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Regulation of surface properties of photocatalysis material TiO2 by strain engineering

Jian Zheng and Dajun Shu

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 Corresponding author: Dajun Shu, email: djshu@nju.edu.cn

DOI: 10.1088/1674-4926/41/9/091703

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Abstract: As a promising photocatalysis material, TiO2 has long been studied by experimental and theoretical methods. The external strain could affect the catalytic reactivity of TiO2 significantly due to the difference in surface elastic properties of different surface structures with different surface adsorption or defects. This article reviews our recent work by using density function theory calculations on the effect of strain on the TiO2 surface properties, including surface relative stability, surface defects, surface adsorption and dissociation.

Key words: semiconductor theory, material, thin film



[1]
Asahi R, Morikawa T, Ohwaki T, et al. Visible-light photocatalysis in nitrogen-doped titanium oxides. Science, 2001, 293(5528), 269 doi: 10.1126/science.1061051
[2]
Campbell C T, Parker S C, Starr D E. The effect of size-dependent nanoparticle energetics on catalyst sintering. Science, 2002, 298(5594), 811 doi: 10.1126/science.1075094
[3]
Bikondoa O, Pang C L, Ithnin R, et al. Direct visualization of defect-mediated dissociation of water on TiO2(110). Nat Mater, 2006, 5(3), 189 doi: 10.1038/nmat1592
[4]
Gratzel M. Photoelectrochemical cells. Nature, 2001, 414(6861), 338 doi: 10.1038/35104607
[5]
Lu G, Linsebigler A, Yates J T. Photooxidation of ch3cl on TiO2(110) — a mechanism not involving H2O. J Phys Chem, 1995, 99(19), 7626 doi: 10.1021/j100019a049
[6]
Pan X Y, Yang M Q, Fu X Z, et al. Defective TiO2 with oxygen vacancies: Synthesis, properties and photocatalytic applications. Nanoscale, 2013, 5(9), 3601 doi: 10.1039/c3nr00476g
[7]
Yang B, Liu F, Lagally M G. Local strain-mediated chemical potential control of quantum dot self-organization in heteroepitaxy. Phys Rev Lett, 2004, 92(2), 4 doi: 10.1103/PhysRevLett.92.025502
[8]
Lu G H, Cuma M, Liu F. First-principles study of strain stabilization of Ge(105) facet on Si(001). Phys Rev B, 2005, 72(12), 6 doi: 10.1103/PhysRevB.72.125415
[9]
Yin W J, Chen S Y, Yang J H, et al. Effective band gap narrowing of anatase TiO2 by strain along a soft crystal direction. Appl Phys Lett, 2010, 96(22), 3 doi: 10.1063/1.3430005
[10]
Shu D J, Ge S T, Wang M, et al. Interplay between external strain and oxygen vacancies on a rutile TiO2(110) surface. Phys Rev Lett, 2008, 101(11), 4 doi: 10.1103/PhysRevLett.101.116102
[11]
Wang Z W, Shu D J, Wang M, et al. Diffusion of oxygen vacancies on a strained rutile TiO2(110) surface. Phys Rev B, 2010, 82(16), 7 doi: 10.1103/PhysRevB.82.165309
[12]
Wang Z W, Shu D J, Wang M, et al. Strain effect on diffusion properties of oxygen vacancies in bulk and subsurface of rutile TiO2. Surf Sci, 2012, 606(3/4), 186 doi: 10.1016/j.susc.2011.09.014
[13]
Jia L, Shu D J, Wang M. Tuning the area percentage of reactive surface of TiO2 by strain engineering. Phys Rev Lett, 2012, 109(15), 5 doi: 10.1103/PhysRevLett.109.156104
[14]
Yang L, Shu D J, Li S C, et al. Influence of strain on water adsorption and dissociation on rutile TiO2(110) surface. Phys Chem Chem Phys, 2016, 18(22), 14833 doi: 10.1039/c6cp01106c
[15]
Wang Z W, Shu D J. Intrinsic interaction between in-plane ferroelectric polarization and surface adsorption. Phys Chem Chem Phys, 2019, 21(34), 18680 doi: 10.1039/c9cp03286j
[16]
Shojaee E, Mohammadizadeh M R. First-principles elastic and thermal properties of TiO2: A phonon approach. J Phys Condens Matter, 2010, 22(1), 8 doi: 10.1088/0953-8984/22/1/015401
[17]
Sato H, Ono K, Sasaki T, et al. First-principles study of two-dimensional titanium dioxides. J Phys Chem B, 2003, 107(36), 9824 doi: 10.1021/jp035017t
[18]
Isaak D G, Carnes J D, Anderson O L, et al. Elasticity of TiO2 rutile to 1800 K. Phys Chem Miner, 1998, 26(1), 31 doi: 10.1007/s002690050158
[19]
Cammarata R C. Surface and interface stress effects in thin-films. Prog Surf Sci, 1994, 46(1), 1 doi: 10.1016/0079-6816(94)90005-1
[20]
Vittadini A, Casarin M, Selloni A. Chemistry of and on TiO2-anatase surfaces by dft calculations: a partial review. Theor Chem Acc, 2007, 117(5/6), 663 doi: 10.1007/s00214-006-0191-4
[21]
Lazzeri M, Vittadini A, Selloni A. Structure and energetics of stoichiometric TiO2 anatase surfaces. Phys Rev B, 2001, 63(15), 9 doi: 10.1103/PhysRevB.63.155409
[22]
Diebold U, Ruzycki N, Herman G S, et al. One step towards bridging the materials gap: surface studies of TiO2 anatase. Catal Today, 2003, 85(2–4), 93 doi: 10.1016/s0920-5861(03)00378-x
[23]
Wendt S, Schaub R, Matthiesen J, et al. Oxygen vacancies on TiO2(110) and their interaction with H2O and O2: A combined high-resolution STM and DFT study. Surf Sci, 2005, 598(1–3), 226 doi: 10.1016/j.susc.2005.08.041
[24]
Thompson T L, Yates J T. Surface science studies of the photoactivation of TiO2 – new photochemical processes. Chem Rev, 2006, 106(10), 4428 doi: 10.1021/cr050172k
[25]
Yim C M, Pang C L, Thornton G. Oxygen vacancy origin of the surface band-gap state of TiO2(110). Phys Rev Lett, 2010, 104(3), 4 doi: 10.1103/PhysRevLett.104.036806
[26]
Diebold U, Lehman J, Mahmoud T, et al. Intrinsic defects on a TiO2(110)(1x1) surface and their reaction with oxygen: A scanning tunneling microscopy study. Surf Sci, 1998, 411(1/2), 137 doi: 10.1016/s0039-6028(98)00356-2
[27]
Wahlstrom E, Lopez N, Schaub R, et al. Bonding of gold nanoclusters to oxygen vacancies on rutile TiO2(110). Phys Rev Lett, 2003, 90(2), 4 doi: 10.1103/PhysRevLett.90.026101
[28]
Schaub R, Wahlstrom E, Ronnau A, et al. Oxygen-mediated diffusion of oxygen vacancies on the TiO2(110) surface. Science, 2003, 299(5605), 377 doi: 10.1126/science.1078962
[29]
Zhang Z R, Rousseau R, Gong J L, et al. Vacancy-assisted diffusion of alkoxy species on rutile TiO2(110). Phys Rev Lett, 2008, 101(15), 4 doi: 10.1103/PhysRevLett.101.156103
[30]
Kimmel G A, Petrik N G. Tetraoxygen on reduced TiO2(110): Oxygen adsorption and reactions with bridging oxygen vacancies. Phys Rev Lett, 2008, 100(19), 4 doi: 10.1103/PhysRevLett.100.196102
[31]
Klenov D O, Donner W, Foran B, et al. Impact of stress on oxygen vacancy ordering in epitaxial (La0.5Sr0.5)CoO3-partial derivative thin films. Appl Phys Lett, 2003, 82(20), 3427 doi: 10.1063/1.1575503
[32]
Kamisaka H, Yamashita K. The surface stress of the (110) and (100) surfaces of rutile 14 and the effect of water adsorbents. Surf Sci, 2007, 601(21), 4824 doi: 10.1016/j.susc.2007.07.033
[33]
Hameeuw K, Cantele G, Ninno D, et al. Influence of surface and subsurface defects on the behavior of the rutile TiO2(110) surface. Phys Status Solidi A, 2006, 203(9), 2219 doi: 10.1002/pssa.200566015
[34]
Bredow T, Giordano L, Cinquini F, et al. Electronic properties of rutile TiO2 ultrathin films: Odd-even oscillations with the number of layers. Phys Rev B, 2004, 70(3), 6 doi: 10.1103/PhysRevB.70.035419
[35]
Lee C, Ghosez P, Gonze X. Lattice-dynamics and dielectric-properties of incipient ferroelectric TiO2 rutile. Phys Rev B, 1994, 50(18), 13379 doi: 10.1103/PhysRevB.50.13379
[36]
Parker R A. Static dielectric constant of rutile (TiO2), 1.6–1060 °K. Phys Rev, 1961, 124(6), 1719 doi: 10.1103/PhysRev.124.1719
[37]
Trayler J G, Smith H G, Nicklow R M, et al. Lattice dynamics of rutile. Phys Rev B, 1971, 3(10), 3457 doi: 10.1103/PhysRevB.3.3457
Fig. 1.  (Color online) (a–c) Variations of surface energies and surface stresses, as well as (d–f) the electronic structure properties with the slab thickness. Black solid curves and red dashed curves are for the unrelaxed and relaxed surfaces, respectively. The valence band maximum (VBM,(e)) and the conduction band minimum (CBM,(f)) are referenced to the vacuum level. These figures are adapted from Ref. [14].

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Fig. 2.  (Color online) (a) The area percentage of anatase (001) facets with variation of the applied strain. The inset displays the equilibrium shape of the anatase crystallite. (b –d) The surface energy ratio $ \gamma(001)/\gamma(101) $ and the ratio of $ 1/ \cos\theta $ with the variation of the applied strain. The anatase (001) surface appears only when the surface energy ratio is smaller than $ 1/ \cos\theta $. These figures are adapted from Ref. [13].

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Fig. 3.  (Color online) Schematic of the rutile TiO2(110) surface. The bridging oxygen (BO), the subbridging oxygen (SBO) and the in-plane oxygen (IPO) atoms are indicated by the arrows. $ R_{\rm{o}} $ and $ R_{\rm{t}} $ denote the atomic rows in [110] direction, with surface terminated by the bridging oxygen atoms or the five-coordinated titanium atoms, respectively. This figure is adapted from Ref. [12].

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Fig. 4.  (Color online) (a) The formation energy of OV and (b) the changes of the surface stresses and surface elastic constants induced by the OV as a function of the OV depth. The depth is defined as the distance below the unrelaxed 1-bridging O atoms. The dashed horizontal line in (a) denotes the bulk vacancy formation energy. Solid or dashed curves in (b) are to guide the eyes. $ \Delta\sigma $ and $ \Delta S $ are in units of eV/$ (1\times 1) $. These figures are adapted from Ref. [10].

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Fig. 5.  Phase diagram of the type of the energetically most favorable OV as a function of the external strain $ \epsilon_{11} $ and $ \epsilon_{22} $. The dashed curves are predicted according to the surface elasticity properties shown in Table 3. It indicates that BOV, IPOV, or SBOV can be energetically most favorable within different range of the external strain. This figure is adapted from Ref. [11].

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Fig. 6.  (Color online) Energy profiles of OV pathways within the primitive cell of rutile TiO$ _{2} $ using different size of supercell, namely $ (2 \times 2 \times 2) $, $ (2 \times 3 \times 2) $ and $ (2 \times 4 \times 2) $. The inset shows the schematic of a primitive cell. Large light spheres and small dark spheres denote the O and Ti atoms, respectively (the same below). The numbers label different oxygen atoms in order for reference of OVs. The notations I, II and III correspond to the paths from OV$ _{1} $ to OV$ _{2} $, from OV$ _{2} $ to OV$ _{3} $ and from OV$ _{3} $ to OV$ _{4} $, respectively. This figure is adapted from Ref. [12].

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Fig. 7.  (Color online) (a) Schematic of bulk OV diffusion along the [110] and $ [1\bar {1}0] $ directions in rutile TiO2. The numbers label different oxygen atom sites for reference in (b–f). (b–f) The energy profiles of OV diffusion in rutile TiO2, when (b) isotropic strain or anisotropic strain applied in directions along (c, d) $ [1\overline {1}0] $ and (e, f) [110]. These figures are adapted from Ref. [12].

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Fig. 8.  (Color online) The strain-dependent diffusion barrier of the surface OV along [001] (Path I) and along $ [1\bar 1 0] $ (Path II, directive hopping between the bridging site; Path III, concerted mechanism mediated by the in-plane OV). Upper panels: The predicted energy profiles of the OV along Path III under external strain along (a) $ [1\overline {1}0] $ and (b) [001]. The solid lines are predicted according to the surface elasticity, and the symbols denote the calculated energy profiles using NEB method when $ \epsilon=0 $ (discrete circles), $ \epsilon_{22}=-0.02 $ (discrete triangles) and $ \epsilon_{22}=0.02 $ (discrete squares) are also shown for comparison. Lower panels: the diffusion barriers of different pathways as a function of the external strain along the (c) $ [1\bar 1 0] $ direction and (d) [001] direction, with discrete points and dashed lines denoting the calculated and predicted values, respectively. These figures are adapted from Ref. [11].

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Fig. 9.  (Color online) Adsorption energies per water molecule in (a) molecular state and (b) dissociative state on the surface with different supercell size and different thickness $ L_n $. The differences between the adsorption energies of the dissociative state and the molecular state are shown in (c). The x and y direction of the surface is along [001] and $ [1\bar 1 0] $ direction, respectively. These figures are adapted from Ref. [14] by the permission of PCCP.

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Fig. 10.  (Color online) The change of the total energy of the s-TiO2(110) surface induced by the in-plane polarization under strain along $ [1\overline {1}0] $ as a function of the doped charge. Negative charge and positive charge correspond to electron doping and hole doping, respectively. This figure is adapted from Ref. [15] by the permission of PCCP.

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Table 1.   The elastic constant $ C_{ij} $, bulk modulus (B), Young’s modulus along the $ a $ axis ($ Y_a $), along the in-plane r direction ($ Y_r $), and along the $ c $ axis ($ Y_c $) of TiO2 rutile and anatase phases, in units of GPa. This table is adapted from Ref. [13].

Parameter $C_{11}$ $C_{12}$ $C_{13}$ $C_{33}$ $C_{44}$ $C_{66}$ $B$ $Y_c$ $Y_r$ $Y_a$
Rutile
PW91[12] 265 179 151 472 116 211 209 369 348 138
Phonon[16] 269 189 166 506 105 217 219 386 349 130
PBE[17] 261 132 137 456 117 204 187 360 311 182
Exp[18] 268 175 147 484 124 190 212 386 354 147
Anatase
PW91[12] 331 144 141 189 46 59 173 105 264 219
Phonon[16] 333 143 140 198 39 57 176 116 278 226
PBE[17] 311 150 138 191 51 59 172 108 262 199
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Table 2.   The calculated surface energy and surface mechanical properties of rutile and anatase phases. $ \gamma $, $ \sigma $, and $ S $ denote surface energy, surface stress, and surface elastic constant, respectively. Subscripts 11 and 22 denote the directions along [100] and [010] for (001) surface, [010] and [001] for (100) surface, $ [10\bar 1] $ and [010] for (101) surface, $ [1\bar1 0] $ and $ [00\bar 1] $ for (110) surface. The units are in J/m2. This table is adapted from Ref. [13].

Parameter $ \gamma $ $ \sigma_{11} $ $ \sigma_{22} $ $ S_{1111} $ $ S_{2222} $ $ S_{1122} $
Rutile
(110) 0.44 2.52 1.14 –73.81 –17.67 –26.30
(100) 0.70 –1.74 1.28 –20.64 –2.88 –9.75
(101) 1.03 –0.08 0.16 –24.62 –25.38 –21.88
(001) 1.30 1.27 1.27 –8.27 –8.27 –15.80
Anatase
(101) 0.52 0.77 2.06 41.33 –2.21 9.99
(100) 0.59 1.90 0.82 –1.31 4.40 –5.06
(001) 1.04 9.58 –2.13 2.64 2.64 –18.01
(110) 1.10 –2.09 1.31 –27.74 16.07 –2.17
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Table 3.   Changes of surface energy, surface stress and surface elasticity induced by different types of oxygen vacancies. The units are eV/$ (1\times 1) $. The subscripts 11 and 22 denote the directions along $ [1\overline {1}0] $ and [001] direction, respectively. This table is adapted from Refs. [10, 11].

Oxygen vacancy $ \Delta\gamma $ $ \Delta\sigma_{11} $ $ \Delta\sigma_{22} $ $ \Delta S_{1111} $ $ \Delta S_{2222} $ $ \Delta S_{1122} $
1-bridging 2.17 0.51 –1.66 –2.42 –29.36 –14.76
1-in-plane 2.40 –5.02 –2.73 –151.01 –34.03 –53.21
1-subbridging 2.21 1.50 –0.63 –51.67 –62.98 –44.09
2-bridging 2.58 0.43 –0.88 –8.38 –12.66
2-in-plane 2.44 –5.51 –2.95 –157.96 –39.62
2-subbridging 2.52 0.18 –0.41 –3.99 –81.19
DownLoad: CSV
[1]
Asahi R, Morikawa T, Ohwaki T, et al. Visible-light photocatalysis in nitrogen-doped titanium oxides. Science, 2001, 293(5528), 269 doi: 10.1126/science.1061051
[2]
Campbell C T, Parker S C, Starr D E. The effect of size-dependent nanoparticle energetics on catalyst sintering. Science, 2002, 298(5594), 811 doi: 10.1126/science.1075094
[3]
Bikondoa O, Pang C L, Ithnin R, et al. Direct visualization of defect-mediated dissociation of water on TiO2(110). Nat Mater, 2006, 5(3), 189 doi: 10.1038/nmat1592
[4]
Gratzel M. Photoelectrochemical cells. Nature, 2001, 414(6861), 338 doi: 10.1038/35104607
[5]
Lu G, Linsebigler A, Yates J T. Photooxidation of ch3cl on TiO2(110) — a mechanism not involving H2O. J Phys Chem, 1995, 99(19), 7626 doi: 10.1021/j100019a049
[6]
Pan X Y, Yang M Q, Fu X Z, et al. Defective TiO2 with oxygen vacancies: Synthesis, properties and photocatalytic applications. Nanoscale, 2013, 5(9), 3601 doi: 10.1039/c3nr00476g
[7]
Yang B, Liu F, Lagally M G. Local strain-mediated chemical potential control of quantum dot self-organization in heteroepitaxy. Phys Rev Lett, 2004, 92(2), 4 doi: 10.1103/PhysRevLett.92.025502
[8]
Lu G H, Cuma M, Liu F. First-principles study of strain stabilization of Ge(105) facet on Si(001). Phys Rev B, 2005, 72(12), 6 doi: 10.1103/PhysRevB.72.125415
[9]
Yin W J, Chen S Y, Yang J H, et al. Effective band gap narrowing of anatase TiO2 by strain along a soft crystal direction. Appl Phys Lett, 2010, 96(22), 3 doi: 10.1063/1.3430005
[10]
Shu D J, Ge S T, Wang M, et al. Interplay between external strain and oxygen vacancies on a rutile TiO2(110) surface. Phys Rev Lett, 2008, 101(11), 4 doi: 10.1103/PhysRevLett.101.116102
[11]
Wang Z W, Shu D J, Wang M, et al. Diffusion of oxygen vacancies on a strained rutile TiO2(110) surface. Phys Rev B, 2010, 82(16), 7 doi: 10.1103/PhysRevB.82.165309
[12]
Wang Z W, Shu D J, Wang M, et al. Strain effect on diffusion properties of oxygen vacancies in bulk and subsurface of rutile TiO2. Surf Sci, 2012, 606(3/4), 186 doi: 10.1016/j.susc.2011.09.014
[13]
Jia L, Shu D J, Wang M. Tuning the area percentage of reactive surface of TiO2 by strain engineering. Phys Rev Lett, 2012, 109(15), 5 doi: 10.1103/PhysRevLett.109.156104
[14]
Yang L, Shu D J, Li S C, et al. Influence of strain on water adsorption and dissociation on rutile TiO2(110) surface. Phys Chem Chem Phys, 2016, 18(22), 14833 doi: 10.1039/c6cp01106c
[15]
Wang Z W, Shu D J. Intrinsic interaction between in-plane ferroelectric polarization and surface adsorption. Phys Chem Chem Phys, 2019, 21(34), 18680 doi: 10.1039/c9cp03286j
[16]
Shojaee E, Mohammadizadeh M R. First-principles elastic and thermal properties of TiO2: A phonon approach. J Phys Condens Matter, 2010, 22(1), 8 doi: 10.1088/0953-8984/22/1/015401
[17]
Sato H, Ono K, Sasaki T, et al. First-principles study of two-dimensional titanium dioxides. J Phys Chem B, 2003, 107(36), 9824 doi: 10.1021/jp035017t
[18]
Isaak D G, Carnes J D, Anderson O L, et al. Elasticity of TiO2 rutile to 1800 K. Phys Chem Miner, 1998, 26(1), 31 doi: 10.1007/s002690050158
[19]
Cammarata R C. Surface and interface stress effects in thin-films. Prog Surf Sci, 1994, 46(1), 1 doi: 10.1016/0079-6816(94)90005-1
[20]
Vittadini A, Casarin M, Selloni A. Chemistry of and on TiO2-anatase surfaces by dft calculations: a partial review. Theor Chem Acc, 2007, 117(5/6), 663 doi: 10.1007/s00214-006-0191-4
[21]
Lazzeri M, Vittadini A, Selloni A. Structure and energetics of stoichiometric TiO2 anatase surfaces. Phys Rev B, 2001, 63(15), 9 doi: 10.1103/PhysRevB.63.155409
[22]
Diebold U, Ruzycki N, Herman G S, et al. One step towards bridging the materials gap: surface studies of TiO2 anatase. Catal Today, 2003, 85(2–4), 93 doi: 10.1016/s0920-5861(03)00378-x
[23]
Wendt S, Schaub R, Matthiesen J, et al. Oxygen vacancies on TiO2(110) and their interaction with H2O and O2: A combined high-resolution STM and DFT study. Surf Sci, 2005, 598(1–3), 226 doi: 10.1016/j.susc.2005.08.041
[24]
Thompson T L, Yates J T. Surface science studies of the photoactivation of TiO2 – new photochemical processes. Chem Rev, 2006, 106(10), 4428 doi: 10.1021/cr050172k
[25]
Yim C M, Pang C L, Thornton G. Oxygen vacancy origin of the surface band-gap state of TiO2(110). Phys Rev Lett, 2010, 104(3), 4 doi: 10.1103/PhysRevLett.104.036806
[26]
Diebold U, Lehman J, Mahmoud T, et al. Intrinsic defects on a TiO2(110)(1x1) surface and their reaction with oxygen: A scanning tunneling microscopy study. Surf Sci, 1998, 411(1/2), 137 doi: 10.1016/s0039-6028(98)00356-2
[27]
Wahlstrom E, Lopez N, Schaub R, et al. Bonding of gold nanoclusters to oxygen vacancies on rutile TiO2(110). Phys Rev Lett, 2003, 90(2), 4 doi: 10.1103/PhysRevLett.90.026101
[28]
Schaub R, Wahlstrom E, Ronnau A, et al. Oxygen-mediated diffusion of oxygen vacancies on the TiO2(110) surface. Science, 2003, 299(5605), 377 doi: 10.1126/science.1078962
[29]
Zhang Z R, Rousseau R, Gong J L, et al. Vacancy-assisted diffusion of alkoxy species on rutile TiO2(110). Phys Rev Lett, 2008, 101(15), 4 doi: 10.1103/PhysRevLett.101.156103
[30]
Kimmel G A, Petrik N G. Tetraoxygen on reduced TiO2(110): Oxygen adsorption and reactions with bridging oxygen vacancies. Phys Rev Lett, 2008, 100(19), 4 doi: 10.1103/PhysRevLett.100.196102
[31]
Klenov D O, Donner W, Foran B, et al. Impact of stress on oxygen vacancy ordering in epitaxial (La0.5Sr0.5)CoO3-partial derivative thin films. Appl Phys Lett, 2003, 82(20), 3427 doi: 10.1063/1.1575503
[32]
Kamisaka H, Yamashita K. The surface stress of the (110) and (100) surfaces of rutile 14 and the effect of water adsorbents. Surf Sci, 2007, 601(21), 4824 doi: 10.1016/j.susc.2007.07.033
[33]
Hameeuw K, Cantele G, Ninno D, et al. Influence of surface and subsurface defects on the behavior of the rutile TiO2(110) surface. Phys Status Solidi A, 2006, 203(9), 2219 doi: 10.1002/pssa.200566015
[34]
Bredow T, Giordano L, Cinquini F, et al. Electronic properties of rutile TiO2 ultrathin films: Odd-even oscillations with the number of layers. Phys Rev B, 2004, 70(3), 6 doi: 10.1103/PhysRevB.70.035419
[35]
Lee C, Ghosez P, Gonze X. Lattice-dynamics and dielectric-properties of incipient ferroelectric TiO2 rutile. Phys Rev B, 1994, 50(18), 13379 doi: 10.1103/PhysRevB.50.13379
[36]
Parker R A. Static dielectric constant of rutile (TiO2), 1.6–1060 °K. Phys Rev, 1961, 124(6), 1719 doi: 10.1103/PhysRev.124.1719
[37]
Trayler J G, Smith H G, Nicklow R M, et al. Lattice dynamics of rutile. Phys Rev B, 1971, 3(10), 3457 doi: 10.1103/PhysRevB.3.3457

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    Received: 30 June 2020 Revised: 24 July 2020 Online: Accepted Manuscript: 20 August 2020Uncorrected proof: 21 August 2020Published: 04 September 2020

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      Article Navigation >  Journal of Semiconductors  > 2020  >  41(9): 091703
      Jian Zheng, Dajun Shu. Regulation of surface properties of photocatalysis material TiO2 by strain engineering[J]. Journal of Semiconductors, 2020, 41(9): 091703. doi: 10.1088/1674-4926/41/9/091703 ****J Zheng, D J Shu, Regulation of surface properties of photocatalysis material TiO2 by strain engineering[J]. J. Semicond., 2020, 41(9): 091703. doi: 10.1088/1674-4926/41/9/091703.
      Citation:
      Jian Zheng, Dajun Shu. Regulation of surface properties of photocatalysis material TiO2 by strain engineering[J]. Journal of Semiconductors, 2020, 41(9): 091703. doi: 10.1088/1674-4926/41/9/091703 ****
      J Zheng, D J Shu, Regulation of surface properties of photocatalysis material TiO2 by strain engineering[J]. J. Semicond., 2020, 41(9): 091703. doi: 10.1088/1674-4926/41/9/091703.
      shu

      Regulation of surface properties of photocatalysis material TiO2 by strain engineering

      DOI: 10.1088/1674-4926/41/9/091703

      • National Laboratory of Solid State Microstructures and School of Physics, Nanjing University, Nanjing 210093, China

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      • Corresponding author: email: djshu@nju.edu.cn
      • Received Date: 2020-06-30
      • Revised Date: 2020-07-24
      • Published Date: 2020-09-10

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