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MgO(0 0 1)
Journal of Alloys and Compounds 485 (2009) 598–603
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Electronic structure and optical properties of In doped SrTiO3 /MgO(0 0 1) K.L. Zhao, D. Chen ∗ , D.X. Li Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, No. 72 Wenhua Road, Shenyang 110016, China
a r t i c l e
i n f o
Article history: Received 9 December 2008 Received in revised form 4 June 2009 Accepted 5 June 2009 Available online 12 June 2009 PACS: 71.15.Mb 73.20.At 78.20.Ci 68.35.Ct
a b s t r a c t The electronic and optical properties of six possible In doped SrTiO3 /MgO(0 0 1) interface models have been studied by using first-principles method based on the density functional theory. From the analysis of the substitution energy, the segregation energy and density of states, it reveals that an In atom would preferably substituted for the Ti atom at the interface. The effects of In doping on the SrTiO3 /MgO(0 0 1) film are discussed in detail by the position optimization of In atoms. The electronic structure and optical properties of In doped SrTiO3 /MgO(0 0 1) are dependent on the concentration of In atoms and the relative positions of the In atoms to the interface. © 2009 Elsevier B.V. All rights reserved.
Keywords: Density functional theory Electronic structure Optical properties Interface structure
1. Introduction Strontium titanate (SrTiO3 ), as a perovskite-structured oxide, is of particular importance due to its potential applications in the fields of ferroelectricity, grain-boundary barrier layer capacitors, oxygen-gas sensors, epitaxial growth substrates for high temperature superconductor thin films, optical switches and so on [1–3]. Recently, the electrical and optical properties of doped SrTiO3 single crystal and thin film have been widely studied [4–14], in which most of them [4–10] are reported on n-type doped SrTiO3 but few on p-type doped SrTiO3 . It is well known that p-type doped SrTiO3 is a very promising material, which could be used as wide-gap semiconductor diodes in a blue-light region and accommodate the protonic conductivity by introducing the acceptor impurity [11–14] for applications in transparent conductive oxide films and oxide heterostructure design. With respect to the experimental study, Higuchi et al. [11] investigated the photoemission spectra of a ptype SrTiO3 single crystal in which the acceptor Sc3+ was introduced into Ti4+ site. Afterwards Dai et al. [12] reported that the In doped SrTiO3 film on a (1 0 0) SrTiO3 substrate exhibits a p-type semiconductor using In3+ as the acceptor ion. Guo et al. [13] have measured the optical transmittance and Raman spectra of p-type In doped
∗ Corresponding author. Tel.: +86 24 83978629; fax: +86 24 23971215. E-mail address: [email protected] (D. Chen). 0925-8388/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2009.06.058
SrTiO3 film on MgO(1 0 0) substrate. Moreover, our group [14] has observed the presence of nanoclusters and chemical aggregation in In doped SrTiO3 film by high-resolution electron microscopy. To the best of our knowledge, there is no theoretical investigation on the optical properties of In doped SrTiO3 film so far. Therefore, it is necessary to use the first-principles method to explore the effects of In doping on SrTiO3 thin film. In this work, the electronic structure and optical properties of In doped SrTiO3 /MgO(0 0 1) are systematically studied by using first-principles method based on the density functional theory. 2. Computational details First-principles method has been proven very useful to study interface materials [15,16] and favorable to enhance the microscopic understanding of perovskites [17,18]. In the present study, plane-wave pseudopotential (PWPP) calculations have been performed within the density functional theory by using the CASTEP code [19]. Exchange-correlation effects are treated with the local density approximation (LDA) in the form of Ceperley and Alder [20] function parameterized by Perdew and Zunger [21], which has been used to investigate the structural and optical properties of bulk SrTiO3 and to acquire the results that agreed with experiments [22,23]. In our calculations, the energy cutoff was set to 350 eV. The 6 × 6 × 1 Monkhorst–Pack k-point meshes [24] are used to sample
K.L. Zhao et al. / Journal of Alloys and Compounds 485 (2009) 598–603 Table 1 Lattice constants a, bulk modulus B0 and band gap of SrTiO3 and MgO according to earlier experiments and recent calculations based on various methods.
SrTiO3
MgO
a (Å)
B0 (GPa)
Band gap (eV)
Method
Reference
3.905 3.863
183 203
3.91 3.862
186 186
3.25 1.84 2.57 4.16 1.87
Expt. LDAa LDA + U B3PWb PP-LDA
[28,29] [30] [31] [32,33] This study
4.210 4.248 4.160 4.165 4.208
160 153
7.83
Expt. FP-KKRc LDAd LDAa PP-LDA
[34,35] [36] [37] [38] This study
5.20 5.00 4.74
171 174
a
Full potential linear augmented plane-wave method. Becke’s three-parameter method with the correlation functionals of Perdew and Wang. c Full potential Korringa–Kohn–Rostoker Green’s function. d Tight-binding linear muffin-tin orbital method. b
each computational cell in the Brillouin zone integration. All the atoms in each computational cell were relaxed until the total energy difference between two steps is smaller than 1 × 10−5 eV/atom. The total energy was minimized by means of a conjugate gradient technique [25]. The ultrasoft pseudopotentials [26] of strontium, titanium, magnesium, and oxygen were taken to determine the appropriate plane-wave basis set. The density-mixing scheme based on the Pulay algorithm [27] was used for self-consistentfield (SCF) calculation, in which the SCF tolerance was set at 1 × 10−6 eV/atom. After relaxation, the remaining forces on the atoms were less than 0.03 eV/Å, and the remaining stress was less than 0.05 GPa. To examine the above-mentioned parameters, we first employed the PWPP method to calculate the structural properties for the bulk form of SrTiO3 and MgO. Table 1 lists the calculated and experimental lattice constants, bulk modulus, and band gaps for bulk form of SrTiO3 and MgO. Note that our results agree well with the experimental and other theoretical values [28–38] for both lattice constants and bulk modulus. Our calculated band gaps are less than the experimental values, which is typical for LDA calculations. Although the better results could be obtained by using LDA + U [31] or hybrid functionals method [32,33], exchangecorrelation effects treated with LDA have been successfully applied to study not only the structural and optical properties of bulk SrTiO3 [22,23], but also the interfacial structure and electronic properties of SrTiO3 /MgO(0 0 1) [39,40]. Accordingly, we use the LDA method to study the electronic structure and optical properties of In doped SrTiO3 /MgO(0 0 1) film. Experimental and theoretical results [39–41] have shown that only the TiO2 /MgO contact across the interface is stable and makes the epitaxial growth of SrTiO3 film on MgO substrate possible. Accordingly, we performed the first-principles calculations to study the SrTiO3 (n)/MgO(m) system, which contains n upper layers of SrTiO3 (0 0 1) (n is the number of layers TiO2 + SrO) and m under layers of MgO(0 0 1).
599
The interfacial energy Einterface (J/m2 ) of SrTiO3 /MgO(0 0 1) computational cell in equilibrium state can be obtained by Einterface =
1 2S
Etot
(SrTiO ) 3 n (MgO)m
− NSrO SrO − mMgO
− NTiO2 TiO2
(1)
where energy Etot [(SrTiO3 )n /(MgO)m ] is the total energy of computational cell which has two identical interfaces with an area of S. NTiO2 and NSrO are the numbers of TiO2 and SrO layers, respectively, and both of them are satisfied to the equation: NTiO2 + NSrO = n. Chemical potentials of SrTiO3 and MgO represented by the symbol are set to their bulk energies, which are calculated by using the same method as the SrTiO3 /MgO(0 0 1) computational cell. In addition, chemical potentials of TiO2 and SrO are satisfied to the equation: TiO2 + SrO = SrTiO3 . PWPP calculations were performed by using the supercell of SrTiO3 (n)/MgO(m) (n = 5, 7, 9; m = 3), in which three MgO layers were chosen according to Refs. [16,40,41]. No significant difference in the interfacial energy (0.889, 0.962, and 1.035 J/m2 ) was observed between them. This means that the supercell (n = 5 and m = 3) is enough to construct the model of In doped SrTiO3 /MgO(0 0 1) with an appropriate compromise between calculation accuracy and computational efficiency. DFT calculations in CASTEP code [42–44] have been successfully used to study the optical properties of many materials. The optical properties of a material are determined by the frequencydependent dielectric function ε(ω) = ε1 (ω) + iε2 (ω), which can be calculated by the sum of all possible direct transitions from the occupied states to the unoccupied states over the Brillouin zone. The absorption coefficient ˛(ω) and reflectivity R(ω) can be derived from ε1 (ω) and ε2 (ω) by Kramer–Kronig transformation. The smearing factor was set to 0.2 eV [31,32]. The theory underlying the calculated optical properties can be seen from Refs. [42–44] in detail. For the underestimated gap within the LDA method, some people [22,31] may apply the scissors operator, which involves a rigid shift of the conduction band with respect to the valence band, so that the band gap matches the experimental value. However, it is not justified in doing so. Therefore, such a rigid shift is not applied in this work. Moreover, there is no excitonic correction in the calculations because no excitonic effects can be found in the p-type doped SrTiO3 in experiments [11–13]. 3. Results and discussion 3.1. Interface models, substitution and segregation energies In previous experiments [12,13], In atoms as an accepter impurity can substitute for Ti atom in the SrTiO3 /MgO(0 0 1) film. Accordingly, we construct six possible SrTiO3 /MgO(0 0 1) computational cells, in which In atomic positions are different near the SrTiO3 /MgO interface. Each one contains five SrTiO3 (0 0 1) upper layers and three MgO(0 0 1) under layers based on the interface structure [Ti (O) of TiO2 layer on O (Mg) of MgO layer]. In Fig. 1(a), we only show three SrTiO3 (0 0 1) upper layers (including one TiO2
Table 2 Calculated substitution and segregation energies for models A–F after they are fully relaxed. Interface models
Number of In atoms
Substitution energy (eV)
Segregation energy (eV)
Relaxation
A B C D E F
0 1 1 2 2 2
6.849 7.214 7.332 7.522 7.046
−1.293 −0.926 −0.815 −0.625 −1.104
Yes Yes Yes Yes Yes Yes
600
K.L. Zhao et al. / Journal of Alloys and Compounds 485 (2009) 598–603
two In atoms simultaneously substitute for Ti(I) and Ti(II) atoms. When both Ti(1) and Ti(2) atoms (both Ti(1) and Ti(3) atoms) are replaced by two In atoms, the computational cell is called model E (model F) as shown in Fig. 1(b) and (c), which show the twodimensional cells of SrTiO3 (5)/MgO(3). The side view of model E (F) along the [1 0 0] direction is illustrated in Fig. 1(b), and the [0 0 1] projection of TiO2 interface layer of the model (dotted line in Fig. 1(b)) is displayed in Fig. 1(c). For a consistent comparison, all of the six possible models have been fully relaxed, not only in the vertical direction but also with lateral relaxation of atoms. For each model of In doped SrTiO3 /MgO(0 0 1) at the equilibrium state, the substitution energy ESub of In for Ti atoms can be expressed as following: ESub =
1 − Eperfect − nEIn + nETi ) (E n doped
(2)
where Edoped and Eperfect are the total energy per unit cell for the doped and perfect system, respectively. n is the number of Indium atoms which substitute for Ti atoms. EIn and ETi are the total energies per atom for bulk In and Ti crystal, respectively. To reflect the local effects of In atoms on each model of In doped SrTiO3 /MgO(0 0 1), the segregation energy ESeg can be calculated by doped
doped
A ) − (EBulk − EBulk ) ESeg = (EInterface − EInterface
(3)
doped
A where EInterface and EInterface are the total energies of each In doped doped
Fig. 1. Schematics of six computational cells of the SrTiO3 /MgO(0 0 1) interface employed in present study. (a) Models A–D, (b) and (c) models E and F (where the bright spheres are Ti, the black spheres are O, the big gray spheres are Sr, and the small gray spheres are Mg).
interface layer) and one MgO(0 0 1) interface layer. The computational cell of the perfect SrTiO3 /MgO interface is called model A, as shown in Fig. 1(a). It can be changed to model B (model C), if an In atom substitutes for the Ti(I) (Ti(II)) atom on the TiO2 interface (noninterface) layer; moreover, it can also be altered to model D if
model and model A. EBulk is the total energy of In doped SrTiO3 supercell, and EBulk is the bulk total energy for the perfect SrTiO3 computational cell. Table 2 lists the substitution and segregation energies obtained from those fully relaxed models. When a Ti atom was replaced by an In atom, the substitution and segregation energies for model B are more favorable than for model C, which indicates that the In atom would like to substitute for the Ti atom on the SrTiO3 /MgO interface layer. When two Ti atoms were replaced by two In atoms, model F is preferred since it has the lowest substitution and segregation energies among the models D–F. From the above discussion, it can be concluded that the formation of In doped SrTiO3 /MgO(0 0 1) is closely dependent on not only the concentration of In atoms but also the relative positions of the In atoms to the interface. 3.2. Electronic structure To understand the fundamental properties of In doped SrTiO3 /MgO(0 0 1), we calculated the electronic structures of six
Fig. 2. TDOSs of six models. The insert shows an enlarged part of the TDOSs in the rectangular field enclosed with dotted lines.
K.L. Zhao et al. / Journal of Alloys and Compounds 485 (2009) 598–603
601
Fig. 3. PDOSs of different atoms (marked in Fig. 1(a)) (a) on the TiO2 interface layer, (b) on the TiO2 noninterface layer, and (c) on the MgO interface layer for models A–C.
models (one perfect and five In doped computational cells) at the equilibrium state. Fig. 2 shows the total density of states (TDOS) of each model with respect to the Fermi level at zero. For model A, the valence band distributed in the energy range between −6.1 and 0 eV mainly comes from O 2p and Ti 3d orbital electrons, while the conduction band is caused mostly by the Ti 3d orbital electrons. In Fig. 2, the band gap is about 0.87 eV, much less than that of bulk SrTiO3 and MgO as presented in Table 1, which implies that the interface interactions would play an important role in determining the electronic properties of SrTiO3 /MgO(0 0 1). For the In doped models, their TDOSs are very different from the perfect model A. The remarkable change is that the peaks of conduction bands are clearly reduced between 1.5 and 2.2 eV. This is because that the bottoms of conduction bands have shifted noticeably to the higher energies, but the tops of valence bands only show a slight shift. As a result, the band gaps of In doped SrTiO3 /MgO(0 0 1) are increased as compared with the model A. For example, the band gap of model B becomes 0.92 eV and that of model F is 0.98 eV. That is to say, the band gap would become wider with the increase of the In atomic concentration on the TiO2 interface layer. Moreover, there are some narrower width peaks with extended tails between −7.3 and −5.0 eV for the
In doped models, which results in the increase of the valance band widths as compared with the perfect interface. For an example, the width of valence band for model F is up to 7.6 eV which is comparable with the experimental value (8.7 eV) [12]. Fig. 3 shows the projected density of states (PDOSs) for different atoms (marked in Fig. 1(a)) on the TiO2 interface layer, TiO2 noninterface layer, and MgO interface layer for models A, B and C, respectively. For model A, the bottom of the conduction band of the interfacial Ti(I) atom (shown in Fig. 3(a)) is lower than that of the noninterface Ti(II) atom (shown in Fig. 3(b)), which dominantly contributes to the conduction band structure of the TDOS for model A. In Fig. 3(a) and (c), the interfacial hybridization results in the 2p electron states of interface O(II) and O(I) atoms with the extended tails crossing the Fermi level. In Fig. 3(b), the noninterface O(III) atom remains insulating due to lack of electron states at the Fermi level. In Fig. 3(a) and (c), all the electron states of Ti(I), O(II), Mg(I) and O(I) atoms on interface layers (mainly between −6 and 0 eV) reflect that the interfacial hybridization between Ti(I) and O(I) atoms is stronger than that between O(II) and Mg(I). Otherwise, the optimized interfacial spacing between Ti and O (2.031 Å) is less than that between O and Mg (2.175 Å), which indicates that the chemical bond between Ti(I)
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Fig. 4. Imaginary part ε2 (ω) of dielectric function of six models along [0 0 1] direction.
and O(I) is stronger than that between O(II) and Mg(I). Therefore, for the perfect model A, the covalent contribution plays a dominant role on the interface interactions. For model B, with an interfacial Ti(I) atom replaced by an In atom, the atomic PDOSs show a significant change as compared with model A. In Fig. 3(a), the width of O(II) 2p valence band becomes larger. The top of O(II) 2p valence band extends through Fermi level and moves to the energy slightly higher than model A. The valence band of Ti(III) 3d orbital becomes wider and the bottom of Ti(III) 3d conduction band also shifts to a higher energy level. However, for the noninterface Ti(II) atom, it can be seen from Fig. 3(b) that the bottom of Ti(II) 3d conduction band almost does not change. Combining these contributions with the fact that interface O(II) and O(I) electron states extend tail crossing Fermi level, the band gap of model B is larger than model A as shown in Fig. 2. For model C, with an In atom substituting for a Ti(II) atom, the PDOSs of interface atoms form a striking contrast to model B as shown in Fig. 3(a) and (c). In this case, the valence band widths of the interfacial oxygen atoms are decreased, and the intensities of additional narrower width peaks at −6.5 to −5.0 eV become much smaller. All the electronic states of the interfacial atoms suggest that the covalent contributions at interface would be less than model B. That is to say, if an In atom doped in SrTiO3 /MgO(0 0 1), model B is a more favorable configuration than model C. This verifies that the Ti atom at interface would like to be substituted by an In atom, which is also consistent with the calculated results for the substitution and segregation energies listed in Table 2. To understand the effects of the In atomic concentration on the electronic properties of SrTiO3 /MgO(0 0 1), we have also calculated the PDOSs of models D–F, in which two Ti atoms are substituted by two In atoms. One of the two In atoms is always on the TiO2 interface layer, which is a common characteristic for the three configurations. All the atomic PDOSs of models D–F (not shown in the present paper) indicate that model F would be preferable, in which two interfacial Ti atoms are replaced by two In atoms at the same time. 3.3. Optical properties To clarify the effects of In doping on the optical properties of SrTiO3 /MgO(0 0 1), we calculated the imaginary parts ε2 (ω), absorption coefficient ˛(ω), and reflectivity R(ω) for each model. Considering the symmetry of the models, we present the imaginary parts ε2 (ω) of dielectric function of six models along [0 0 1] direction as shown in Fig. 4. For model A, the threshold peak of
Fig. 5. Other optical parameters of each model along the [0 0 1] direction. ˛(ω) and R(ω) are (a) absorption coefficient and (b) reflectivity, respectively.
imaginary part ε2 (ω) along [0 0 1] direction appears to be about 1.5 eV. In the energy range between 1.5 and 8.5 eV, the ε2 (ω) spectrum is mainly composed of three-peak structures similar to the spectrum features of bulk SrTiO3 [22,23]. For models B and C, new peaks appear at the lower energy (<1.5 eV), the main features of ε2 (ω) curves have been changed into two-peak structure and shifted to higher energy level compared to model A. For model B, both the intensity of new peak and the shifting distance of two-peak structure are lower than model C, which reflects that the property of ε2 (ω) spectrum is closely related to the position of In atoms. With the increase of the In atomic concentration, it can be seen that the new peak is intensified and one-peak structure becomes the main feature of ε2 (ω) spectrum as shown in Fig. 4. Although the concentration of In atoms is identical for the three models D–F, the curves of imaginary part ε2 (ω) are different. When two In atoms are both located at interface layer (model F), the shifting distance of ε2 (ω) one-peak structure is the smallest as compared with model A. Fig. 5 shows the absorption spectra and optical reflectivity of six models along the [0 0 1] direction, which can further illustrate the effects of In doping on the optical properties of SrTiO3 /MgO(0 0 1). The absorption spectra of each model are displayed in Fig. 5(a). For model A, the absorption edge starts from about 1.5 eV, and the absorption band is composed of three-peak structure between 1.5 and 8.5 eV, corresponding to the transition of electrons in O 2p orbital to the conduction band. For each of the other models for
K.L. Zhao et al. / Journal of Alloys and Compounds 485 (2009) 598–603
the In doped interfaces, there is a weak peak appearing on the left side of absorption band. In addition, it is noticeable that the absorption band becomes narrower and shows a buleshift as compared with the perfect SrTiO3 /MgO(0 0 1) interface. These features of the absorption spectrum are similar to the ε2 (ω) spectrum as shown in Fig. 4, which reflects that there is a close relationship between the absorption coefficient and the imaginary part ε2 (ω) of dielectric function. Comparing with the absorption spectra of models A, B and F, it can be found that the absorption edge shifts to the higher energy and the peaks of absorption band are reduced with the increase of the In atomic concentration. From the above discussion, it is therefore believed that the buleshift of the absorption edge could be observed with an increase in the concentration of In atoms, which is in good agreement with the experimental results [13]. Fig. 5(b) shows the spectra of optical reflectivity R(ω) for each model. For model A, the curve of reflectivity R(ω) gradually raises between 0 and 4.0 eV, then three peaks appear in the energy range from 4.0 to 9.0 eV. The maximum value of reflectivity occurs at around 7.0 eV in the ultraviolet region. When the energy is higher than 9.0 eV, the perfect SrTiO3 /MgO material becomes transparent. In Fig. 5(b), it can be found that the R(0) value becomes larger and the reflectivity peaks shift towards the higher energy with the increase of the In atomic concentration (such as models A, B and F). It is particularly worth mentioning that the R(ω) spectra are gradually decreased from model A to B and then to F in the energy range between 1.6 and 3.1 eV, which is in the visible region. However, when the concentration of In atoms keeps unchanged, the R(ω) value of model F is larger than models D and E in the range of visible light. This indicates that model F has a transmission less than models D and E if at the same frequency. For example, on a certain visible frequency, if a nanocluster rich in Indium is formed near the interface in the In doped SrTiO3 film, it could happen that the part of nanocluster close to the interface will be darker and the other part far from the interface will be brighter. 4. Conclusions The crystal structure, electronic structure, and optical properties of In doped SrTiO3 /MgO(0 0 1) interface are systematically investigated by using first-principles calculations based on the density functional theory. The In atomic position optimization reveals that an interfacial Ti atom would like to be substituted by an In atom, and the band gap will be widened with the increase of In atomic concentration on the interface layer. It is found that the electronic structure and optical properties of In doped SrTiO3 /MgO(0 0 1) are dependent not only on the concentration of In atoms but also on the In atomic position relative to the interface. Acknowledgements This work was supported by the National Basic Research Program of China (2002CB613503 and 2009CB623705) and the National Natural Science Foundation of China (Grant No. 50571100).
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Journal of Alloys and Compounds journal homepage: www.elsevier.com/locate/jallcom
Electronic structure and optical properties of In doped SrTiO3 /MgO(0 0 1) K.L. Zhao, D. Chen ∗ , D.X. Li Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, No. 72 Wenhua Road, Shenyang 110016, China
a r t i c l e
i n f o
Article history: Received 9 December 2008 Received in revised form 4 June 2009 Accepted 5 June 2009 Available online 12 June 2009 PACS: 71.15.Mb 73.20.At 78.20.Ci 68.35.Ct
a b s t r a c t The electronic and optical properties of six possible In doped SrTiO3 /MgO(0 0 1) interface models have been studied by using first-principles method based on the density functional theory. From the analysis of the substitution energy, the segregation energy and density of states, it reveals that an In atom would preferably substituted for the Ti atom at the interface. The effects of In doping on the SrTiO3 /MgO(0 0 1) film are discussed in detail by the position optimization of In atoms. The electronic structure and optical properties of In doped SrTiO3 /MgO(0 0 1) are dependent on the concentration of In atoms and the relative positions of the In atoms to the interface. © 2009 Elsevier B.V. All rights reserved.
Keywords: Density functional theory Electronic structure Optical properties Interface structure
1. Introduction Strontium titanate (SrTiO3 ), as a perovskite-structured oxide, is of particular importance due to its potential applications in the fields of ferroelectricity, grain-boundary barrier layer capacitors, oxygen-gas sensors, epitaxial growth substrates for high temperature superconductor thin films, optical switches and so on [1–3]. Recently, the electrical and optical properties of doped SrTiO3 single crystal and thin film have been widely studied [4–14], in which most of them [4–10] are reported on n-type doped SrTiO3 but few on p-type doped SrTiO3 . It is well known that p-type doped SrTiO3 is a very promising material, which could be used as wide-gap semiconductor diodes in a blue-light region and accommodate the protonic conductivity by introducing the acceptor impurity [11–14] for applications in transparent conductive oxide films and oxide heterostructure design. With respect to the experimental study, Higuchi et al. [11] investigated the photoemission spectra of a ptype SrTiO3 single crystal in which the acceptor Sc3+ was introduced into Ti4+ site. Afterwards Dai et al. [12] reported that the In doped SrTiO3 film on a (1 0 0) SrTiO3 substrate exhibits a p-type semiconductor using In3+ as the acceptor ion. Guo et al. [13] have measured the optical transmittance and Raman spectra of p-type In doped
∗ Corresponding author. Tel.: +86 24 83978629; fax: +86 24 23971215. E-mail address: [email protected] (D. Chen). 0925-8388/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2009.06.058
SrTiO3 film on MgO(1 0 0) substrate. Moreover, our group [14] has observed the presence of nanoclusters and chemical aggregation in In doped SrTiO3 film by high-resolution electron microscopy. To the best of our knowledge, there is no theoretical investigation on the optical properties of In doped SrTiO3 film so far. Therefore, it is necessary to use the first-principles method to explore the effects of In doping on SrTiO3 thin film. In this work, the electronic structure and optical properties of In doped SrTiO3 /MgO(0 0 1) are systematically studied by using first-principles method based on the density functional theory. 2. Computational details First-principles method has been proven very useful to study interface materials [15,16] and favorable to enhance the microscopic understanding of perovskites [17,18]. In the present study, plane-wave pseudopotential (PWPP) calculations have been performed within the density functional theory by using the CASTEP code [19]. Exchange-correlation effects are treated with the local density approximation (LDA) in the form of Ceperley and Alder [20] function parameterized by Perdew and Zunger [21], which has been used to investigate the structural and optical properties of bulk SrTiO3 and to acquire the results that agreed with experiments [22,23]. In our calculations, the energy cutoff was set to 350 eV. The 6 × 6 × 1 Monkhorst–Pack k-point meshes [24] are used to sample
K.L. Zhao et al. / Journal of Alloys and Compounds 485 (2009) 598–603 Table 1 Lattice constants a, bulk modulus B0 and band gap of SrTiO3 and MgO according to earlier experiments and recent calculations based on various methods.
SrTiO3
MgO
a (Å)
B0 (GPa)
Band gap (eV)
Method
Reference
3.905 3.863
183 203
3.91 3.862
186 186
3.25 1.84 2.57 4.16 1.87
Expt. LDAa LDA + U B3PWb PP-LDA
[28,29] [30] [31] [32,33] This study
4.210 4.248 4.160 4.165 4.208
160 153
7.83
Expt. FP-KKRc LDAd LDAa PP-LDA
[34,35] [36] [37] [38] This study
5.20 5.00 4.74
171 174
a
Full potential linear augmented plane-wave method. Becke’s three-parameter method with the correlation functionals of Perdew and Wang. c Full potential Korringa–Kohn–Rostoker Green’s function. d Tight-binding linear muffin-tin orbital method. b
each computational cell in the Brillouin zone integration. All the atoms in each computational cell were relaxed until the total energy difference between two steps is smaller than 1 × 10−5 eV/atom. The total energy was minimized by means of a conjugate gradient technique [25]. The ultrasoft pseudopotentials [26] of strontium, titanium, magnesium, and oxygen were taken to determine the appropriate plane-wave basis set. The density-mixing scheme based on the Pulay algorithm [27] was used for self-consistentfield (SCF) calculation, in which the SCF tolerance was set at 1 × 10−6 eV/atom. After relaxation, the remaining forces on the atoms were less than 0.03 eV/Å, and the remaining stress was less than 0.05 GPa. To examine the above-mentioned parameters, we first employed the PWPP method to calculate the structural properties for the bulk form of SrTiO3 and MgO. Table 1 lists the calculated and experimental lattice constants, bulk modulus, and band gaps for bulk form of SrTiO3 and MgO. Note that our results agree well with the experimental and other theoretical values [28–38] for both lattice constants and bulk modulus. Our calculated band gaps are less than the experimental values, which is typical for LDA calculations. Although the better results could be obtained by using LDA + U [31] or hybrid functionals method [32,33], exchangecorrelation effects treated with LDA have been successfully applied to study not only the structural and optical properties of bulk SrTiO3 [22,23], but also the interfacial structure and electronic properties of SrTiO3 /MgO(0 0 1) [39,40]. Accordingly, we use the LDA method to study the electronic structure and optical properties of In doped SrTiO3 /MgO(0 0 1) film. Experimental and theoretical results [39–41] have shown that only the TiO2 /MgO contact across the interface is stable and makes the epitaxial growth of SrTiO3 film on MgO substrate possible. Accordingly, we performed the first-principles calculations to study the SrTiO3 (n)/MgO(m) system, which contains n upper layers of SrTiO3 (0 0 1) (n is the number of layers TiO2 + SrO) and m under layers of MgO(0 0 1).
599
The interfacial energy Einterface (J/m2 ) of SrTiO3 /MgO(0 0 1) computational cell in equilibrium state can be obtained by Einterface =
1 2S
Etot
(SrTiO ) 3 n (MgO)m
− NSrO SrO − mMgO
− NTiO2 TiO2
(1)
where energy Etot [(SrTiO3 )n /(MgO)m ] is the total energy of computational cell which has two identical interfaces with an area of S. NTiO2 and NSrO are the numbers of TiO2 and SrO layers, respectively, and both of them are satisfied to the equation: NTiO2 + NSrO = n. Chemical potentials of SrTiO3 and MgO represented by the symbol are set to their bulk energies, which are calculated by using the same method as the SrTiO3 /MgO(0 0 1) computational cell. In addition, chemical potentials of TiO2 and SrO are satisfied to the equation: TiO2 + SrO = SrTiO3 . PWPP calculations were performed by using the supercell of SrTiO3 (n)/MgO(m) (n = 5, 7, 9; m = 3), in which three MgO layers were chosen according to Refs. [16,40,41]. No significant difference in the interfacial energy (0.889, 0.962, and 1.035 J/m2 ) was observed between them. This means that the supercell (n = 5 and m = 3) is enough to construct the model of In doped SrTiO3 /MgO(0 0 1) with an appropriate compromise between calculation accuracy and computational efficiency. DFT calculations in CASTEP code [42–44] have been successfully used to study the optical properties of many materials. The optical properties of a material are determined by the frequencydependent dielectric function ε(ω) = ε1 (ω) + iε2 (ω), which can be calculated by the sum of all possible direct transitions from the occupied states to the unoccupied states over the Brillouin zone. The absorption coefficient ˛(ω) and reflectivity R(ω) can be derived from ε1 (ω) and ε2 (ω) by Kramer–Kronig transformation. The smearing factor was set to 0.2 eV [31,32]. The theory underlying the calculated optical properties can be seen from Refs. [42–44] in detail. For the underestimated gap within the LDA method, some people [22,31] may apply the scissors operator, which involves a rigid shift of the conduction band with respect to the valence band, so that the band gap matches the experimental value. However, it is not justified in doing so. Therefore, such a rigid shift is not applied in this work. Moreover, there is no excitonic correction in the calculations because no excitonic effects can be found in the p-type doped SrTiO3 in experiments [11–13]. 3. Results and discussion 3.1. Interface models, substitution and segregation energies In previous experiments [12,13], In atoms as an accepter impurity can substitute for Ti atom in the SrTiO3 /MgO(0 0 1) film. Accordingly, we construct six possible SrTiO3 /MgO(0 0 1) computational cells, in which In atomic positions are different near the SrTiO3 /MgO interface. Each one contains five SrTiO3 (0 0 1) upper layers and three MgO(0 0 1) under layers based on the interface structure [Ti (O) of TiO2 layer on O (Mg) of MgO layer]. In Fig. 1(a), we only show three SrTiO3 (0 0 1) upper layers (including one TiO2
Table 2 Calculated substitution and segregation energies for models A–F after they are fully relaxed. Interface models
Number of In atoms
Substitution energy (eV)
Segregation energy (eV)
Relaxation
A B C D E F
0 1 1 2 2 2
6.849 7.214 7.332 7.522 7.046
−1.293 −0.926 −0.815 −0.625 −1.104
Yes Yes Yes Yes Yes Yes
600
K.L. Zhao et al. / Journal of Alloys and Compounds 485 (2009) 598–603
two In atoms simultaneously substitute for Ti(I) and Ti(II) atoms. When both Ti(1) and Ti(2) atoms (both Ti(1) and Ti(3) atoms) are replaced by two In atoms, the computational cell is called model E (model F) as shown in Fig. 1(b) and (c), which show the twodimensional cells of SrTiO3 (5)/MgO(3). The side view of model E (F) along the [1 0 0] direction is illustrated in Fig. 1(b), and the [0 0 1] projection of TiO2 interface layer of the model (dotted line in Fig. 1(b)) is displayed in Fig. 1(c). For a consistent comparison, all of the six possible models have been fully relaxed, not only in the vertical direction but also with lateral relaxation of atoms. For each model of In doped SrTiO3 /MgO(0 0 1) at the equilibrium state, the substitution energy ESub of In for Ti atoms can be expressed as following: ESub =
1 − Eperfect − nEIn + nETi ) (E n doped
(2)
where Edoped and Eperfect are the total energy per unit cell for the doped and perfect system, respectively. n is the number of Indium atoms which substitute for Ti atoms. EIn and ETi are the total energies per atom for bulk In and Ti crystal, respectively. To reflect the local effects of In atoms on each model of In doped SrTiO3 /MgO(0 0 1), the segregation energy ESeg can be calculated by doped
doped
A ) − (EBulk − EBulk ) ESeg = (EInterface − EInterface
(3)
doped
A where EInterface and EInterface are the total energies of each In doped doped
Fig. 1. Schematics of six computational cells of the SrTiO3 /MgO(0 0 1) interface employed in present study. (a) Models A–D, (b) and (c) models E and F (where the bright spheres are Ti, the black spheres are O, the big gray spheres are Sr, and the small gray spheres are Mg).
interface layer) and one MgO(0 0 1) interface layer. The computational cell of the perfect SrTiO3 /MgO interface is called model A, as shown in Fig. 1(a). It can be changed to model B (model C), if an In atom substitutes for the Ti(I) (Ti(II)) atom on the TiO2 interface (noninterface) layer; moreover, it can also be altered to model D if
model and model A. EBulk is the total energy of In doped SrTiO3 supercell, and EBulk is the bulk total energy for the perfect SrTiO3 computational cell. Table 2 lists the substitution and segregation energies obtained from those fully relaxed models. When a Ti atom was replaced by an In atom, the substitution and segregation energies for model B are more favorable than for model C, which indicates that the In atom would like to substitute for the Ti atom on the SrTiO3 /MgO interface layer. When two Ti atoms were replaced by two In atoms, model F is preferred since it has the lowest substitution and segregation energies among the models D–F. From the above discussion, it can be concluded that the formation of In doped SrTiO3 /MgO(0 0 1) is closely dependent on not only the concentration of In atoms but also the relative positions of the In atoms to the interface. 3.2. Electronic structure To understand the fundamental properties of In doped SrTiO3 /MgO(0 0 1), we calculated the electronic structures of six
Fig. 2. TDOSs of six models. The insert shows an enlarged part of the TDOSs in the rectangular field enclosed with dotted lines.
K.L. Zhao et al. / Journal of Alloys and Compounds 485 (2009) 598–603
601
Fig. 3. PDOSs of different atoms (marked in Fig. 1(a)) (a) on the TiO2 interface layer, (b) on the TiO2 noninterface layer, and (c) on the MgO interface layer for models A–C.
models (one perfect and five In doped computational cells) at the equilibrium state. Fig. 2 shows the total density of states (TDOS) of each model with respect to the Fermi level at zero. For model A, the valence band distributed in the energy range between −6.1 and 0 eV mainly comes from O 2p and Ti 3d orbital electrons, while the conduction band is caused mostly by the Ti 3d orbital electrons. In Fig. 2, the band gap is about 0.87 eV, much less than that of bulk SrTiO3 and MgO as presented in Table 1, which implies that the interface interactions would play an important role in determining the electronic properties of SrTiO3 /MgO(0 0 1). For the In doped models, their TDOSs are very different from the perfect model A. The remarkable change is that the peaks of conduction bands are clearly reduced between 1.5 and 2.2 eV. This is because that the bottoms of conduction bands have shifted noticeably to the higher energies, but the tops of valence bands only show a slight shift. As a result, the band gaps of In doped SrTiO3 /MgO(0 0 1) are increased as compared with the model A. For example, the band gap of model B becomes 0.92 eV and that of model F is 0.98 eV. That is to say, the band gap would become wider with the increase of the In atomic concentration on the TiO2 interface layer. Moreover, there are some narrower width peaks with extended tails between −7.3 and −5.0 eV for the
In doped models, which results in the increase of the valance band widths as compared with the perfect interface. For an example, the width of valence band for model F is up to 7.6 eV which is comparable with the experimental value (8.7 eV) [12]. Fig. 3 shows the projected density of states (PDOSs) for different atoms (marked in Fig. 1(a)) on the TiO2 interface layer, TiO2 noninterface layer, and MgO interface layer for models A, B and C, respectively. For model A, the bottom of the conduction band of the interfacial Ti(I) atom (shown in Fig. 3(a)) is lower than that of the noninterface Ti(II) atom (shown in Fig. 3(b)), which dominantly contributes to the conduction band structure of the TDOS for model A. In Fig. 3(a) and (c), the interfacial hybridization results in the 2p electron states of interface O(II) and O(I) atoms with the extended tails crossing the Fermi level. In Fig. 3(b), the noninterface O(III) atom remains insulating due to lack of electron states at the Fermi level. In Fig. 3(a) and (c), all the electron states of Ti(I), O(II), Mg(I) and O(I) atoms on interface layers (mainly between −6 and 0 eV) reflect that the interfacial hybridization between Ti(I) and O(I) atoms is stronger than that between O(II) and Mg(I). Otherwise, the optimized interfacial spacing between Ti and O (2.031 Å) is less than that between O and Mg (2.175 Å), which indicates that the chemical bond between Ti(I)
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K.L. Zhao et al. / Journal of Alloys and Compounds 485 (2009) 598–603
Fig. 4. Imaginary part ε2 (ω) of dielectric function of six models along [0 0 1] direction.
and O(I) is stronger than that between O(II) and Mg(I). Therefore, for the perfect model A, the covalent contribution plays a dominant role on the interface interactions. For model B, with an interfacial Ti(I) atom replaced by an In atom, the atomic PDOSs show a significant change as compared with model A. In Fig. 3(a), the width of O(II) 2p valence band becomes larger. The top of O(II) 2p valence band extends through Fermi level and moves to the energy slightly higher than model A. The valence band of Ti(III) 3d orbital becomes wider and the bottom of Ti(III) 3d conduction band also shifts to a higher energy level. However, for the noninterface Ti(II) atom, it can be seen from Fig. 3(b) that the bottom of Ti(II) 3d conduction band almost does not change. Combining these contributions with the fact that interface O(II) and O(I) electron states extend tail crossing Fermi level, the band gap of model B is larger than model A as shown in Fig. 2. For model C, with an In atom substituting for a Ti(II) atom, the PDOSs of interface atoms form a striking contrast to model B as shown in Fig. 3(a) and (c). In this case, the valence band widths of the interfacial oxygen atoms are decreased, and the intensities of additional narrower width peaks at −6.5 to −5.0 eV become much smaller. All the electronic states of the interfacial atoms suggest that the covalent contributions at interface would be less than model B. That is to say, if an In atom doped in SrTiO3 /MgO(0 0 1), model B is a more favorable configuration than model C. This verifies that the Ti atom at interface would like to be substituted by an In atom, which is also consistent with the calculated results for the substitution and segregation energies listed in Table 2. To understand the effects of the In atomic concentration on the electronic properties of SrTiO3 /MgO(0 0 1), we have also calculated the PDOSs of models D–F, in which two Ti atoms are substituted by two In atoms. One of the two In atoms is always on the TiO2 interface layer, which is a common characteristic for the three configurations. All the atomic PDOSs of models D–F (not shown in the present paper) indicate that model F would be preferable, in which two interfacial Ti atoms are replaced by two In atoms at the same time. 3.3. Optical properties To clarify the effects of In doping on the optical properties of SrTiO3 /MgO(0 0 1), we calculated the imaginary parts ε2 (ω), absorption coefficient ˛(ω), and reflectivity R(ω) for each model. Considering the symmetry of the models, we present the imaginary parts ε2 (ω) of dielectric function of six models along [0 0 1] direction as shown in Fig. 4. For model A, the threshold peak of
Fig. 5. Other optical parameters of each model along the [0 0 1] direction. ˛(ω) and R(ω) are (a) absorption coefficient and (b) reflectivity, respectively.
imaginary part ε2 (ω) along [0 0 1] direction appears to be about 1.5 eV. In the energy range between 1.5 and 8.5 eV, the ε2 (ω) spectrum is mainly composed of three-peak structures similar to the spectrum features of bulk SrTiO3 [22,23]. For models B and C, new peaks appear at the lower energy (<1.5 eV), the main features of ε2 (ω) curves have been changed into two-peak structure and shifted to higher energy level compared to model A. For model B, both the intensity of new peak and the shifting distance of two-peak structure are lower than model C, which reflects that the property of ε2 (ω) spectrum is closely related to the position of In atoms. With the increase of the In atomic concentration, it can be seen that the new peak is intensified and one-peak structure becomes the main feature of ε2 (ω) spectrum as shown in Fig. 4. Although the concentration of In atoms is identical for the three models D–F, the curves of imaginary part ε2 (ω) are different. When two In atoms are both located at interface layer (model F), the shifting distance of ε2 (ω) one-peak structure is the smallest as compared with model A. Fig. 5 shows the absorption spectra and optical reflectivity of six models along the [0 0 1] direction, which can further illustrate the effects of In doping on the optical properties of SrTiO3 /MgO(0 0 1). The absorption spectra of each model are displayed in Fig. 5(a). For model A, the absorption edge starts from about 1.5 eV, and the absorption band is composed of three-peak structure between 1.5 and 8.5 eV, corresponding to the transition of electrons in O 2p orbital to the conduction band. For each of the other models for
K.L. Zhao et al. / Journal of Alloys and Compounds 485 (2009) 598–603
the In doped interfaces, there is a weak peak appearing on the left side of absorption band. In addition, it is noticeable that the absorption band becomes narrower and shows a buleshift as compared with the perfect SrTiO3 /MgO(0 0 1) interface. These features of the absorption spectrum are similar to the ε2 (ω) spectrum as shown in Fig. 4, which reflects that there is a close relationship between the absorption coefficient and the imaginary part ε2 (ω) of dielectric function. Comparing with the absorption spectra of models A, B and F, it can be found that the absorption edge shifts to the higher energy and the peaks of absorption band are reduced with the increase of the In atomic concentration. From the above discussion, it is therefore believed that the buleshift of the absorption edge could be observed with an increase in the concentration of In atoms, which is in good agreement with the experimental results [13]. Fig. 5(b) shows the spectra of optical reflectivity R(ω) for each model. For model A, the curve of reflectivity R(ω) gradually raises between 0 and 4.0 eV, then three peaks appear in the energy range from 4.0 to 9.0 eV. The maximum value of reflectivity occurs at around 7.0 eV in the ultraviolet region. When the energy is higher than 9.0 eV, the perfect SrTiO3 /MgO material becomes transparent. In Fig. 5(b), it can be found that the R(0) value becomes larger and the reflectivity peaks shift towards the higher energy with the increase of the In atomic concentration (such as models A, B and F). It is particularly worth mentioning that the R(ω) spectra are gradually decreased from model A to B and then to F in the energy range between 1.6 and 3.1 eV, which is in the visible region. However, when the concentration of In atoms keeps unchanged, the R(ω) value of model F is larger than models D and E in the range of visible light. This indicates that model F has a transmission less than models D and E if at the same frequency. For example, on a certain visible frequency, if a nanocluster rich in Indium is formed near the interface in the In doped SrTiO3 film, it could happen that the part of nanocluster close to the interface will be darker and the other part far from the interface will be brighter. 4. Conclusions The crystal structure, electronic structure, and optical properties of In doped SrTiO3 /MgO(0 0 1) interface are systematically investigated by using first-principles calculations based on the density functional theory. The In atomic position optimization reveals that an interfacial Ti atom would like to be substituted by an In atom, and the band gap will be widened with the increase of In atomic concentration on the interface layer. It is found that the electronic structure and optical properties of In doped SrTiO3 /MgO(0 0 1) are dependent not only on the concentration of In atoms but also on the In atomic position relative to the interface. Acknowledgements This work was supported by the National Basic Research Program of China (2002CB613503 and 2009CB623705) and the National Natural Science Foundation of China (Grant No. 50571100).
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