSSION
For unstrained ETO films, the lattice constant a¼3.915 A˚ and the G-type AFM ground state are obtained via the PBEþU calculation and are consistent with the experimental results.18Because of the largeU, the energy of the G-type AFM state is only 3 meV less than that of the FM phase per formula unit, and the magnetic moment obtained for Eu (6.92lB) is consistent with the nominal net magnetic moment of the Eu ion (7lB).20 Next, we assume that a compressive-tensile strain of 1%, 2%, 3%, and 4% is imposed on the ETO film and investigate the physical prop- erties as a function of strain. Note that, although bulk ferroic oxides are brittle and typically crack under moderate strains of 0.1%, strains of about 63% are common in epitaxial oxide films. Moreover, epitaxial ETO films deposited on DyScO3or (LaAlO3)0.3-(SrAl0.5Ta0.5O3)0.7experience vary- ing compressive or tensile strains, which leads to several new equilibrium phases. Therefore, we believe that a strain of magnitude no greater than 4%, which can be achieved by growing ETO films on the appropriate substrates, will induce neither imaginary modes nor structure instability in the film.
Figure2(a)shows the in-plane polarizationPaband the out-of-plane polarization Pc of ETO films as a function of strain. These results indicate that an increasing strain leads to a nonzero FE polarization, confirming the strain-induced FE state in the ETO thin film.16Note that we do not give the exact critical strain required for inducing the FE state; how- ever, based on our estimate, a 1%-magnitude strain should suffice to induce the FE order, particularly for tensile strains.
According to our calculation, the out-of-plane polarization Pcof the ETO thin film increases nonlinearly with increasing compressive strain (from 1% to 4%), and then saturates at a sufficiently high compressive strain, whereas the in-plane
FIG. 1. Geometric structure of cubic perovskite EuTiO3: the blue, red, and purple spheres represent the Ti, O, and Eu atoms, respectively.
polarizationPabis linear in the applied tensile strain, which is consistent with the theoretical results.25 Moreover,Pabis enhanced more than Pc as the magnitude of the strain increases from 1% to 4%. Therefore,Pabis much larger than Pc for a given magnitude of strain, indicating that tensile strain should have a more obvious effect on the band gap of the ETO film than compressive strain.
Figure 2(b) shows the band gap and magnetic moment of Eu in ETO thin films as a function of strain. The magnetic moment of Eu is linear in strain in the low-strain range. It decreases (increases) with increasing compressive (tensile) strain, reaching saturation for tensile strains exceeding 5%.
In addition, we find that tensile strain affects the band gap in the ETO film more significantly than does compressive strain. The band gap of ETO films under tensile strains of 1%, 2%, 3%, 4%, and 5% gradually increases (1.00, 1.17, 1.32, 1.52, and 1.63 eV, respectively), reaching the band-gap range for efficient solar cells. According to this calculation, compressive strain leads to a small decrease in the band gap, which is consistent with the results obtained from the optical absorption spectra presented in Fig. 6(a) and with
experimental results.19 Consequently, the desired band gap may be achieved by choosing the appropriate substrate so that the desired tensile strain is imposed on the multiferroic ETO thin film. Most importantly, these changes in band gap and magnetic moment caused by the strain are associated with variations in polarization.
To further discuss the band gap and polarization as a function of strain, the Ti-O1, 2 bond lengths and O1-Ti-O2 bond angles in ETO thin films with strains of 0%,3%, andþ3% are presented in TableI. Here, O1denotes the api- cal oxygen atom above or below the Ti atom and O2denotes the basal ab-plane oxygen. Modifications of these bond lengths and bond angles indicate that the off-center deviation of Ti ions along the c axis contributes to the out-of-plane polarizationPcunder a compressive strain of3%, whereas the movement of Ti ions in the ab plane results in the in- plane polarization Pabunder aþ3% tensile strain, as shown in Fig. 2(a). In addition, the changes in bond angles under the tensile strain suggest the tilts and rotations of oxygen octahedrons, which also strongly influence the increase of the band gap in ETO films.
The electronic structure of ETO films as a function of applied strain is shown in Fig. 3. The left panels show the evolution of the total density of states (TDOS) with and without strain. Compared with the strain-free case, the effect of strain on the electronic structure is quite clear. The tensile strain leads to a smaller band gap and a movement away from the Fermi level EF at the bottom of the conduction band, whereas the compressive strain induces a larger band gap and a slight movement towards EFat the bottom of the conduction band. Furthermore, the local density of states (LDOS) of representative Eu, Ti, and O ions indicates that the valence band mainly consists of O 2pand a few Ti 3d states, and the top of the valence band consists of localized Eu 4f states, while the bottom of the conduction band con- sists of Ti 3d states, as seen in the right panels of Fig. 3.
These electronic distributions are consistent with the results of recent studies.18,19,24 Half-occupied Eu 4f states have a strong spin-polarization character, so the net magnetic moment of the ETO film comes mainly from these states.
More importantly, a large number of Eu 4f states near the Fermi surface contribute greatly to the production of photo- generated electron-hole pairs.26 For unstrained ETO films, two peaks appear around4 and2 eV below EF, corre- sponding to the bonding and antibonding states from the hybridization of the Ti 3dand O 2pwave functions, respec- tively. When a compressive strain is applied, the bond length of Ti-O2 decreases and the bonding states shift down in energy, resulting in a stronger and broader covalent bond between Ti 3dand O 2pstates. However, the opposite seems
FIG. 2. (a) FE polarization of FM ETO films under various strains. (b) Magnetic moment of Eu ion and band gap of the ETO film as a function of strain. The negative (positive) values of strain represent the compressive (tensile) strain.
TABLE I. Ti-O1, 2bond lengths and O1-Ti-O2 bond angles for ETO thin films with strains of 0%,3%, andþ3%.
Ti-O1(A˚ ) Ti-O2(A˚ ) O1-Ti-O2(deg)
Unstrained 1.9525 1.9525 90.00
Compressive strain (3%) 2.0185 1.8952 89.89
Tensile strain (þ3%) 1.8972 2.1586 85.88
to be the case for tensile-strained films, in which the bond length of Ti-O2 increases, weakening the covalent bond between Ti 3dand O 2pand leading to the smaller band gap.
Meanwhile, with increasing tensile strain, Eu 4f states become more localized and Ti 3dstates in the conduction band shift away fromEF, explaining why tensile strain more strongly affects the band gap between the Eu 4f and Ti 3d orbitals compared to compressive strain.27
To better understand in detail the strain-dependent varia- tion of the band gap from the electronic structure, Fig. 4 shows the partial density of states (PDOS) of Tit2g andeg
and O 2pof ETO films with different strains. Compared to the electronic distribution in unstrained ETO films, thedxy, dyz, anddxzstates of the conduction band of the Ti 3dorbital become more localized under the tensile strain, moving the bottom of conduction further away from EF and thereby increasing the band gap. In addition, thep-dorbital hybridi- zation between the empty Ti 3d and O2 2py states about 3.5 eV belowEFdrives the in-plane off-centered deviation of
Ti ions in the oxygen octahedron, giving rise to the in-plane FE polarization.13,16Conversely, with O 2pand Ti 3dstates shifting to lower energy, the strong p bond between the Ti dxy/dyz/dxzand O22pzstates caused by the increased overlap of the wave functions results in a decrease in energy under the compressive strain, and the hybridization between Ti 3d3z2r2and O12pzat5 eV strengthens therbond, generat- ing out-of-plane FE polarization.12,13,16 Thus, we deduce that strain significantly modifies the band gap between the Eu 4fand Ti 3dstates, mainly by regulating Ti-O hybridiza- tion and breaking the local symmetry in the oxygen octahe- dral distortion.25,28
The variations in the band structure plotted in Figs.
5(a)–5(c) verify the effect of strain on the band gap. The ETO thin film with 3% tensile strain presents the largest band gap [see Fig.5(c)]. With increasing compressive strain, the band gap decreases, as shown in Fig. 2(b). Despite the difference between strained and unstrained ETO thin films, both the top of the valence band and the bottom of the
FIG. 3. Evolution of TDOS in the ETO film (left panels) and LDOS of Eu, Ti, O1, and O2in ETO films (right panels) with strains of (a) 0%, (b)3%, and (c)þ3%.
FIG. 4. PDOS of Ti 3dand O 2pstates in the ETO film. The black, red, and blue lines correspond to 0%,3%, andþ3% strain, respectively.
conduction band are at theC point, which means that the band gap is direct and that an intrinsic absorption is allowed without electron-phonon coupling. Thus, photogenerated carriers can be produced with large spin polarization.27
In addition to a suitable band gap, the effective mass of carriers in ETO films is another important factor for potential photovoltaic applications. Thus, we calculate the electron effective mass m* along different directions in reciprocal space by fitting the band structure around the conduction- band minimum with the equationm¼h2=ðd2E=dk2Þ29(see TableII). Because of the equivalence of the [100] and [010]
directions, we only give the effective mass along the [100]
direction. The calculated effective electron mass along the various directions shows only small fluctuations for a given strain, indicating that electronic transport in ETO films is weak and anisotropic. The electron effective mass obtained here for the ETO thin film is slightly larger than that of (CH3NH3)2Pb(SCN)2I2.29 However, in the ETO thin film subjected to aþ3% tensile strain, as shown in Table II, a smaller effective electron mass is obtained, indicating that photogenerated electronic transport is easier in ETO thin films under tensile strain than in films with compressive strain.
The absorption coefficient a and optical band gap for ETO films with different strains can be obtained by using the formula a¼ ffiffiffi
p2E
hcfðe21þe22Þ1=2e1g1=2 and from the Tauc plot of (aE)2E, as shown in Fig.6. In this formula,handc have their usual meaning,Eis the photon energy, ande1and e2 are the real and imaginary parts of the dielectric constant, respectively. From Fig. 6(a), the absorption edge of the unstrained ETO thin film is 0.81 eV, which shifts by0.7 andþ1.31 eV for ETO films with3% andþ3% strain, respectively. Meanwhile, absorption occurs in the visible region of 380–780 nm (3.3–1.59 eV), as shown in Fig.6(a).
The optical band gap can be obtained by a linear extrapola- tion of (aE)2Eto zero, as shown in Fig. 6(b). The optical band gap of the strain-free ETO film is thus estimated to be 0.86 eV, which is comparable with the reported values of
FIG. 5. Band structure of the ETO film under (a) 0%, (b)3%, and (c)þ3%
strain.
TABLE II. Electron effective mass based on the band structure without strain and with strains of3% andþ3%.
Unstrained Compressive strain (3%) Tensile strain (þ3%) m*/m0 m*/m0 m*/m0
[010] 2.8 0.531 0.225
[001] 2.8 0.411 0.304 FIG. 6. (a) Absorption coefficients and (b) Tauc plots for ETO films under
0%,3%, andþ3% strain.
ETO nanoparticles and ETO thin films.17,18 In addition, the optical band gap for the ETO film with3% andþ3% strain is 0.78 and 1.34 eV, respectively, which is also in good agreement with the evolution of the band gap shown in Fig.
2(b), reflecting the substantial influence of strain on the opti- cal properties of the ETO film. Moreover, similar to the strain-induced modification of the electronic band gap, the tensile strain causes a large increase of the optical band gap in films, which is a highly desirable property for potential photovoltaic solar cell applications. For example, ETO films grown on BaFe0.5Ta0.5O3(BFT)/BaSnO3substrates are sub- ject to a tensile strain of 4%–5% and thereby provide a larger optical band gap of about 1.4–1.5 eV and a concomitantly higher photoelectric conversion efficiency.6,30
IV. CONCLUSION
In summary, the electronic structure, magnetic moments, and optical absorption of ETO films under various strains are investigated in detail by using PBEþU calculations.
Ferroelectric and ferromagnetic orders coexist under certain applied strain, verifying the prediction of a large magnetoelec- tric effect for the multiferroic ETO film with strain. The direct band gap decreases slowly (increases rapidly) with increasing compressive (tensile) strain, mainly because of the shift in the energy of electronic states originating from Ti 3d states.
Moreover, an optical band gap of 1.42 eV can be obtained in the ETO film by imposing a tensile strain ofþ3.5%, which is close to the ideal band gap of 1.4 eV for efficient solar cells.
These results thus suggest that multiferroic ETO films may play an important role in high-efficiency photovoltaics.
ACKNOWLEDGMENTS
This work was supported by the National Natural Science Foundation of China (Grant Nos. 11447229 and 11604163), the Natural Science Foundation of the Jiangsu Province (Grant No. BK2012655), the Innovation Fund Project for Graduate Student of Jiangsu Province (Grant No.
KYLX16_0969), and the Modern Education Technology Center of the NTU.
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