Sn doped (1 1 0) surface properties

Sn doped (1 1 0) surface properties

Surface Science 580 (2005) 71–79 www.elsevier.com/locate/susc A theoretical analysis of the TiO2/Sn doped (1 1 0) surface properties J.R. Sambrano a,...

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Surface Science 580 (2005) 71–79 www.elsevier.com/locate/susc

A theoretical analysis of the TiO2/Sn doped (1 1 0) surface properties J.R. Sambrano a, G.F. No´brega a, C.A. Taft a

b,*

, J. Andre´s c, A. Beltra´n

c

Laborato´rio de Simulac¸a˜o Molecular, DM, Unesp, Universidade Estadual Paulista, P.O. Box 473, 17033-360 Bauru, SP, Brazil b Centro Brasileiro de Pesquisas Fı´sicas, CMF, Rua Dr. Xavier Sigaud, 150, Urca, 22290-180 Rio de Janeiro, Brazil c Departament de Cie`ncies Experimentals, Universitat Jaume I, P.O. Box 6029, 12080 Castello´, Spain Received 24 July 2004; accepted for publication 9 February 2005

Abstract We have used the periodic quantum-mechanical method with density functional theory at the B3LYP level in order to study TiO2/Sn doped (1 1 0) surfaces and have investigated the structural, electronic and energy band properties of these oxides. Our calculated relaxation directions for TiO2 is the experimental one and is also in agreement with other theoretical results. We also observe for the doped systems relaxation of lattice positions of the atoms. Modification of Sn, O and Ti charges depend on the planes and positions of the substituted atoms. Doping can modify the Fermi levels, energy gaps as well as the localization and composition of both valence and conduction band main components. Doping can also modify the chemical, electronic and optical properties of these oxides surfaces increasing their suitability for use as gas sensors and optoelectronic devices. Ó 2005 Elsevier B.V. All rights reserved. Keywords: TiO2; SnO2; Mixed oxide; Doping process; DFT; Semiconductor surface

1. Introduction Theoretical, experimental and technological interest in oxides has grown rapidly due to their physical–chemical properties and important technological applications [1–5]. In particular, com*

Corresponding author. Tel./fax: +55 22 2141 7201. E-mail addresses: [email protected] (J.R. Sambrano), catff@terra.com.br, [email protected] (C.A. Taft).

pounds such as isostructural TiO2 and SnO2 have attracted considerable attention in catalytic processes and gas detection [6–10]. These materials are n-type semiconductors with high non-linearity between current density and electric field. TiO2 and SnO2 have a wide spectrum of applications in surface science [1]. The rutile (1 1 0) surface, which is often used, as a model system for metal oxides, has been the focus of several surface science theoretical studies [11–17]. The sensor

0039-6028/$ - see front matter Ó 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.susc.2005.02.010

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properties of SnO2, combined with the chemical stability of TiO2 at high temperatures, stimulate the study of these mixed oxides. Most of the chemistry of metal oxides is due to the presence of highly reactive defective sites such as cations, anion vacancies and/or doping processes by substitution of metal cations. Impurity doping with several kinds of transition metals is often done in order to create photo-catalysts operating under visible light irradiation or modification of optical, electrical and magnetic properties [6,9,18–21]. A major concern is the effect of doping on the electronic structure of TiO2 and its impact on the gas-sensor performance in order to develop new sensor materials with better sensitivity, selectivity and shorter response time. It has been observed that doping with suitable cations modifies the electronic and catalytic properties for gas interactions on the exposed surface. The substitution of Sn for Ti in the lattice structure is expected to aid the formation of solid solutions, alter the structure and contribute to the thermal stability of TiO2. Radecka and co-workers [7,22,23] investigated the transport properties of these mixed oxides indicating the effect of Nb, Cr and Sn additions on the electronic structure of TiO2 and showed that small additions of Sn on the TiO2 lattice improves the sensor characteristics. Cluster and periodic ab initio calculations to study TiO2, SnO2 and TiO2/ metal were previously investigated by our group [24–26]. Theoretical–computational studies can yield important information regarding the electronic and structural properties of solids, which can provide a framework for the interpretation of experimental data in order to determine the influence of defects and impurities that often control important aspects of solid-state chemistry. In this paper, we report periodic quantummechanical calculations based on periodic density functional theory (DFT) in order to elucidate the structural and electronic properties of the TiO2/ Sn doped (1 1 0) surface.

2. Models and method of calculation TiO2 and SnO2 crystallize in the rutile structure, which has tetragonal symmetry D14 4h -P42/mnm. In

particular, the structure of the conventional rutile unit cell of TiO2 is characterized by two lattice parameters, a and c, (see Fig. 1a) and an internal parameter u associated with the O atomic position. There are two formula units per primitive unit cell; with the threefold-coordinated oxygen atoms forming distorted octahedral configurations around the Ti atoms. The c/a ratio and u value can be used to determine the distortion of the octahedral configuration around the Ti atoms. The periodic DFT calculations with BeckeÕs three-parameter hybrid non-local exchange functional [27] combined with the Lee–Yang–Parr gradient-corrected correlation functional [28], B3LYP, were made with the new version of the CRYSTAL03 computer code [29]. The functional used in this work have yielded results comparable with more sophisticated correlated calculations or perturbation models [30]. In particular, we have employed this functional in studies of the electronic and structural properties of the bulk and surfaces of SnO2 [31] and TiO2 (anatase) [24]. The standard 6-31G basis set was selected for the oxygen and titanium atom [32]. We have employed this basis set with good results in previous studies of the TiO2 anatase system [24,33]. For the Sn center the all electron basis set were used and can be found in the CRYSTAL03 web site. The geometrical parameters have been opti˚ , c = 2.9683 A ˚ and mized, yielding a = 4.6400 A ˚ u = 0.3050 A, in agreement with experimental ˚ , c = 2.9587 A ˚ , and u = data, of a = 4.5936 A ˚ 0.3048 A, respectively [34]. The bulk modulus, B, and its first derivative with respect to pressure, B 0 was determined from the energy of each unit cell at different volumes, and by fitting the energy-volume results to the third-order Birch–Murnaghan equation of state [35]. The calculated values of B = 200.07 GPa and B 0 = 4, are in good agreement with the experimental values of 211.00(10) GPa and B 0 = 6.5(7) [36]. We calculated bulk TiO2 band structure (not shown). The calculated band gap is located at the C-point of the Brillouin Zone and corresponds to a direct transition of 3.30 eV, in agreement with the experimental value of 3.1 eV. Experimental and theoretical analysis [1,2,37] indicate that the (1 1 0) surface is the most stable of the rutile struc-

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Fig. 1. (a) Primitive unit cell of TiO2 rutile structure. The black spheres represent the oxygen atoms and the grey spheres titanium atoms. (b) and (c) Side and perspective view of the TiO2(1 1 0) relaxed surface, respectively.

ture with the lowest surface energy, which is thus investigated in this work. From our optimized structure, we built a 2D slab model (finite in the z-direction but periodic in the x and y-direction). The periodically repeating unit cell representing this slab is depicted in Fig. 1c. Previous periodic calculations on rutile surfaces have indicated that the properties such as surface energy and Mulliken charges are converged with a 9-layers slab model [11]. We have thus used in this work the 9-layer surface model to describe the surface geometry. As a consequence

of the symmetry, we have an equivalent relaxation of the first (last) three layers. The number of layers plays a role in the accuracy of the calculations of the atomic positions. Thus we have also investigated a 15 layer slab which indicated the same trends for directions of atomic displacements calculated in our 9-layer model and observed in experimental and theoretical work by other authors. The (1 1 0) termination results in an outermost plane of oxygen atoms that appear in rows along the [0 0 1] direction (see Fig. 1b and c). These O

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atoms are called ‘‘bridging’’ (Ob) atoms. In the second layer, there are fivefold-coordinated (Ti5c), and sixfold-coordinated (Ti6c) Ti atoms and O atoms in the same plane (Op). A third, (O1), and fourth, (O2) plane of oxygen atoms are located below. We consider that the titanium oxide surface is doped with Sn atoms, which substitute the Ti atoms. We calculated and compared the Mulliken charge distribution and overlap populations for the slab models. The XCrysDen program [38] has been used for the band structure diagram, density of states (DOS) as well as electronic density maps.

layer. Our calculated displacements are in the same range reported by other studies [12,15,34,39,40]. Since the thickness of the slab may play a role in the accuracy of the calculated atomic positions, we built for comparison, a relaxed model with 15-layer slab which indicated the same trends observed in our 9-layer model. The experimentally determined most striking feature in the relaxed coordinates is the large relaxation of the Ob bridg˚ . The measured ing oxygen atoms by 0.27 A geometry would indicate a smaller bond length between the sixfold-coordinated Ti atom and the ˚ exbridging oxygen Ob as compared to the 1.95 A pected from the bulk structure. The directions of our calculated relaxations and those of other authors (using LCAOs, plane-wave, periodic, free-standing supercells, different number of layers) agree in (almost) all our theoretical papers with the coordinates determined experimentally. The bridging oxygen atoms are measured to relax downwards and the sixfold-coordinated Ti atoms upwards. The fivefold-coordinated Ti atoms move downwards. Only the in-plane oxygens move laterally towards the fivefold coordinate Ti atoms; the neighboring threefold-coordinated oxygen atoms move upwards. The quantitative agreement from state-of-the art ab initio calculations is not as good as one could expect. DFT and HF calculations should reproduce experimental bond lengths for ˚ the bulk oxides to somewhat better than 0.1 A All the calculations find a much smaller relaxation for the position of the bridging oxygen atom. The theoretical results are valid strictly at zero temperature only. Strong anharmonic thermal vibrations at the surface could cause discrepancy between the

3. Results and discussion 3.1. Relaxed slab models The effect of optimization has been analyzed for the (1 1 0) surface, by relaxing all atoms of the 9layers, keeping constant the volume. Geometrical displacements and Mulliken charges for TiO2 and TiO2/Sn slabs are summarized in Table 1. The positive displacements indicate outwards relaxation and the magnitudes are measured with respect to the optimized bulk geometry without relaxation. In our models the top and bottom slabs are equivalent by symmetry (mirror plane). The relaxation of the bare TiO2 slab (Fig. 1b and c) indicates a positive displacement (upwards) of the Ti6c, Op and O2 atoms as well as a negative displacement (downwards) of the Ob, Ti5c and O1 atoms. The opposite displacement (upwards) of Op and Ti5c yield a corrugation of the second

Table 1 ˚ ) from their lattice positions as well as Mulliken charge distribution, Q, (in jej) for TiO2 and Displacements in [1 1 0] direction, Dz (A TiO2/Sn slabs. The positive displacements denote relaxations toward the vacuum region and the negative displacement denote relaxations inwards the bulk Me6ca

Ob TiO2 TiO2/Sn6c TiO2/Sn5c TiO2/Sn6-in TiO2/Sn5-in a

Me5ca

Op

O1

Me6-ina

O2

Dz

Q

Dz

Q

Dz

Q

Dz

Q

Dz

Q

0.083 0.250 0.021 0.015 0.052

0.63 0.82 0.65 0.64 0.64

0.124 0.245 0.184 0.222 0.153

1.52 1.87 1.53 1.52 1.50

0.136 0.145 0.010 0.112 0.020

1.66 1.67 2.04 1.65 1.67

0.137 0.109 0.304 0.182 0.226

0.85 0.89 0.97 0.85 0.85

0.066 0.052 0.018 0.054 0.034

0.85 0.014 0.88 0.0 0.94 0.002 0.88 0.0 0.86 0.014 0.96 0.0 0.94 0.025 0.88 0.0 0.86 0.132 1.00 0.0

Me = Ti or Sn.

Dz

Q

Dz

Me5-ina

Q

Dz

Q

– 1.74 1.71 2.19 1.72

0.0 0.0 0.0 0.0 0.0

– 1.76 1.72 1.75 2.23

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Table 2 ˚ ) and Overlap populations (jej, in brackets) Bond distances (A TiO2 Ob–Me6c Op–Me6c Op–Me5c O1–Me6c O2–Me5c O1–Me6-in O2–Me5-in

1.831 2.066 1.938 2.065 1.853 1.936 1.968

(172) (86) (122) (86) (130) (160) (83)

TiO2/Sn6c

TiO2/Sn5c

TiO2/Sn6-in

TiO2/Sn5-in

1.963 2.107 1.912 2.165 1.854 1.950 1.961

1.83 (165) 1.989 (64) 1.995 (139) 2.097 (117) 2.006 (122) 1.983 (163) 1.950 (96)

1.831 2.070 1.988 2.072 1.865 2.056 1.976

1.832 2.069 1.933 2.086 1.890 1.968 2.047

(220) (32) (114) (86) (119) (142) (84)

experimental and theoretical results. Finite temperature effects may have to be taken into account.

(172) (84) (123) (115) (134) (177) (86)

(171) (83) (120) (119) (112) (161) (90)

One may also need to keep in mind the substantial distortions and bond length changes that take

Fig. 2. (a) 2D Brillouin zone and (b) TiO2, (c) TiO2/Sn6c, (d) TiO2/Sn5c, (e) TiO2/Sn6-in and (f) TiO2/Sn5-in band structures.

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place during large amplitude vibrations. Adsorbates, often have also a significant influence on re-relaxing the surface. We also note that the modelling, optimization of layer slabs may not allow representing accurately the bulk position [1–3,41]. We analyzed the effect of relaxation by the substitution of Sn for Ti atoms on the optimized TiO2 slab. Doping at the Ti6c positions yield ˚ ), Op (0.109 A ˚ ) O1 displacements of Ob (0.250 A ˚ ), and O2 (0.002 A ˚ ) atoms. The relaxa(0.005 A tion of the TiO2/Sn5c model yields displacements of the Ob, Op, O1 and O2 by 0.021, 0.304 and ˚ , respectively. There are also 0.018 and 0.014 A relaxation of the lattice positions of the metal atoms. For the surface substitution sites we observe a large stability for the Sn5c as compared to the Sn6c site. Table 1 shows the Mulliken population analysis for the different models. The scheme is useful for comparing trends of calculations performed using similar models. The results indicate that there is in general an increase in the magnitude of the negative charges of the bridge oxygen, and Op and O1 atoms when Sn atom substitutes the Ti atoms. The bond lengths and overlap populations for all doping models are given in Table 2. The oxygen (Ob, Op, O1)–Metal(5c, 6c) distances are also modified. 3.2. Band structure and density of states Figs. 2 and 3 show the 2D Brillouin zone, band structure and total density of states (DOS) for all

Table 3 Calculated Fermi Energy and optical band gap (eV) TiO2 TiO2/Sn6c TiO2/Sn5c TiO2/Sn6-in TiO2/Sn5-in Fermi Energy C–C X 0 –C M–C X–C

8.40 8.75 2.84 2.96 3.03 3.12

2.05 2.35 1.88 1.79

7.92

8.71

8.30

3.07 3.09 3.24 3.29

3.00 3.14 3.20 3.16

3.34 3.40 3.49 3.46

models investigated. The values of the optical gap are summarized in Table 3. The top of the valence band (VB) coincides with the Fermi Energy (see Table 3). The analysis of the principal atomic orbitals (AO) component of the selected bands, are performed with the ANBD option (with a threshold of 0.15 a.u. for the important eigenvector coefficients) of the CRYSTAL software. Our theoretical results indicate that the upper VB for the TiO2 slab is located at C, i.e 8.40 eV, on the 2D Brillouin zone (Figs. 2a and 3a). The principal AO component indicates that the upper VB at C consists mainly of 2py and 2pz orbitals of O1, O2 and Op atoms. The lowest conduction band (CB) at C have dominant Ti 3dx2 y 2 and Ti 3dz2 orbital character, whereas the subsequent band is composed of Ti 3dxy orbitals. For the TiO2/Sn6c (Figs. 2b and 3b) model the top of the VB is located at X. When Sn atoms substitute at the sixfold position (Ti6c), the optical band gap becomes indirect between X and C. The VB maximum of TiO2/Sn5c (Figs. 2c and 3c) is located at C. The direct band gap is 3.07 eV. The

Fig. 3. Total DOS of (a) TiO2, (b) TiO2/Sn6c, (c) TiO2/Sn5c, (d) TiO2/Sn6-in and (e) TiO2/Sn5-in. Some important contributions are showed.

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Fig. 4. Electron density maps of (a) (1 1 0) plane including Sn6c substituting Ti6c, (b) (1 1 0) plane including Sn5c, (c) (1 1 0) plane including Sn6-in and (d) (1 1 0) plane including Sn5-in. The black spheres represent the oxygen atoms, the grey spheres titanium atoms and the slight grey spheres the tin atoms.

highest band of VB consists of 2px orbitals of Ob and O1 atoms. The lowest CB is essentially a mixture of the Ti 3d2z and Sn 5s orbitals. The CB minimum in TiO2/Sn5c also has 5s character, which suggests a modification of components of the electronic structure from d to s-type. For TiO2/Sn6-in (Figs. 2d and 3d) and TiO2/Sn5-in (Figs. 2e and 3e) the band gaps are direct at C. The top of VB in TiO2/Sn6-in (Figs. 2d and 3d) is composed of O 2py orbitals and the CB minimum consists of 3d (Ti). The gap is direct at C. TiO2/Sn5-in (Figs. 2e and 3e) indicates that the VB maximum, located at C, is composed of 2py and 2pz orbitals of O atoms. The bottom of CB is located at and is a mixture of Ti 3d2z and 3dx2 y 2 as well as Sn 5s and O 2s atomic orbitals respectively. Fig. 3 shows DOS for the surface and intermediate planes which indicate strong modifications of

charge densities near the top of VB and the bottom of the CB. New energy levels and charge densities may thus be created in the vicinity of the Fermi level and in the band gap region modifying the physical–chemical properties of these doped oxides. In Fig. 4 we give the charge density contours for different planes and doping positions of Sn. which indicate a dependence of the charge densities with planes and doping positions.

4. Conclusions The structural and electronic and energy band properties of the (1 1 0) surface of TiO2 and TiO2/ Sn systems was investigated using periodic firstprinciples calculations based on DFT/B3LYP theory. The conclusion can be summarized as follows.

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(i) Our optimized geometries for the Sn doped system indicate relaxations of the lattice positions of the atoms in the crystal (restructuring and rumpling). (ii) For the bare TiO2 the directions of the calculated relaxations agree with the theoretical and experimental results. The bridging oxygen atoms relax downwards, the sixfold coordinate Ti atoms upwards, the fivefoldcoordinated Ti atoms move downwards. (iii) The band gap values are affected by the presence of Sn atoms in the TiO2 lattice. The gaps are dependent on the planes and doping positions. (iv) Substitution of Ti for Sn yields relaxation of the lattice positions and magnitude of the charges of metal and oxygen atoms. Modification of the charge distribution around the metals can create charge gradients within the crystal. (v) Doping modifies the Fermi Energy Levels and the main components of the highest VB as well as the lowest CB. Modification of the higher VB electronic levels can also increase the oxidation-reduction potentials of these doped oxides.

[4] [5]

[6]

[7] [8] [9] [10] [11] [12] [13] [14] [15] [16]

Acknowledgments

[17] [18]

This work is supported by FAPESP, FUNDUNESP, CAPES, FAPERJ, CNPq, Generalitat Valenciana (project: GV04B-020) and Fundacio´ Caixa Castello´-Bancaixa. We also acknowledge use of the Computer facilities of the Laborato´rio de Modelagem e Simulac¸a˜o Molecular, Unesp, Bauru and Servei dÕInforma´tica, Universitat Jaume I. The constructive comments of the referees are gratefully acknowledged.

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