مقایسة تابعی‌های PBE و HSE06 در محاسبه ساختار نواری الکترونی TiO2

نوع مقاله: مقاله پژوهشی کامل

نویسندگان

1 گروه فیزیک، دانشکده علوم، دانشگاه زابل، زابل، ایران

2 دانشکدۀ فیزیک، دانشگاه تحصیلات تکمیلی در علوم پایة زنجان، زنجان، ایران

چکیده

ساختار و گاف نواری الکترونی چند دستۀ مختلف از ساختارهای TiO2 به وسیلۀ نظریۀ تابعی چگالی و با تابعی‌های PBE و HSE06 محاسبه شد. مقادیرگاف نواری محاسبه شده توسط HSE06 برای فازهای روتیل و آناتاس به ترتیب 3.4 و 3.58 الکترون‌ولت بدست آمد که با مقادیر تجربی 3 و 3.2 الکترون‌ولت در توافق است. مدول حجمی نیز برای فازهای روتیل و آناتاس توسطPBE محاسبه گردید و به ترتیب مقادیر 226 و 205 گیگاپاسکال برای آنها به‌دست آمد که با مقادیر متناظر تجربی به ترتیب به اندازة 7 و 14 درصد اختلاف دارد. مقایسۀ دو تابعی مذکور در محاسبۀ ساختار نواری الکترونی ساختارهای مختلف TiO2 نشان داد که شکل ساختار نواری محاسبه شده توسط این دو تابعی، حداقل برای ساختارهای بررسی شده در این‌جا، مشابه است. مخصوصاً قسمت‌های بالایی نوار ظرفیت و قسمت‌های پایینی نوار رسانش دقیقاً یکسان هستند. بنابراین نوع (مستقیم یا غیرمستقیم) گاف نواری محاسبه شده با این دو تابعی یکسان خواهد بود. مهم‌ترین تفاوت این دو تابعی در محاسبۀ ساختار نواری، فاصلۀ بین نوارهای رسانش و ظرفیت و بنابراین اندازۀ گاف نواری است. اختلاف گاف محاسبه شده توسط این دو تابعی برای همۀ ساختارهای بررسی شده در این‌جا مقدار تقریبا یکسان eV 1.6 است.

کلیدواژه‌ها


عنوان مقاله [English]

Comparison between PBE and HSE06 functionals for the calculation of electronic band-structure of TiO2

نویسندگان [English]

  • Hossein Asnaashari Eivari 1
  • Seyed Alireza Ghasemi 2
1 Department of Physics, University of Zabol, Zabol, Iran P.O. Box 98615-538, Zabol 98613-35856, Iran
2 Department of Physics, IASBS, Zanjan, Iran
چکیده [English]

Electronic structure of various structures of TiO2 were calculated using PBE and HSE06 functionals. Calculated band gap in HSE06 level for rutile and anatase phases was 3.4 and 3.58 eV respectively which are in agreement with experimental values of 3 and 3.2 eV. Calculated bulk moduli for the mentioned phases were to be 226 and 205 Gpa. The difference of these values with reported experimental values are %7 and %14 respectively. Comparison between the two mentioned functionals shows that the overall form of band structures is independent of the functional. Especially the top of valence band and the bottom of conduction band are the same in PBE and HSE06. So both functionals give the same result for the type (direct or indirect) of band-gap. Distance between conduction and valence bands, and so the band-gap, is the main difference in calculating the band-structure using these two functionals. Band-gap difference calculated by these functionals is almost 1.6 eV for all structures studied in here. So one can calculate the band-gap of TiO2 with PBE and sum the result by 1.6 eV instead of calculating the band gap in expensive HSE06 level which is close to experimental value.

کلیدواژه‌ها [English]

  • TiO2
  • DFT
  • band-structure
  • GGA functional
  • hybrid functional
[1]

H. Zhang, J. Banfield, Structural characteristics and mechanical and thermodynamic properties of anocrystalline TiO2, Chemical Reviews 114 (2014) 9613-9644.

[2]

L. Wang, T. Sasaki, Titanium oxide nanosheets: graphene analogues with versatile functionalities, Chemical Reviews 114 (2014) 9455-9486.

[3]

H.A. Eivari, S.A. Ghasemi, H. Tahmasbi, S. Rostami, S. Faraji, R. Rasoulkhani, et al., A two-dimensional hexagonal sheet of TiO2, Chemistry of Materials 29 (2017) 8594-8603.

[4]

A. Atrei, A.M. Ferrari, D. Szieberth, B. Cortigia, Lepidocrocite-like structure of the TiO2monolayer grown on Ag (100),Physical Chemistry Chemical Physics 12 (2010) 11587-11595.

[5]

A.V. Bandura, R.A. Evarestov, S.I. Lukyanov, Structure Reconstruction of TiO2-Based Multi-Wall Nanotubes: First-Principles Calculations, Physical Chemistry Chemical Physics 16 (2014) 14781-14791.

[6]

A.M. Ferrari, D. Szieberth, C.M. Zicovich-Wilson, D. Demichelis, Anatase (001) 3 ML nanotubes, the first TiO2 nanotube with negative strain energies: A DFT prediction, Journal of Physical Chemistry Letters 1 (2010)  2854-2857.

[7]

M. Niu, D. Cheng, D. Cao, Fluorite TiO2 (111) surface phase for enhanced visible-light solar energy conversion, Journal of Physical Chemistry C 118 (2014) 20107-20111.

[8]

A. Vittadini, F. Sedona, S. Agnoli, L. Artiglia, M. Casarin, G.A. Rizzi, et al. , Stability of TiO2 polymorphs: exploring the extreme frontier of the nanoscale, ChemPhysChem 11 (2010) 1550-1557.

[9]

T. Zhu, S.P. Gao, The stability, electronic structure, and optical property of TiO2 polymorphs, Journal of Physical Chemistry C 118 (2014) 11385-11396.

[10]

R. Asahi, T. Morikawa, T. Ohwaki, K. Aoki, Y. Taga, Visible-light photocatalysis in nitrogen-doped titanium oxides, Science  293 (2001) 269-271.

[11]

S. Livraghi, M.C. Paganini, E. Giamello, A. Selloni, C.D. Valentin, G. Pacchioni, Origin of photoactivity of nitrogen-doped titanium dioxide under visible light, Journal of the American Chemical Society 128 (2006) 15666-15671.

[12]

R.M.N. Yerga, M.C.Á. Galván, F.D. Valle, J.A.V. Mano, J.L. Fierro, Water Splitting on Semiconductor Catalysts under Visible‐Light Irradiation, ChemSusChem  2 (2009) 471-485.

[13]

M.A. Henderson, A surface science perspective on photocatalysis, Surface Science Reports 66 (2011) 185-297.

[14]

R. Rasoulkhani, H. Tahmasbi, S.A. Ghasemi, S. Faraji, S. Rostami, M. Amsler, Energy landscape of ZnO clusters and low-density polymorphs, Physical Review B 96 (2017) 064108-064121.

[15]

M. Mattesini, J.S. Almeida, L. Dubrovinsky, N. Dubrovinskaia, B.R. Johansson, R. Ahuja, High-pressure and high-temperature synthesis of the cubic TiO2 polymorph, Physical Review B 70 (2004) 212101-212104.

[16]

J.P. Perdew, Y. Wang, Accurate and simple analytic representation of the electron-gas correlation energy, Physical Review B 45 (1992) 13244-13249.

[17]

J.P. Perdew, K. Burke, M. Ernzerhof, Generalized gradient approximation made simple, Physical Review Letters 77 (1996) 3865-3868.

[18]

R.W. Godby, M. Schlter, L.J. Sham, Self-energy operators and exchange-correlation potentials in semiconductors, Physical Review B 37 (1988) 10159-10175.

[19]

R.O. Jones, O. Gunnarsson, The density functional formalism, its applications and prospects, Reviews of Modern Physics 61 (1989) 689-746.

[20]

J. Paier, R. Hirschl, M. Marsman, G. Kresse, The Perdew-Burke-Ernzerhof exchange-correlation functional applied to the G2-1 test set using a plane-wave basis set, Journal of Chemical Physics 122 (2005) 234102-23414.

[21]

J. Heyd, G.E. Scuseria, M. Ernzerhof, Erratum: Hybrid functionals based on a screened Coulomb potential, Journal of Chemical Physics 124 (2006) 219906-219906.

[22]

H. Liu, W. Cui, Y. Ma, Hybrid functional study rationalizes the simple cubic phase of calcium at high pressures, Journal of Chemical Physics 137 (2012) 184502-184506.

[23]

H. Salehi, H.A. Badehian, M. Farbod, First principle study of the physical properties of semiconducting binary antimonide compounds under hydrostatic pressures, Materials Science in Semiconductor Processing 26 (2014) 477–490.

[24]

Z. Javdani, H.A. Badehian, H. Salehi, P. Amiri, First principles calculations of optical and magnetic properties of SrFe2O4 compound under pressure, Physics Letters A 378 (2014) 2644–2650.

[25]

Y. Li, W.G. Schmidt, S. Sanna, Intrinsic LiNbO3 point defects from hybrid density functional calculations, Physical Review B  89 (2014) 094111-094118.

[26]

V. Blum, R. Gehrke, F. Hanke, P. Havu, V. Havu, X. Ren, Ab initio molecular simulations with numeric atom-centered orbitals, Computer Physics Communications 180 (2009) 2175-2196.

[27]

D. Forrer, A. Vittadini, 2D vs. 3D titanium dioxide: Role of dispersion interactions, Chemical Physics Letters  516 (2011) 72-75.

[28]

F. Birch, Finite Elastic Strain of Cubic Crystals, Physical Review 71 (1947) 809-824.

[29]

T. Arlt, M. Bermejo, M.A. Blanco, L. Gerward, J.Z. Jiang, J.S. Olsen, J.M. Recio, High-pressure polymorphs of anatase TiO2., Physical Review B 61 (2000) 14414-14419.

[30]

M. Iuga, G. Steinle-Neumann, J. Meinhardt, Ab-initio simulation of elastic constants for some ceramic materials., The European Physical Journal B 58 (2007) 127-133.

[31]

T. Mahmood, C. Cao, R. Ahmed, M. Ahmed, M.A. Saed, A.A. Zafar, T. Husain, A.M. Kamran, Pressure Induced Structural and Electronic Bandgap properties of Anatase and Rutile TiO2, Sains Malaysiana 42 (2013) 231–237.

[32]

Y. Al-Khatabeh, K.K.M. Lee, B. Kiefer, High-pressure behavior of TiO2 as determined by experiment and theory., Physical Review B 79 (2009) 134114-134122.

[33]

V. Swamy, B.C. Muddle, Ultrastiff Cubic TiO2 Identified via First-Principles Calculations, Physical Review Letters 98 (2007) 035502-035505.

[34]

J.K. Burdett, T. Hughbanks, G.J. Miller, J. W. Richardson, J.V. Smith, Structural-electronic relationships in inorganic solids: powder neutron diffraction studies of the rutile and anatase polymorphs of titanium dioxide at 15 and 295 K, Journal of the American Chemical Society 109 (1987) 3639-3646.

[35]

Y. Tezuka, S. Shin, T. Ishii, T. Ejima, S. Suzuki, S. Sato, Photoemission and bremsstrahlung isochromat spectroscopy studies of TiO2 (rutile) and SrTiO3, Journal of the Physical Society of Japan.  63 (1994) 347-357.

[36]

J. Zhang, P. Zhou, J. Liu, J. Yu, New understanding of the difference of photocatalytic activity among anatase, rutile and brookite TiO2, Physical Chemistry Chemical Physics 16 (2014) 20382-20386.

[37]

H. Sato, K. Ono, T. Sasaki, A. Yamagishi, First-principles study of two-dimensional titanium dioxides, The Journal of Physical Chemistry B 107 (2003) 9824-9828.

[38]

J. Muscat, V. Swamy, N.M. Harrison, First-principles calculations of the phase stability of TiO2, Physical Review B 65 (2002) 224112-224126.

[39]

T. Orzali, M. Casarin, G. Granozzi, M. Sambi, A. Vittadin, Bottom-Up Assembly of Single-Domain Titania Nanosheets on (1× 2) Pt (110), Physical Review Letters  97 (2006) 156101-156105.

[40]

M. Landmann, E. Rauls, W.G. Schmidt, The electronic structure and optical response of rutile, anatase and brookite TiO2, Journal of Physics: Condensed Matter 24 (2012) 195503-195509.

[41]

P. Deak, B. Aradi, T. Frauenheim, Polaronic effects in TiO2 calculated by the HSE06 hybrid functional: Dopant passivation by carrier self-trapping, Physical Review B 83 (2011) 155207-155213.

[42]

J. Tao, T. Luttrell, M. Batzill, A two-dimensional phase of TiO2 with a reduced bandgap, Nature chemistry 3 (2011) 296-300.