Effects of internal relaxation under inplane strain on the structural, electronic and optical properties of perovskite BaZrO₃

Abstract

We present the specific ab-initio calculations that detail the variations of perovskite BaZrO₃ caused by in-plane strain. Specifically, the internal relaxation, which was not captured in the widely used biaxial strain model, was included in a complementary manner to lattice relaxation. Density functional theory as well as a hybrid functional method based on a plane wave basis set was employed to calculate the lattice structure, elastic constants, electronic properties and optical properties of perovskite BaZrO₃. The lattice parameter c exhibited a clear linear dependence on the imposed in-plane strain, but the Poisson’s ratio caused by internal relaxation was smaller than the elastic deformation, indicating an “inelastic” or “plastic” relaxation manner caused by the introduction of internal relaxation. As a result, the related electronic and optical properties of perovskite BaZrO₃ were also strongly affected by the in-plane strain, which revealed an effective way to adjust the properties of perovskite BaZrO₃ via internal relaxation.

Keywords

thin films / internal relaxation / in-plane strain / perovskite / electronic band structure / computer simulations / optical properties

References

[1] Noorden RV. Cheap Solar Cells Tempt Businesses[J]. Nature, 2014, 513: 470.

[2] Fernández-Posada CM, Amorín H, Correas C, et al. Mechano sSynthesis and Multiferroic Properties of the BiFeO₃-BiMnO₃-PbTiO₃ Ternary System along Its Morphotropic Phase Boundary[J]. J. Mater. Chem. A, 2015, 3: 2255.

[3] Ahn CW, Choi JJ, Ryu J, et al. Composition Design Rule for Energy Harvesting Devices in Piezoelectric Perovskite Ceramics[J]. Mater. Lett., 2015, 141: 323-326.

[4] Verbraeken MC, Ramos T, Agersted K, et al. Modified Strontium Titanates: From Defect Chemistry to SOFC Anodes[J]. RSC Adv., 2015, 5: 1168-1180.

[5] Bae K, Jang DY, Choi SM, et al. Influence of Background Oxygen Pressure on Film Properties of Pulsed Laser Deposited Y:BaZrO₃[J]. Thin Solid Films, 2014, 552: 24-31.

[6] Bai G, Ma WH. Phenomenological Analysis of Phase Transitions in Epitaxial Perovskite Ferroelectric Thin Films[J]. Phys. B, 2010, 405: 1901-1907.

[7] Landau LD, Lifschitz EM. Course on Theoretical Physics Pergamon Press, 1985

[8] Hammerschmidt T, Kratzer P, Scheffler M. Elastic Response of Cubic Crystals to Biaxial Strain: Analytic Results and Comparison to Density Functional Theory for InAs[J]. Phys. Rev. B, 2007, 75: 235328.

[9] Perdew JP, Burke K, Ernzerhof M. Generalized Gradient Approximation Made Simple[J]. Phys. Rev. Lett., 1996, 77: 3865-3868.

[10] Perdew JP, Wang Y. Accurate and Simple Analytic Representation of the Electron-Gas Correlation Energy[J]. Phys. Rev. B, 1992, 45: 13244-13249.

[11] Vanderbilt D. Soft Self-consistent Pseudopotentials in a Generalized Eigenvalue Formalism [J]. Phys. Rev. B, 1990, 41: 7892-7895.

[12] Qin GQ, Zhang GL, Li DC, et al. Lattice and Internal Relaxation of ZnO Thin Film Under In-Plane Strain[J]. Thin Solid Films, 2010, 519: 378-384.

[13] Amour H, Denner W, Schulz H, et al. A Uniaxial Stress Apparatus for Single-Crystal X-ray Diffraction on a Four-Circle Ciffractometer: Application to Silicon and Diamond[J]. J. Appl. Cryst., 1982, 15: 148.

[14] Qin GQ, Zhang GL, Yu G, et al. Electronic Band Gap of ZnO Under Triaxial Strain [J]. J.Wuhan.Univ.Technol-Mater. Sci. Ed., 2013, 28: 48-51.

[15] Iles N, Kellou A, Khodja KD, et al. Atomistic Study of Structural, Elastic, Electronic and Thermal Properties of Perovskites Ba(Ti, Zr, Nb) O₃ [J]. Comp. Mater. Sci., 2007, 39: 896-902.

[16] Khenata R, Sahnoun M, Baltache H, et al. First-Principle Calculations of Structural, Electronic and Optical Properties of BaTiO₃ and BaZrO₃ Under Hydrostatic Pressure[J]. Solid State Commun., 2005, 136: 120-125.

[17] King-Smith RD, Vanderbilt D. First-principles Investigation of Ferroelectricity in Perovskite Compounds[J]. Phys. Rev. B, 1994, 49: 5828.

[18] Borja-Urby R, Diaz-Torres LA, Salas P, et al. Blue and Red Emission in Wide Band Gap BaZrO₃:Yb³⁺, Tm³⁺[J]. Mat. Sci. Eng. B, 2010, 174: 169-173.

[19] Yamanaka S, Fujikane M, Hamaguchi T, et al. Thermophysical Properties of BaZrO₃ and BaCeO₃[J]. J. Alloy. Compd., 2003, 359: 109-113.

[20] Robertson J. Band Offsets of Wide-Band-Gap Oxides and Implications for Future Electronic Devices[J]. J. Vac. Sci. Technol. B, 2000, 18: 1785.

[21] Yuan Y, Zhang X, Liu L, et al. Synthesis and Photocatalytic Characterization of a New Photocatalyst BaZrO₃[J]. Int. J. Hydrogen Energ., 2008, 33: 5941-5946.

[22] Cavalcante LS, Longo VM, Zampieri M, et al. Experimental and Theoretical Correlation of Very Intense Visible Green Photoluminescence in BaZrO₃ Powders[J]. J. Appl. Phys., 2008, 103: 063527.

[23] Fursenko O, Bauer J, Lupina G, et al. Optical Properties and Band Gap Characterization of High Dielectric Constant Oxides[J]. Thin Solid Films, 2012, 520: 4532-4535.

[24] Sanchez-Porta D, Artacho E, Soler JM. Projection of Plane-Wave Calculations into Atomic Orbitals[J]. Solid State Commun., 1995, 95: 685.

[25] Ma XL, Zhang JC, Li HH, et al. Violet Blue Long-Lasting Phosphorescence Properties of Mg-doped BaZrO₃ and Its Ability to Assist Photocatalysis[J]. J. Alloy. Compd., 2013, 580: 564-569.