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DFT study of Ag and La codoped BaTiO3
Author’s Accepted Manuscript DFT study of Ag and La codoped BaTiO3 Frank Maldonado, Arvids Stashans
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S0022-3697(16)30735-1 http://dx.doi.org/10.1016/j.jpcs.2016.11.016 PCS7903
To appear in: Journal of Physical and Chemistry of Solids Received date: 21 September 2016 Revised date: 4 November 2016 Accepted date: 20 November 2016 Cite this article as: Frank Maldonado and Arvids Stashans, DFT study of Ag and La codoped BaTiO3, Journal of Physical and Chemistry of Solids, http://dx.doi.org/10.1016/j.jpcs.2016.11.016 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
DFT study of Ag and La codoped BaTiO3 Frank Maldonado*, Arvids Stashans Grupo de Fisicoquímica de Materiales, Universidad Técnica Particular de Loja, Apartado 11-01-608, Loja, Ecuador *
Corresponding author. [email protected]
Abstract Density functional theory and generalized gradient approximation including a Hubbard-like term was used in the present work to analyse structure as well as electronic and electrical properties of Ag and La codoped BaTiO3 material. Intrinsic oxygen vacancy defect has been taken into consideration throughout the calculations. Results on atomic shifts indicate the significance of Coulomb electrostatic interaction in finding equilibrium state of the system. It is shown that the n-type electrical conductivity should be expected as a result of codoping. Computed concentrations of free-carriers manifest the advantage of codoping procedure compared to the single impurity doping in the BaTiO3 crystal. It is also shown that oxygen vacancy alone can produce the n-type conductivity.
Keywords: BaTiO3; DFT+U; Density of states; n-type conductivity
1. Introduction
Barium titanate (BaTiO3) is one of the most noticeable perovskite-type crystals. Since its discovery in 1941 [1], it has attracted numerous experimental and theoretical studies because of its outstanding properties such as ferroelectricity, piezoelectricity, pyroelectricity, high dielectric permittivity and high voltage tunability [2-6]. These features make BaTiO3 suitable for a wide range of applications including multilayer ceramic capacitors, posistors,
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piezoelectric and ultrasonic actuators, pyroelectric detectors, temperature sensors and controllers as well as tuneable elements in microwave circuits [7-13]. BaTiO3 also may be utilised as a semiconductor with positive temperature coefficient of resistivity if doped adequately. Low resistivity BaTiO3 materials are suitable in applications for conductive powders. This has prompted various studies focused on the research of electrical conductivity of BaTiO3 doped with different impurities such as Y, Dy, Ho, Er, La, Sm, Cu, Al, Zn and Ag [14-17]. It is important to state that codoping improves the performance of BaTiO3 even further [18, 19] with La and Ag codoping being especially beneficial since it allows reducing the resistivity from 4.30*109 m till 7.13*102 m [20]. Despite a number of experimental investigations carried out on this subject there is a clear lack of theoretical fundamental research of effects produced by codoping on the BaTiO3 materials.
The present work is focused on the analysis of electrical conductivity of Ag and La codoped BaTiO3 material by means of the density of states (DOS) patterns as well as electron concentration, n, numbers obtained from the spin-polarized DFT+U computations. To the best of our knowledge, there is no theoretical study done so far on this important subject. Besides, we take into account the influence of oxygen vacancy (VO), which is an intrinsic defect normally present in perovskite oxides [21, 22] and thus influences structural, electrical and electronic properties of the codoped material and consequently has to be considered in the calculations.
2. Brief outline of the method
The present study has been performed employing the Vienna ab initio Simulation Package (VASP) [23, 24] code, which is based on the first-principles density functional theory (DFT) approach within the generalized gradient approximation (GGA) [25] method. In this framework, the valence electronic states are expanded in a set of periodic plane waves, and the interaction among core electrons and valence electrons is implemented 2
through the projector augmented wave (PAW) method [26]. The following valence configurations have been used in our computations: 4d105s1 for Ag, 5s25p65d16s2 for La, 5s25p66s2 for Ba, 3s23p63d24s2 for Ti, and 2s22p4 for O atoms, respectively. Perdew–Burke– Ernzerhof (PBE) [27] parametrized GGA functionals are used to describe the exchange– correlation interactions. It is known that standard DFT has some difficulties to describe properly the strong correlation between d electrons. In order to take into account these issues, an intra-site Coulomb repulsion U-term has been included, which leads to the so-called DFT+U method [28]. Specifically, the rotationally invariant approach to the GGA+U has been employed [29]. The following values of the U parameter: U = 3.5 eV for the Ti 3d electrons [30] and U = 6.0 eV for the Ag 4d [31] and the La 5d electrons [32], were applied respectively. In the present study we have considered BaTiO3 in its tetragonal crystallographic form, P4mm space group symmetry, which is stable at room temperature. Cut-off kinetic energy of 450 eV was used. This number was obtained by converging the total energy of BaTiO3 primitive tetragonal unit cell to less than 1 meV/atom. Γ-centred Monkhorst–Pack (MP) grid with a 0.04 Å-1 separation has been exploited corresponding to a k-point mesh of 6 x 6 x 6 for the 5-atom primitive unit cell. In order to study effects generated by the Ag and La dopants as well as the VO defect, the 5-atom primitive unit cell was expanded 27 times, 3 x 3 x 3 extension, resulting in a 135-atom supercell. A k-point mesh of 2 x 2 x 2 was used for supercell keeping the same MP grid and separation as that obtained for the primitive unit cell. These computational parameters were attained by calculating total energy of the system with convergence criterion being equal to 1 meV. Size of 135-atom supercell was considered to be adequate for our task taking into account (i) our computational capabilities (upper limit) and low experimentally employed impurity concentration [20] (lower limit). Spin-polarized calculations within the DFT+U framework have been applied throughout the study. The electron concentration, n, was obtained by integrating the product of the density of states (
( ) ) with the Fermi-Dirac distribution function ( ( ) ) from the bottom of the
conduction band (CB) (labelled as
) up to the top of the CB in the corresponding density of
states (DOS) pattern and is expressed as follows [33]:
3
∫
( ) ( )
(1) 3. Results and discussion 3.1 Pure crystal
Computations of pure BaTiO3 have been performed using 135-atom supercell model. Calculated lattice parameters for the tetragonal BaTiO3 (a = b = 4.0443 Å and c = 4.0536 Å) were found to be close to the experimentally available data (a = b = 3.999 Å and c = 4.0180 Å) [34]. Obtained c/a relation of 1.0023 is somewhat smaller than experimental estimate. Tetragonality problem in BaTiO3 is of general knowledge [35] and it is believed that this difficulty occurs due to the low-frequency phonon modes being remarkably sensitive to the kpoint sampling. Because of very large-size supercell we were unable to use more dense mesh and describe more adequately the ferroelectricity phenomenon. However, codoping study carried out in the present work is not related to the ferroelectric instability and thus our results cannot be affected by the c/a relation. The computed forbidden band-gap width is equal to 2.17 eV, which is less than the experimental value of 3.2 eV [36]. The underestimation of the band-gap width is expected due to the known faults of the DFT methodology and the intrasite Coulomb repulsion U-term can improve the results only partially. Nevertheless, taking into consideration that standard DFT gives only 1.88 eV for the band-gap value, there is 15.4% improvement due to the DFT+U approach.
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Fig. 1. Band structure with DOS pattern (on the right-hand side) of the BaTiO3 crystal.
It has been found that the upper valence band (VB) is composed mainly of the O 2p states with a small contribution of the Ti 3d and Ba 5p states (Fig. 1). These results coincide with the outcomes of previous Hartree-Fock calculations [37, 38]. Experimental X-ray photoemission spectra data [39] stands by our results suggesting that the upper VB is mainly O 2p in nature. The computed upper VB width is found to be equal to 4.4 eV, which is acceptable result compared to the available experimental outcome of 4.8 eV [39] and HartreeFock value of 4.2 eV [38]. The conduction band (CB) region is formed predominantly by the Ti 3d states with some admixture of the O 2p states (Fig. 1), similarly as in the Hartree-Fock computations [38], indicating the importance in a Ti 3d–O2p hybridization for the BaTiO3 tetragonal phase. Band structure of BaTiO3 crystal (Fig. 1) computed by means of the Atomistic ToolKit software [40] and using the coordinates of high symmetry k-path [41] in the Brillouin zone is very similar to that obtained previously in Ref. 39. The resemblance is 5
not only for the upper VB but also for the lower VB being composed of the O 2s states as well as inner states of the Ti 3s, Ti 3p and Ba 5s.
3.2 Oxygen vacancy defect within the crystal
Materials in the nature are not perfect crystals, since distinct defects and lattice imperfections are always present. Oxygen vacancies (VO) are intrinsic ubiquitous defects in any oxide material. Thus it is very important to consider the effects, which VO might produce upon different features in the BaTiO3 crystal. Oxygen vacancy defect was created by removing a neutral oxygen atom in order to maintain the electrical neutrality of the system. It has to be stated that use of the supercell model containing charged point defect might be tricky due to the problems in evaluating Coulomb long-range interaction energy for periodic systems [42]. Unless some compensating mechanisms are employed, the calculation of charged defects can lead to unphysical outcomes and therefore it is advised to maintain electrical neutrality of the system, which was done in the present work. It was found after careful geometry optimization that the vacancy-closest cations move outwards from the VO site, i.e. the average displacements are equal to 0.15 Å for the Ti atoms and 0.03 Å for the Ba atoms, respectively. Defect-nearest O atoms move towards the VO by approximately 0.07 Å. All these displacements are logical from the Coulomb electrostatic interaction point of view: anion removal implies that its closest anions are not repelled and its closest cations are not attracted. Computed DOS (Fig. 2) displays a band-gap width being equal to 1.92 eV. It is important to point out that the Fermi level is found within the CB bottom indicating the existence of free electrons within the CB region and therefore n-type electrical conductivity in the material, i.e. the material can be treated as a polarizable continuum with conduction electrons moving through the lattice. Nevertheless, it has to be considered that mobility of free electrons is often limited by scattering due to the optical phonons as a result of strong electro-optical-phonon coupling in some crystals. It is necessary to mention that some experimental studies also back up the suggestion of the presence of n-type conductivity in undoped BaTiO3 [43, 44]. 6
Fig. 2. Total DOS and PDOS for the BaTiO3 crystal containing a VO. The calculated band-gap width is equal to 1.92 eV. The vertical dotted line marks the Fermi level (EF). The Fermi level is clearly located within the CB region indicating presence of free electrons in the material and consequently the n-type conductivity.
In order to estimate the free-carrier density (n) we applied equation (1) integrating from the bottom of the CB up to the EF obtaining a value of 3.219 [e/supercell] which corresponds to 1.801*1021 in [e/cm3] units. Our spin-polarized computations also indicated that the oxygen vacancy induce certain magnetism in the material. The computed magnetic moment of the supercell was found to be equal to 0.67 µB, which is principally due to the Ti atoms (mainly 3d states), and particularly because of the two vacancy-closest Ti atoms (each one contributes 0.18 µB). It is worth to mention that we also noticed a change in the direction of the magnetic moment, i.e. when the VO is located along the c-axis a positive value of the magnetic moment is observed and when the VO is situated along any other position the same value is obtained but with the opposite sign.
7
3.3 Ag and La codoped BaTiO3+VO
In order to study codoping effects in the BaTiO3 crystal, some Ba host atoms were replaced by the La and Ag impurities. In particular, Ag impurity substituted for one of the host Ba atom. In case of La doping there are contradictory experimental reports. Some studies state that the La impurity replaces Ba host atom [45, 46] while the others assert that the substitution of the Ti host atom by the La impurity [20, 47] takes place. To elucidate this inconsistency, we employed the so-called substitutional defect formation energy and computed its value for both possible substitution mechanisms. Here, the substitutional defect formation energy was estimated as follows [48-50]: E f [La] = ETotal [BaTiO3 + La] – ETotal [BaTiO3] – E(La) + E(Ba). (2) In equation (2) E f [La] is the formation energy for La impurity substituting for a Ba atom, ETotal[BaTiO3 + La] is the total energy of the supercell containing the La impurity, ETotal [BaTiO3] is the total energy of the pure crystal bulk, E(La) and E(Ba) are energies of free La and Ba atoms, respectively. Free atoms were computed separately by embedding them into a box of 10 Å3 to prevent any possible artificial effect of mutual atom–atom interaction. The same formula (2) was used to calculate the substitutional formation energy when La impurity is substituting for a Ti atom. The obtained formation energies were found to be equal to 1.20 eV for the LaTi substitution and -6.93 eV for the LaBa substitution. There is a significant difference of 8.13 eV between the formation energies and therefore it is obvious that LaBa replacement will occur. A simple comparison of ionic radii for La, Ba and Ag atoms also points out to the same conclusion. In particular, Ba2+ having coordination number (CN) equal to twelve has ionic radius of 1.61 Å [51], La3+ with CN=12 has radius of 1.36 Å [51] while Ti4+ with CN=8 has ionic radius of only 0.74 Å [51]. Since it is expected that BaTiO3 material contains oxygen vacancies, the substitutional formation energies were also calculated for BaTiO3 with one oxygen vacancy. Equation (2) has been used for this purpose but we replaced ETotal [BaTiO3 + La] by ETotal [BaTiO3 + La + VO] and ETotal [BaTiO3] by ETotal [BaTiO3 +VO], respectively. As a result, the obtained formation energies were found to be 8
3.31 eV for LaBa replacement and 0.78 eV for LaTi substitution. This outcome shows again the favourability of LaBa substitution. Accordingly, we substituted one of the host Ba atoms by a La impurity.
Fig. 3. Schematic representation of relative defect positions for the Ag and La codoped BaTiO 3+VO crystal.
In order to carry out codoping in the BaTiO3 crystal two hosts Ba atoms were replaced by the La and Ag impurities. We also took into account the presence of the intrinsic VO defect for the codoping case. Twelve different configurations were initially selected for the geometry optimization process with different initial defect-defect distances. Within each one of the configurations, one of the Ba atoms was substituted by a La impurity while another Ba atom was replaced by an Ag atom. The following six initial inter-atomic distances were considered between the newly incorporated dopants: 4.04, 4.05, 5.72, 7.01, 8.09 and 9.91 Å, respectively. Additionally, one of the impurity-closest oxygen atoms has been removed from the system in order to form the VO defect. Geometry optimization carried out for each one of the configurations conducted us to the lowest total energy configuration being depicted in Fig. 3. We assume that is configuration can be expected to occur in the nature and in the experimentally used samples. In order to analyse atomic shifts, we take as a reference the initial position of the removed oxygen, i.e. the VO site. In the case of impurities, they displace themselves by approximately 0.13 Å outwards with respect to the VO position. Additionally, 9
the O atoms move towards the VO site while the Ti atoms displace themselves outwards with respect to the VO defect. Thus, the atomic displacements are mainly due to Coulomb electrostatic interactions because the VO-nearest anions are not repelled and the VO-closest cations are not attracted. Computed DOS (Fig. 4) displays a band-gap width being equal to 2.15 eV. Contribution of the Ag 4d states in the VB and presence of the La 5d in the CB can be noted. It is important to point out that the Fermi level is found within the CB bottom indicating the existence of free electrons within the CB and consequently n-type electrical conductivity in the material.
Fig. 4. Total DOS and PDOS for the Ag and La codoped BaTiO3 + VO. The calculated band-gap width is equal to 2.15 eV. The vertical dotted line marks the Fermi level (EF). The Fermi level is visibly positioned within the CB region indicating presence of free electrons in the material and consequently the n-type conductivity.
Formation of local magnetic moments has been observed in the material due to the performed codoping. The computed magnetic moment of supercell is found to be equal to
10
0.75 µB. This magnitude is distributed within the material as follows: 0.02 µB on the La impurity, 0.03 µB on Ba atoms, 0.79 µB on Ti atoms and -0.09 µB on O atoms. Table 1 shows the computed Bader charges [52] obtained for different doping cases. It is noticeable that atomic charges of the impurities essentially remain the same regardless of the doping case or the VO inclusion. That means the electrons left by the VO creation are not confined in a specific region or directly interact with the impurities, rather they are free to move within the material, which confirms the n-type conductivity revealed by the DOS patterns. Table 1. Bader charges on the impurities for different doping cases in the BaTiO 3 crystal.
Defect Doped Ag La
Doped + VO
0.64 e 2.27 e
Codoped + VO
0.64 e
0.63 e
2.20 e
2.23 e
Table 2 lists the computed values of free-carrier density (n), band-gap width and the supercell magnetic moment obtained for the codoping case as well as for individual defect (VO, Ag, La) doping and also considering defect pair (VO plus either Ag or La) calculations. According to the free-carrier densities depicted in Table 2 it is very clear that VO plays a major role in the conductivity of the material. The inclusion of solely VO already generates ntype conductivity and when two VO defects are considered n value practically doubles. Besides, in cases of single impurity doping, n value further increases if VO is present in the system. Additionally, VO also induces some magnetism in the material and single impurity doping cases exhibit magnetic moment only if the VO is present. Single Ag doping displays p-type electrical conductivity. However, materials in nature are not perfect and due to the experimental procedure or charge compensation, VO will be generated. Therefore, normally Ag + VO would be detectable experimentally [17] and according to our computations the Ag + VO defect pair possesses n-type conductivity. Single
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La doping shows n-type conductivity. That means a decrease of the resistivity compared to the undoped crystal in concordance with the available experimental results [46]. It is important to point out that Ag and La codoped BaTiO3 crystal exhibits n-type conductivity and displays free-carrier density, which is larger compared to that of single impurity doping cases. This means that the material increases its conductivity and lowers its resistivity due to the codoping, thus showing the favourability of codoping compared to single doping procedures. This outcome is in agreement with the experimental findings arguing for resistivity reduction due to the codoping [20, 47]. We should note that although it is speculated that La replaces for one of the Ti atoms in Refs. 20 and 47, we clearly demonstrate in the present work, i.e. due to the formation energies and difference in ionic radii, that in fact LaBa substitution takes place in the codoped BaTiO3. In fact, to be completely sure that La and Ag impurities can truly replace two host Ba atoms, extra computations on substitutional formation energies were carried out. Firstly, LaBa and LaTi substitutional formation energies were computed for the BaTiO3 material already containing Ag impurity giving -5.98 eV and 2.88 eV, respectively. Difference between the formation energies, 8.86 eV, in favour of LaBa replacement is very large. Secondly, LaBa and LaTi substitutional formation energies were calculated for the BaTiO3 material containing not only Ag dopant but also VO defect (BaTiO3 + Ag + VO) giving -3.99 eV and 0.47 eV, respectively. Energy difference, 4.46 eV, is still considerable and we suggest that LaTi substitution in BaTiO3 material cannot occur. Thus, we suppose that more probably the LaBa replacement took place in the sol-gel fabricated barium titanate [20, 47]. There is a tendency for small band-gap shrinkage except the case of single La doping and La + VO defect pair. It also appears that VO defect presence is beneficial for the band-gap narrowing and consequently could be advantageous for potential visible light photocatalytic applications of this material. Table 2. Different defects in the BaTiO3 crystal and DFT+U computed free-carrier density, band-gap width and magnetic moment of the supercell.
Defect
n (e / supercell)
n (e / cm3) 12
Band-gap (eV)
Magn. moment (µB)
VO
3.22
1.801*1021
1.92
0.68
2VO
6.02
3.351*1021
2.16
-0.01
Ag*
3.56
1.997*1021
2.17
Ag+VO
3.72
2.081*1021
1.92
0.60
La
1.52
8.488*1020
2.40
La+VO
4.01
2.242*1021
2.39
1.14
Ag + La+VO
4.26
2.391*1021
2.15
0.75
* In the case of Ag-doped BaTiO3 p-type conductivity was found. Thus, the free-carrier density makes reference to holes instead of electrons.
As one can see from Table 2, Ag doping produces p-type conductivity if VO defect is not present in the system. We suggest that experimentally observed n-type conductivity for the Ag-doped BaTiO3 material [53] is actually due to the intrinsic point defects, e.g. VO, rather that Ag impurity. Thus, in our mind it would be recommendable to use La impurity in combination with another doping element instead of Ag in order to further decrease the resistivity in the n-type BaTiO3 material.
4. Conclusions
Spin-polarized DFT+U calculations have been performed to investigate tetragonal barium titanate crystal codoped with La and Ag impurities. Oxygen vacancy as an intrinsic point defect has been taken into consideration in the majority of computations. According to our results, oxygen vacancy has a significant impact on a number of features of the BaTiO3 material. This intrinsic point defect is responsible for the n-type conductivity in undoped BaTiO3 with the value of free-carrier concentration being equal to 1.801*1021 e/cm3. Oxygen vacancy presence also improves materials conductivity in case of the La- and Ag-doping. In fact, Ag-doped BaTiO3 tend to show p-type conductivity if oxygen 13
vacancy is not present in the system and only the combination of Ag + VO delivers expected n-type electrical conductivity. Our computations indicate that oxygen vacancy can be responsible for the generation of 0.67 µB magnetic moment within the crystalline lattice. Computed free-carrier densities point out to the fact that codoping is more favourable compared to single impurity doping in order to obtain higher sample conductivity and lower resistivity. Codoped material containing oxygen vacancy defect shows 6.6% higher conductivity compared to La-doped BaTiO3 and 14.9% higher conductivity as Ag-doped sample.
References [1] H. Thurnaurer and J. Deaderick, U.S. Patent No. 2,429,588, (1947); filed (1941). [2] A. Ianculescu, L. Mitoseriu, D. Berger, C.E. Ciomaga, D. Piazza, C. Galassi, Composition-dependent ferroelectric properties of Ba1 − xSrxTiO3 ceramics, Phase Transitions. 79 (2006) 375–388. doi:10.1080/01411590600892062. [3] A. Ianculescu, D. Berger, L. Mitoşeriu, L.P. Curecheriu, N. Drăgan, D. Crişan, E. Vasile, Properties of Ba1− xSrxTiO3 ceramics prepared by the modified-Pechini method, Ferroelectrics 369 (2008) 22–34. doi:10.1080/00150190802371424. [4] L.P. Curecheriu, L. Mitoseriu, A. Ianculescu, Nonlinear dielectric properties of Ba1xSrxTiO3
ceramics, J. Alloys Compd. 482 (2009) 1–4. doi:10.1016/j.jallcom.2009.04.036.
[5] M.B. Smith, K. Page, T. Siegrist, P.L. Redmond, E.C. Walter, R. Seshadri, L.E. Brus, M.L. Steigerwald, Crystal structure and the paraelectric-to-ferroelectric phase transition of nanoscale BaTiO3, J. Am. Chem. Soc. 130 (2008) 6955–6963. doi:10.1021/ja0758436. [6] T. Tsurumi, H. Adachi, H. Kakemoto, S. Wada, Y. Mizuno, H. Chazono, H. Kishi, Dielectric properties of BaTiO3-based ceramics under high electric field, Jpn. J. Appl. Phys. 41 (2002) 6929–6933. doi:10.1143/JJAP.41.6929.
14
[7] Z. Tian, X. Wang, L. Shu, T. Wang, T.H. Song, Z. Gui, L. Li, Preparation of nano BaTiO3-based ceramics for multilayer ceramic capacitor application by chemical coating method, J. Am. Ceram. Soc. 92 (2009) 830–833. doi:10.1111/j.1551-2916.2009.02979.x. [8] S.-S. Park, J.-H. Ha, H.N. Wadley, Preparation of BaTiO3 films for MLCCs by direct vapor deposition, Integr. Ferroelectrics 95 (2007) 251–259. doi:10.1080/10584580701759437. [9] W. Heywang, Semiconducting barium titanate, J. Mater. Sci. 6 (1971) 1214–1224. doi:10.1007/BF00550094. [10] G.H. Jonker, Some aspects of semiconducting barium titanate, Solid. State. Electron. 7 (1964) 895–903. doi:10.1016/0038-1101(64)90068-1. [11] B.G. Brahmecha, K.P. Sinha, Resistivity anomaly in semiconducting BaTiO3, Jpn. J. Appl. Phys. 10 (1971) 496–504. doi:10.1143/JJAP.10.496. [12] V. Sreenivas Puli, P. Li, S. Adireddy, D.B. Chrisey, Crystal structure, dielectric, ferroelectric and energy storage properties of La-doped BaTiO3 semiconducting ceramics, J. Adv. Dielectrics 5 (2015) 1550027. doi: 10.1142/S2010135X15500277. [13] A.C. Ianculescu, C.A. Vasilescu, M. Crisan, M. Raileanu, B.S. Vasile, M. Calugaru, D. Crisan, N. Dragan, L. Curecheriu, L. Mitoseriu, Formation mechanism and characteristics of lanthanum-doped BaTiO3 powders and ceramics prepared by the sol–gel process, Mater. Characterization 106 (2015) 195-207. doi: 10.1016/j.matchar.2015.05.022. [14] P. Yongping, Y. Wenhu, C. Shoutian, Influence of rare earths on electric properties and microstructure of barium titanate ceramics, J. Rare Earths 25 (2007) 154–157. doi: doi:10.1016/S1002-0721(07)60546-8. [15] C.H. Wu, J.P. Chu, S.F. Wang, T.N. Lin, W.Z. Chang, V.S. John, Effects of post annealing on the material characteristics and electrical properties of La doped BaTiO3 sputtered films, Surf. Coatings Technol. 202 (2008) 5448–5451. doi:10.1016/j.surfcoat.2008.06.112.
15
[16] J.L. Li, S.E. Hao, C.Y. Wang, F.X. Kong, W. Wang, Preparation and characterization of different metal modified BaTiO3 powders, Adv. Mater. Res. 105–106 (2010) 342–344. doi:10.4028/www.scientific.net/AMR.105-106.342. [17] S. Hao, D. Fu, J. Li, W. Wang, B. Shen, Preparation and characterization of Ag-doped BaTiO3 conductive powders, Int. J. Inorg. Chem. 2011 (2011) 837091–83713. doi:10.1155/2011/837091. [18] S.K. Jo, J.S. Park, Y.H. Hana, Effects of multi-doping of rare-earth oxides on the microstructure and dielectric properties of BaTiO3, J. Alloy. Compd. 501 (2010) 259–264. doi:10.1016/j.jallcom.2010.04.085. [19] C.E. Lee, S.H. Kang, D.S. Sinn, Co-doping effect of Mn and Y on charge and mass transport properties of BaTiO3, J. Electroceram. 13 (2004) 785–791. doi: 10.1007/s10832004-5193-9. [20] S. Hao, J. Li, W. Wang, D. Fu, C. Wang, Q. Shang, Effects of Ag-La codoping on structure and electrical properties of BaTiO3 powder, Res. Chem. Intermed. 39 (2013) 2705– 2713. doi:10.1007/s11164-012-0791-7. [21] A. Stashans, Defects in titanates, Int. J. Nanotechnology 1 (2004) 399-430. doi:10.1504/IJNT.2004.005977. [22] H. Pinto, S. Elliott, A. Stashans, Theoretical study of structural and optical properties of F-centers in tetragonal BaTiO3, SPIE Proceed. 5122 (2003) 303-309. doi: 10.1117/12.515781. [23] G. Kresse, J. Furthmüller, Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set, Comput. Mater. Sci. 6 (1996) 15–50. doi:10.1016/0927-0256(96)00008-0. [24] G. Kresse, J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B 54 (1996) 11169–11186. doi:10.1103/PhysRevB.54.11169. [25] J. Perdew, J. Chevary, S. Vosko, K. Jackson, M. Pederson, D. Singh, C. Fiolhais, Erratum: Atoms, molecules, solids, and surfaces: Applications of the generalized gradient 16
approximation for exchange and correlation, Phys. Rev. B 48 (1993) 4978–4978. doi:10.1103/PhysRevB.48.4978.2. [26] G. Kresse, From ultrasoft pseudopotentials to the projector augmented-wave method, Phys. Rev. B 59 (1999) 1758–1775. doi:10.1103/PhysRevB.59.1758. [27] J.P. Perdew, K. Burke, M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77 (1996) 3865–3868. doi:10.1103/PhysRevLett.77.3865. [28] A.I. Liechtenstein, V.I. Anisimov, J. Zaanen, Density-functional theory and strong interactions: Orbital ordering in Mott-Hubbard insulators, Phys. Rev. B 52 (1995) 5467– 5471. doi:10.1103/PhysRevB.52.R5467. [29] S.L. Dudarev, S.Y. Savrasov, C.J. Humphreys, A.P. Sutton, Electron-energy-loss spectra and the structural stability of nickel oxide: An LSDA+U study, Phys. Rev. B 57 (1998) 1505–1509. doi:10.1103/PhysRevB.57.1505. [30] A. Stashans, Y. Bravo, Large hole polarons in Sc-doped TiO2 crystals, Mod. Phys. Lett. B 27 (2013) 1350113. doi:10.1142/S0217984913501133. [31] J.P. Allen, D.O. Scanlon, G.W. Watson, Electronic structures of silver oxides, Phys. Rev. B 84 (2011) 1–14. doi:10.1103/PhysRevB.84.115141. [32] S. Goumri-Said, M.B. Kanoun, DFT+U study of the oxide-ion conductor pentalanthanum hexamolybdenum henicosaoxide, J. Solid State Chem. 197 (2013) 304–311. doi:10.1016/j.jssc.2012.08.042. [33] C.C. Hu, Modern semiconductor devices for integrated circuits, first ed., Prentice Hall, 2010. [34] R.H. Buttner, E.N. Maslen, Electron difference density and vibration tensors in SrTiO3, Acta Crystallogr. B 48 (1992) 639–644. doi:10.1107/S0108768192004488. [35] R.D. King-Smith, D. Vanderbilt, First-principles investigation of ferroelectricity in perovskite compounds, Phys. Rev. B 49 (1994) 5828-5844. doi: 10.1103/PhysRevB.49.5828.
17
[36] S.H. Wemple, M. Didomenico, I. Camlibel, Dielectric and optical properties of meltgrown BaTiO3, J. Phys. Chem. Solids 29 (1968) 1797–1803. doi:10.1016/00223697(68)90164-9. [37] A. Stashans, H. Pinto, Hole polarons in pure BaTiO3 studied by computer modeling, Int. J. Quantum Chem. 79 (2000) 358-366. doi:10.1002/1097-461X(2000)79:6<358::AIDQUA4>3.0.CO;2-2. [38] H. Pinto, A. Stashans, Computational study of self-trapped hole polarons in tetragonal BaTiO3, Phys. Rev. B 65 (2002) 134304. doi:10.1103/PhysRevB.65.134304. [39] P. Pertosa, F.M. Michel-Calendini, X-ray photoelectron spectra, theoretical band structures, and densities of states for BaTiO3 and KNbO3, Phys. Rev. B 17 (1978) 2011-2020. doi:10.1103/PhysRevB.17.2011. [40] Virtual NanoLab, versión 2015.1, QuantumWise A/S (www.quantumwise.com). [41] W. Setyawan, S. Curtarolo, High-throughput electronic band structure calculations: Challenges and tools, Comput. Mater. Sci. 49 (2010) 299–312. doi:10.1016/j.commatsci.2010.05.010. [42] V.C. Sahni, P.W.M. Jacobs, A calculation of the vibrational entropy of anion Frenkel defects in fluorite crystals, Phil. Mag. A 46 (1982) 817-827. doi:10.1080/01418618208236933. [43] T. Kolodiazhnyi, A. Petric, M. Niewczas, C. Bridges, A. Safa-Sefat, J.E. Greedan, Thermoelectric power, Hall effect, and mobility of n-type BaTiO3, Phys. Rev. B 68 (2003) 85205. doi:10.1103/PhysRevB.68.085205. [44] T. Yamamoto, Y. Sato, T. Tanaka, K. Hamashi, Y. Ikura, T. Sakuma, Electron transport behaviors across single grain boundaries in n-type BaTiO3 , SrTiO3 and ZnO, J. Mater. Sci. 40 (2005) 881–887. doi:10.1007/s10853-005-6505-4. [45] A. Ianculescu, Z. V. Mocanu, L.P. Curecheriu, L. Mitoseriu, L. Padurariu, R. Truşcă, Dielectric and tunability properties of La-doped BaTiO3 ceramics, J. Alloys Compd. 509 (2011) 10040–10049. doi:10.1016/j.jallcom.2011.08.027.
18
[46] M.M. Vijatović, B.D. Stojanović, J.D. Bobić, T. Ramoska, P. Bowen, Properties of lanthanum doped BaTiO3 produced from nanopowders, Ceram. Int. 36 (2010) 1817–1824. doi:10.1016/j.ceramint.2010.03.010. [47] J. Li, S. Hao, D. Fu, W. Wang, T. Ma, C. Wang, Modification of Ag-doped BaTiO3 powders through La gaseous penetration route, J. Rare Earths 28 (2010) 154–157. doi:10.1016/S1002-0721(10)60288-8. [48] M. Menadakis, G. Maroulis, P.G. Koutsoukos, A quantum chemical study of doped CaCO3 (calcite), Comput. Mater. Sci. 38 (2007) 522–525. doi:10.1016/j.commatsci.2006.02.016. [49] A. Stashans, K. Rivera, Iron impurity in zircon by DFT computations, Mod. Phys. Lett. B 27 (2013) 1350145. doi:10.1142/S0217984913501455. [50] A. Stashans, J. Escobar, Effects of vanadium impurity on TiO2 properties, Int. J. Mod. Phys. B 29 (2015) 1550094. doi:10.1142/S0217979215500940. [51] R.D. Shannon, Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides, Acta Cryst. A 32 (1976) 751-767. doi: 10.1107/S0567739476001551. [52] R. F. W. Bader, The international series of monographs on chemistry, Vol. 22, Oxford University Press, Oxford, 1990. [53] H. Ikushima, S. Hayakawa, Electrical properties of Ag-doped barium titanate ceramics, Jpn. J. Appl. Phys. 4 (1965) 328. doi: 10.1143/JJAP.4.328.
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Highlights
Spin-polarized DFT+U study of Ag and La codoped BaTiO3 containing oxygen vacancies.
Indispensability of oxygen vacancy to produce n-type conductivity and magnetism.
Codoping advantage over single impurity doping to reduce resistivity in BaTiO3.
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S0022-3697(16)30735-1 http://dx.doi.org/10.1016/j.jpcs.2016.11.016 PCS7903
To appear in: Journal of Physical and Chemistry of Solids Received date: 21 September 2016 Revised date: 4 November 2016 Accepted date: 20 November 2016 Cite this article as: Frank Maldonado and Arvids Stashans, DFT study of Ag and La codoped BaTiO3, Journal of Physical and Chemistry of Solids, http://dx.doi.org/10.1016/j.jpcs.2016.11.016 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
DFT study of Ag and La codoped BaTiO3 Frank Maldonado*, Arvids Stashans Grupo de Fisicoquímica de Materiales, Universidad Técnica Particular de Loja, Apartado 11-01-608, Loja, Ecuador *
Corresponding author. [email protected]
Abstract Density functional theory and generalized gradient approximation including a Hubbard-like term was used in the present work to analyse structure as well as electronic and electrical properties of Ag and La codoped BaTiO3 material. Intrinsic oxygen vacancy defect has been taken into consideration throughout the calculations. Results on atomic shifts indicate the significance of Coulomb electrostatic interaction in finding equilibrium state of the system. It is shown that the n-type electrical conductivity should be expected as a result of codoping. Computed concentrations of free-carriers manifest the advantage of codoping procedure compared to the single impurity doping in the BaTiO3 crystal. It is also shown that oxygen vacancy alone can produce the n-type conductivity.
Keywords: BaTiO3; DFT+U; Density of states; n-type conductivity
1. Introduction
Barium titanate (BaTiO3) is one of the most noticeable perovskite-type crystals. Since its discovery in 1941 [1], it has attracted numerous experimental and theoretical studies because of its outstanding properties such as ferroelectricity, piezoelectricity, pyroelectricity, high dielectric permittivity and high voltage tunability [2-6]. These features make BaTiO3 suitable for a wide range of applications including multilayer ceramic capacitors, posistors,
1
piezoelectric and ultrasonic actuators, pyroelectric detectors, temperature sensors and controllers as well as tuneable elements in microwave circuits [7-13]. BaTiO3 also may be utilised as a semiconductor with positive temperature coefficient of resistivity if doped adequately. Low resistivity BaTiO3 materials are suitable in applications for conductive powders. This has prompted various studies focused on the research of electrical conductivity of BaTiO3 doped with different impurities such as Y, Dy, Ho, Er, La, Sm, Cu, Al, Zn and Ag [14-17]. It is important to state that codoping improves the performance of BaTiO3 even further [18, 19] with La and Ag codoping being especially beneficial since it allows reducing the resistivity from 4.30*109 m till 7.13*102 m [20]. Despite a number of experimental investigations carried out on this subject there is a clear lack of theoretical fundamental research of effects produced by codoping on the BaTiO3 materials.
The present work is focused on the analysis of electrical conductivity of Ag and La codoped BaTiO3 material by means of the density of states (DOS) patterns as well as electron concentration, n, numbers obtained from the spin-polarized DFT+U computations. To the best of our knowledge, there is no theoretical study done so far on this important subject. Besides, we take into account the influence of oxygen vacancy (VO), which is an intrinsic defect normally present in perovskite oxides [21, 22] and thus influences structural, electrical and electronic properties of the codoped material and consequently has to be considered in the calculations.
2. Brief outline of the method
The present study has been performed employing the Vienna ab initio Simulation Package (VASP) [23, 24] code, which is based on the first-principles density functional theory (DFT) approach within the generalized gradient approximation (GGA) [25] method. In this framework, the valence electronic states are expanded in a set of periodic plane waves, and the interaction among core electrons and valence electrons is implemented 2
through the projector augmented wave (PAW) method [26]. The following valence configurations have been used in our computations: 4d105s1 for Ag, 5s25p65d16s2 for La, 5s25p66s2 for Ba, 3s23p63d24s2 for Ti, and 2s22p4 for O atoms, respectively. Perdew–Burke– Ernzerhof (PBE) [27] parametrized GGA functionals are used to describe the exchange– correlation interactions. It is known that standard DFT has some difficulties to describe properly the strong correlation between d electrons. In order to take into account these issues, an intra-site Coulomb repulsion U-term has been included, which leads to the so-called DFT+U method [28]. Specifically, the rotationally invariant approach to the GGA+U has been employed [29]. The following values of the U parameter: U = 3.5 eV for the Ti 3d electrons [30] and U = 6.0 eV for the Ag 4d [31] and the La 5d electrons [32], were applied respectively. In the present study we have considered BaTiO3 in its tetragonal crystallographic form, P4mm space group symmetry, which is stable at room temperature. Cut-off kinetic energy of 450 eV was used. This number was obtained by converging the total energy of BaTiO3 primitive tetragonal unit cell to less than 1 meV/atom. Γ-centred Monkhorst–Pack (MP) grid with a 0.04 Å-1 separation has been exploited corresponding to a k-point mesh of 6 x 6 x 6 for the 5-atom primitive unit cell. In order to study effects generated by the Ag and La dopants as well as the VO defect, the 5-atom primitive unit cell was expanded 27 times, 3 x 3 x 3 extension, resulting in a 135-atom supercell. A k-point mesh of 2 x 2 x 2 was used for supercell keeping the same MP grid and separation as that obtained for the primitive unit cell. These computational parameters were attained by calculating total energy of the system with convergence criterion being equal to 1 meV. Size of 135-atom supercell was considered to be adequate for our task taking into account (i) our computational capabilities (upper limit) and low experimentally employed impurity concentration [20] (lower limit). Spin-polarized calculations within the DFT+U framework have been applied throughout the study. The electron concentration, n, was obtained by integrating the product of the density of states (
( ) ) with the Fermi-Dirac distribution function ( ( ) ) from the bottom of the
conduction band (CB) (labelled as
) up to the top of the CB in the corresponding density of
states (DOS) pattern and is expressed as follows [33]:
3
∫
( ) ( )
(1) 3. Results and discussion 3.1 Pure crystal
Computations of pure BaTiO3 have been performed using 135-atom supercell model. Calculated lattice parameters for the tetragonal BaTiO3 (a = b = 4.0443 Å and c = 4.0536 Å) were found to be close to the experimentally available data (a = b = 3.999 Å and c = 4.0180 Å) [34]. Obtained c/a relation of 1.0023 is somewhat smaller than experimental estimate. Tetragonality problem in BaTiO3 is of general knowledge [35] and it is believed that this difficulty occurs due to the low-frequency phonon modes being remarkably sensitive to the kpoint sampling. Because of very large-size supercell we were unable to use more dense mesh and describe more adequately the ferroelectricity phenomenon. However, codoping study carried out in the present work is not related to the ferroelectric instability and thus our results cannot be affected by the c/a relation. The computed forbidden band-gap width is equal to 2.17 eV, which is less than the experimental value of 3.2 eV [36]. The underestimation of the band-gap width is expected due to the known faults of the DFT methodology and the intrasite Coulomb repulsion U-term can improve the results only partially. Nevertheless, taking into consideration that standard DFT gives only 1.88 eV for the band-gap value, there is 15.4% improvement due to the DFT+U approach.
4
Fig. 1. Band structure with DOS pattern (on the right-hand side) of the BaTiO3 crystal.
It has been found that the upper valence band (VB) is composed mainly of the O 2p states with a small contribution of the Ti 3d and Ba 5p states (Fig. 1). These results coincide with the outcomes of previous Hartree-Fock calculations [37, 38]. Experimental X-ray photoemission spectra data [39] stands by our results suggesting that the upper VB is mainly O 2p in nature. The computed upper VB width is found to be equal to 4.4 eV, which is acceptable result compared to the available experimental outcome of 4.8 eV [39] and HartreeFock value of 4.2 eV [38]. The conduction band (CB) region is formed predominantly by the Ti 3d states with some admixture of the O 2p states (Fig. 1), similarly as in the Hartree-Fock computations [38], indicating the importance in a Ti 3d–O2p hybridization for the BaTiO3 tetragonal phase. Band structure of BaTiO3 crystal (Fig. 1) computed by means of the Atomistic ToolKit software [40] and using the coordinates of high symmetry k-path [41] in the Brillouin zone is very similar to that obtained previously in Ref. 39. The resemblance is 5
not only for the upper VB but also for the lower VB being composed of the O 2s states as well as inner states of the Ti 3s, Ti 3p and Ba 5s.
3.2 Oxygen vacancy defect within the crystal
Materials in the nature are not perfect crystals, since distinct defects and lattice imperfections are always present. Oxygen vacancies (VO) are intrinsic ubiquitous defects in any oxide material. Thus it is very important to consider the effects, which VO might produce upon different features in the BaTiO3 crystal. Oxygen vacancy defect was created by removing a neutral oxygen atom in order to maintain the electrical neutrality of the system. It has to be stated that use of the supercell model containing charged point defect might be tricky due to the problems in evaluating Coulomb long-range interaction energy for periodic systems [42]. Unless some compensating mechanisms are employed, the calculation of charged defects can lead to unphysical outcomes and therefore it is advised to maintain electrical neutrality of the system, which was done in the present work. It was found after careful geometry optimization that the vacancy-closest cations move outwards from the VO site, i.e. the average displacements are equal to 0.15 Å for the Ti atoms and 0.03 Å for the Ba atoms, respectively. Defect-nearest O atoms move towards the VO by approximately 0.07 Å. All these displacements are logical from the Coulomb electrostatic interaction point of view: anion removal implies that its closest anions are not repelled and its closest cations are not attracted. Computed DOS (Fig. 2) displays a band-gap width being equal to 1.92 eV. It is important to point out that the Fermi level is found within the CB bottom indicating the existence of free electrons within the CB region and therefore n-type electrical conductivity in the material, i.e. the material can be treated as a polarizable continuum with conduction electrons moving through the lattice. Nevertheless, it has to be considered that mobility of free electrons is often limited by scattering due to the optical phonons as a result of strong electro-optical-phonon coupling in some crystals. It is necessary to mention that some experimental studies also back up the suggestion of the presence of n-type conductivity in undoped BaTiO3 [43, 44]. 6
Fig. 2. Total DOS and PDOS for the BaTiO3 crystal containing a VO. The calculated band-gap width is equal to 1.92 eV. The vertical dotted line marks the Fermi level (EF). The Fermi level is clearly located within the CB region indicating presence of free electrons in the material and consequently the n-type conductivity.
In order to estimate the free-carrier density (n) we applied equation (1) integrating from the bottom of the CB up to the EF obtaining a value of 3.219 [e/supercell] which corresponds to 1.801*1021 in [e/cm3] units. Our spin-polarized computations also indicated that the oxygen vacancy induce certain magnetism in the material. The computed magnetic moment of the supercell was found to be equal to 0.67 µB, which is principally due to the Ti atoms (mainly 3d states), and particularly because of the two vacancy-closest Ti atoms (each one contributes 0.18 µB). It is worth to mention that we also noticed a change in the direction of the magnetic moment, i.e. when the VO is located along the c-axis a positive value of the magnetic moment is observed and when the VO is situated along any other position the same value is obtained but with the opposite sign.
7
3.3 Ag and La codoped BaTiO3+VO
In order to study codoping effects in the BaTiO3 crystal, some Ba host atoms were replaced by the La and Ag impurities. In particular, Ag impurity substituted for one of the host Ba atom. In case of La doping there are contradictory experimental reports. Some studies state that the La impurity replaces Ba host atom [45, 46] while the others assert that the substitution of the Ti host atom by the La impurity [20, 47] takes place. To elucidate this inconsistency, we employed the so-called substitutional defect formation energy and computed its value for both possible substitution mechanisms. Here, the substitutional defect formation energy was estimated as follows [48-50]: E f [La] = ETotal [BaTiO3 + La] – ETotal [BaTiO3] – E(La) + E(Ba). (2) In equation (2) E f [La] is the formation energy for La impurity substituting for a Ba atom, ETotal[BaTiO3 + La] is the total energy of the supercell containing the La impurity, ETotal [BaTiO3] is the total energy of the pure crystal bulk, E(La) and E(Ba) are energies of free La and Ba atoms, respectively. Free atoms were computed separately by embedding them into a box of 10 Å3 to prevent any possible artificial effect of mutual atom–atom interaction. The same formula (2) was used to calculate the substitutional formation energy when La impurity is substituting for a Ti atom. The obtained formation energies were found to be equal to 1.20 eV for the LaTi substitution and -6.93 eV for the LaBa substitution. There is a significant difference of 8.13 eV between the formation energies and therefore it is obvious that LaBa replacement will occur. A simple comparison of ionic radii for La, Ba and Ag atoms also points out to the same conclusion. In particular, Ba2+ having coordination number (CN) equal to twelve has ionic radius of 1.61 Å [51], La3+ with CN=12 has radius of 1.36 Å [51] while Ti4+ with CN=8 has ionic radius of only 0.74 Å [51]. Since it is expected that BaTiO3 material contains oxygen vacancies, the substitutional formation energies were also calculated for BaTiO3 with one oxygen vacancy. Equation (2) has been used for this purpose but we replaced ETotal [BaTiO3 + La] by ETotal [BaTiO3 + La + VO] and ETotal [BaTiO3] by ETotal [BaTiO3 +VO], respectively. As a result, the obtained formation energies were found to be 8
3.31 eV for LaBa replacement and 0.78 eV for LaTi substitution. This outcome shows again the favourability of LaBa substitution. Accordingly, we substituted one of the host Ba atoms by a La impurity.
Fig. 3. Schematic representation of relative defect positions for the Ag and La codoped BaTiO 3+VO crystal.
In order to carry out codoping in the BaTiO3 crystal two hosts Ba atoms were replaced by the La and Ag impurities. We also took into account the presence of the intrinsic VO defect for the codoping case. Twelve different configurations were initially selected for the geometry optimization process with different initial defect-defect distances. Within each one of the configurations, one of the Ba atoms was substituted by a La impurity while another Ba atom was replaced by an Ag atom. The following six initial inter-atomic distances were considered between the newly incorporated dopants: 4.04, 4.05, 5.72, 7.01, 8.09 and 9.91 Å, respectively. Additionally, one of the impurity-closest oxygen atoms has been removed from the system in order to form the VO defect. Geometry optimization carried out for each one of the configurations conducted us to the lowest total energy configuration being depicted in Fig. 3. We assume that is configuration can be expected to occur in the nature and in the experimentally used samples. In order to analyse atomic shifts, we take as a reference the initial position of the removed oxygen, i.e. the VO site. In the case of impurities, they displace themselves by approximately 0.13 Å outwards with respect to the VO position. Additionally, 9
the O atoms move towards the VO site while the Ti atoms displace themselves outwards with respect to the VO defect. Thus, the atomic displacements are mainly due to Coulomb electrostatic interactions because the VO-nearest anions are not repelled and the VO-closest cations are not attracted. Computed DOS (Fig. 4) displays a band-gap width being equal to 2.15 eV. Contribution of the Ag 4d states in the VB and presence of the La 5d in the CB can be noted. It is important to point out that the Fermi level is found within the CB bottom indicating the existence of free electrons within the CB and consequently n-type electrical conductivity in the material.
Fig. 4. Total DOS and PDOS for the Ag and La codoped BaTiO3 + VO. The calculated band-gap width is equal to 2.15 eV. The vertical dotted line marks the Fermi level (EF). The Fermi level is visibly positioned within the CB region indicating presence of free electrons in the material and consequently the n-type conductivity.
Formation of local magnetic moments has been observed in the material due to the performed codoping. The computed magnetic moment of supercell is found to be equal to
10
0.75 µB. This magnitude is distributed within the material as follows: 0.02 µB on the La impurity, 0.03 µB on Ba atoms, 0.79 µB on Ti atoms and -0.09 µB on O atoms. Table 1 shows the computed Bader charges [52] obtained for different doping cases. It is noticeable that atomic charges of the impurities essentially remain the same regardless of the doping case or the VO inclusion. That means the electrons left by the VO creation are not confined in a specific region or directly interact with the impurities, rather they are free to move within the material, which confirms the n-type conductivity revealed by the DOS patterns. Table 1. Bader charges on the impurities for different doping cases in the BaTiO 3 crystal.
Defect Doped Ag La
Doped + VO
0.64 e 2.27 e
Codoped + VO
0.64 e
0.63 e
2.20 e
2.23 e
Table 2 lists the computed values of free-carrier density (n), band-gap width and the supercell magnetic moment obtained for the codoping case as well as for individual defect (VO, Ag, La) doping and also considering defect pair (VO plus either Ag or La) calculations. According to the free-carrier densities depicted in Table 2 it is very clear that VO plays a major role in the conductivity of the material. The inclusion of solely VO already generates ntype conductivity and when two VO defects are considered n value practically doubles. Besides, in cases of single impurity doping, n value further increases if VO is present in the system. Additionally, VO also induces some magnetism in the material and single impurity doping cases exhibit magnetic moment only if the VO is present. Single Ag doping displays p-type electrical conductivity. However, materials in nature are not perfect and due to the experimental procedure or charge compensation, VO will be generated. Therefore, normally Ag + VO would be detectable experimentally [17] and according to our computations the Ag + VO defect pair possesses n-type conductivity. Single
11
La doping shows n-type conductivity. That means a decrease of the resistivity compared to the undoped crystal in concordance with the available experimental results [46]. It is important to point out that Ag and La codoped BaTiO3 crystal exhibits n-type conductivity and displays free-carrier density, which is larger compared to that of single impurity doping cases. This means that the material increases its conductivity and lowers its resistivity due to the codoping, thus showing the favourability of codoping compared to single doping procedures. This outcome is in agreement with the experimental findings arguing for resistivity reduction due to the codoping [20, 47]. We should note that although it is speculated that La replaces for one of the Ti atoms in Refs. 20 and 47, we clearly demonstrate in the present work, i.e. due to the formation energies and difference in ionic radii, that in fact LaBa substitution takes place in the codoped BaTiO3. In fact, to be completely sure that La and Ag impurities can truly replace two host Ba atoms, extra computations on substitutional formation energies were carried out. Firstly, LaBa and LaTi substitutional formation energies were computed for the BaTiO3 material already containing Ag impurity giving -5.98 eV and 2.88 eV, respectively. Difference between the formation energies, 8.86 eV, in favour of LaBa replacement is very large. Secondly, LaBa and LaTi substitutional formation energies were calculated for the BaTiO3 material containing not only Ag dopant but also VO defect (BaTiO3 + Ag + VO) giving -3.99 eV and 0.47 eV, respectively. Energy difference, 4.46 eV, is still considerable and we suggest that LaTi substitution in BaTiO3 material cannot occur. Thus, we suppose that more probably the LaBa replacement took place in the sol-gel fabricated barium titanate [20, 47]. There is a tendency for small band-gap shrinkage except the case of single La doping and La + VO defect pair. It also appears that VO defect presence is beneficial for the band-gap narrowing and consequently could be advantageous for potential visible light photocatalytic applications of this material. Table 2. Different defects in the BaTiO3 crystal and DFT+U computed free-carrier density, band-gap width and magnetic moment of the supercell.
Defect
n (e / supercell)
n (e / cm3) 12
Band-gap (eV)
Magn. moment (µB)
VO
3.22
1.801*1021
1.92
0.68
2VO
6.02
3.351*1021
2.16
-0.01
Ag*
3.56
1.997*1021
2.17
Ag+VO
3.72
2.081*1021
1.92
0.60
La
1.52
8.488*1020
2.40
La+VO
4.01
2.242*1021
2.39
1.14
Ag + La+VO
4.26
2.391*1021
2.15
0.75
* In the case of Ag-doped BaTiO3 p-type conductivity was found. Thus, the free-carrier density makes reference to holes instead of electrons.
As one can see from Table 2, Ag doping produces p-type conductivity if VO defect is not present in the system. We suggest that experimentally observed n-type conductivity for the Ag-doped BaTiO3 material [53] is actually due to the intrinsic point defects, e.g. VO, rather that Ag impurity. Thus, in our mind it would be recommendable to use La impurity in combination with another doping element instead of Ag in order to further decrease the resistivity in the n-type BaTiO3 material.
4. Conclusions
Spin-polarized DFT+U calculations have been performed to investigate tetragonal barium titanate crystal codoped with La and Ag impurities. Oxygen vacancy as an intrinsic point defect has been taken into consideration in the majority of computations. According to our results, oxygen vacancy has a significant impact on a number of features of the BaTiO3 material. This intrinsic point defect is responsible for the n-type conductivity in undoped BaTiO3 with the value of free-carrier concentration being equal to 1.801*1021 e/cm3. Oxygen vacancy presence also improves materials conductivity in case of the La- and Ag-doping. In fact, Ag-doped BaTiO3 tend to show p-type conductivity if oxygen 13
vacancy is not present in the system and only the combination of Ag + VO delivers expected n-type electrical conductivity. Our computations indicate that oxygen vacancy can be responsible for the generation of 0.67 µB magnetic moment within the crystalline lattice. Computed free-carrier densities point out to the fact that codoping is more favourable compared to single impurity doping in order to obtain higher sample conductivity and lower resistivity. Codoped material containing oxygen vacancy defect shows 6.6% higher conductivity compared to La-doped BaTiO3 and 14.9% higher conductivity as Ag-doped sample.
References [1] H. Thurnaurer and J. Deaderick, U.S. Patent No. 2,429,588, (1947); filed (1941). [2] A. Ianculescu, L. Mitoseriu, D. Berger, C.E. Ciomaga, D. Piazza, C. Galassi, Composition-dependent ferroelectric properties of Ba1 − xSrxTiO3 ceramics, Phase Transitions. 79 (2006) 375–388. doi:10.1080/01411590600892062. [3] A. Ianculescu, D. Berger, L. Mitoşeriu, L.P. Curecheriu, N. Drăgan, D. Crişan, E. Vasile, Properties of Ba1− xSrxTiO3 ceramics prepared by the modified-Pechini method, Ferroelectrics 369 (2008) 22–34. doi:10.1080/00150190802371424. [4] L.P. Curecheriu, L. Mitoseriu, A. Ianculescu, Nonlinear dielectric properties of Ba1xSrxTiO3
ceramics, J. Alloys Compd. 482 (2009) 1–4. doi:10.1016/j.jallcom.2009.04.036.
[5] M.B. Smith, K. Page, T. Siegrist, P.L. Redmond, E.C. Walter, R. Seshadri, L.E. Brus, M.L. Steigerwald, Crystal structure and the paraelectric-to-ferroelectric phase transition of nanoscale BaTiO3, J. Am. Chem. Soc. 130 (2008) 6955–6963. doi:10.1021/ja0758436. [6] T. Tsurumi, H. Adachi, H. Kakemoto, S. Wada, Y. Mizuno, H. Chazono, H. Kishi, Dielectric properties of BaTiO3-based ceramics under high electric field, Jpn. J. Appl. Phys. 41 (2002) 6929–6933. doi:10.1143/JJAP.41.6929.
14
[7] Z. Tian, X. Wang, L. Shu, T. Wang, T.H. Song, Z. Gui, L. Li, Preparation of nano BaTiO3-based ceramics for multilayer ceramic capacitor application by chemical coating method, J. Am. Ceram. Soc. 92 (2009) 830–833. doi:10.1111/j.1551-2916.2009.02979.x. [8] S.-S. Park, J.-H. Ha, H.N. Wadley, Preparation of BaTiO3 films for MLCCs by direct vapor deposition, Integr. Ferroelectrics 95 (2007) 251–259. doi:10.1080/10584580701759437. [9] W. Heywang, Semiconducting barium titanate, J. Mater. Sci. 6 (1971) 1214–1224. doi:10.1007/BF00550094. [10] G.H. Jonker, Some aspects of semiconducting barium titanate, Solid. State. Electron. 7 (1964) 895–903. doi:10.1016/0038-1101(64)90068-1. [11] B.G. Brahmecha, K.P. Sinha, Resistivity anomaly in semiconducting BaTiO3, Jpn. J. Appl. Phys. 10 (1971) 496–504. doi:10.1143/JJAP.10.496. [12] V. Sreenivas Puli, P. Li, S. Adireddy, D.B. Chrisey, Crystal structure, dielectric, ferroelectric and energy storage properties of La-doped BaTiO3 semiconducting ceramics, J. Adv. Dielectrics 5 (2015) 1550027. doi: 10.1142/S2010135X15500277. [13] A.C. Ianculescu, C.A. Vasilescu, M. Crisan, M. Raileanu, B.S. Vasile, M. Calugaru, D. Crisan, N. Dragan, L. Curecheriu, L. Mitoseriu, Formation mechanism and characteristics of lanthanum-doped BaTiO3 powders and ceramics prepared by the sol–gel process, Mater. Characterization 106 (2015) 195-207. doi: 10.1016/j.matchar.2015.05.022. [14] P. Yongping, Y. Wenhu, C. Shoutian, Influence of rare earths on electric properties and microstructure of barium titanate ceramics, J. Rare Earths 25 (2007) 154–157. doi: doi:10.1016/S1002-0721(07)60546-8. [15] C.H. Wu, J.P. Chu, S.F. Wang, T.N. Lin, W.Z. Chang, V.S. John, Effects of post annealing on the material characteristics and electrical properties of La doped BaTiO3 sputtered films, Surf. Coatings Technol. 202 (2008) 5448–5451. doi:10.1016/j.surfcoat.2008.06.112.
15
[16] J.L. Li, S.E. Hao, C.Y. Wang, F.X. Kong, W. Wang, Preparation and characterization of different metal modified BaTiO3 powders, Adv. Mater. Res. 105–106 (2010) 342–344. doi:10.4028/www.scientific.net/AMR.105-106.342. [17] S. Hao, D. Fu, J. Li, W. Wang, B. Shen, Preparation and characterization of Ag-doped BaTiO3 conductive powders, Int. J. Inorg. Chem. 2011 (2011) 837091–83713. doi:10.1155/2011/837091. [18] S.K. Jo, J.S. Park, Y.H. Hana, Effects of multi-doping of rare-earth oxides on the microstructure and dielectric properties of BaTiO3, J. Alloy. Compd. 501 (2010) 259–264. doi:10.1016/j.jallcom.2010.04.085. [19] C.E. Lee, S.H. Kang, D.S. Sinn, Co-doping effect of Mn and Y on charge and mass transport properties of BaTiO3, J. Electroceram. 13 (2004) 785–791. doi: 10.1007/s10832004-5193-9. [20] S. Hao, J. Li, W. Wang, D. Fu, C. Wang, Q. Shang, Effects of Ag-La codoping on structure and electrical properties of BaTiO3 powder, Res. Chem. Intermed. 39 (2013) 2705– 2713. doi:10.1007/s11164-012-0791-7. [21] A. Stashans, Defects in titanates, Int. J. Nanotechnology 1 (2004) 399-430. doi:10.1504/IJNT.2004.005977. [22] H. Pinto, S. Elliott, A. Stashans, Theoretical study of structural and optical properties of F-centers in tetragonal BaTiO3, SPIE Proceed. 5122 (2003) 303-309. doi: 10.1117/12.515781. [23] G. Kresse, J. Furthmüller, Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set, Comput. Mater. Sci. 6 (1996) 15–50. doi:10.1016/0927-0256(96)00008-0. [24] G. Kresse, J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B 54 (1996) 11169–11186. doi:10.1103/PhysRevB.54.11169. [25] J. Perdew, J. Chevary, S. Vosko, K. Jackson, M. Pederson, D. Singh, C. Fiolhais, Erratum: Atoms, molecules, solids, and surfaces: Applications of the generalized gradient 16
approximation for exchange and correlation, Phys. Rev. B 48 (1993) 4978–4978. doi:10.1103/PhysRevB.48.4978.2. [26] G. Kresse, From ultrasoft pseudopotentials to the projector augmented-wave method, Phys. Rev. B 59 (1999) 1758–1775. doi:10.1103/PhysRevB.59.1758. [27] J.P. Perdew, K. Burke, M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77 (1996) 3865–3868. doi:10.1103/PhysRevLett.77.3865. [28] A.I. Liechtenstein, V.I. Anisimov, J. Zaanen, Density-functional theory and strong interactions: Orbital ordering in Mott-Hubbard insulators, Phys. Rev. B 52 (1995) 5467– 5471. doi:10.1103/PhysRevB.52.R5467. [29] S.L. Dudarev, S.Y. Savrasov, C.J. Humphreys, A.P. Sutton, Electron-energy-loss spectra and the structural stability of nickel oxide: An LSDA+U study, Phys. Rev. B 57 (1998) 1505–1509. doi:10.1103/PhysRevB.57.1505. [30] A. Stashans, Y. Bravo, Large hole polarons in Sc-doped TiO2 crystals, Mod. Phys. Lett. B 27 (2013) 1350113. doi:10.1142/S0217984913501133. [31] J.P. Allen, D.O. Scanlon, G.W. Watson, Electronic structures of silver oxides, Phys. Rev. B 84 (2011) 1–14. doi:10.1103/PhysRevB.84.115141. [32] S. Goumri-Said, M.B. Kanoun, DFT+U study of the oxide-ion conductor pentalanthanum hexamolybdenum henicosaoxide, J. Solid State Chem. 197 (2013) 304–311. doi:10.1016/j.jssc.2012.08.042. [33] C.C. Hu, Modern semiconductor devices for integrated circuits, first ed., Prentice Hall, 2010. [34] R.H. Buttner, E.N. Maslen, Electron difference density and vibration tensors in SrTiO3, Acta Crystallogr. B 48 (1992) 639–644. doi:10.1107/S0108768192004488. [35] R.D. King-Smith, D. Vanderbilt, First-principles investigation of ferroelectricity in perovskite compounds, Phys. Rev. B 49 (1994) 5828-5844. doi: 10.1103/PhysRevB.49.5828.
17
[36] S.H. Wemple, M. Didomenico, I. Camlibel, Dielectric and optical properties of meltgrown BaTiO3, J. Phys. Chem. Solids 29 (1968) 1797–1803. doi:10.1016/00223697(68)90164-9. [37] A. Stashans, H. Pinto, Hole polarons in pure BaTiO3 studied by computer modeling, Int. J. Quantum Chem. 79 (2000) 358-366. doi:10.1002/1097-461X(2000)79:6<358::AIDQUA4>3.0.CO;2-2. [38] H. Pinto, A. Stashans, Computational study of self-trapped hole polarons in tetragonal BaTiO3, Phys. Rev. B 65 (2002) 134304. doi:10.1103/PhysRevB.65.134304. [39] P. Pertosa, F.M. Michel-Calendini, X-ray photoelectron spectra, theoretical band structures, and densities of states for BaTiO3 and KNbO3, Phys. Rev. B 17 (1978) 2011-2020. doi:10.1103/PhysRevB.17.2011. [40] Virtual NanoLab, versión 2015.1, QuantumWise A/S (www.quantumwise.com). [41] W. Setyawan, S. Curtarolo, High-throughput electronic band structure calculations: Challenges and tools, Comput. Mater. Sci. 49 (2010) 299–312. doi:10.1016/j.commatsci.2010.05.010. [42] V.C. Sahni, P.W.M. Jacobs, A calculation of the vibrational entropy of anion Frenkel defects in fluorite crystals, Phil. Mag. A 46 (1982) 817-827. doi:10.1080/01418618208236933. [43] T. Kolodiazhnyi, A. Petric, M. Niewczas, C. Bridges, A. Safa-Sefat, J.E. Greedan, Thermoelectric power, Hall effect, and mobility of n-type BaTiO3, Phys. Rev. B 68 (2003) 85205. doi:10.1103/PhysRevB.68.085205. [44] T. Yamamoto, Y. Sato, T. Tanaka, K. Hamashi, Y. Ikura, T. Sakuma, Electron transport behaviors across single grain boundaries in n-type BaTiO3 , SrTiO3 and ZnO, J. Mater. Sci. 40 (2005) 881–887. doi:10.1007/s10853-005-6505-4. [45] A. Ianculescu, Z. V. Mocanu, L.P. Curecheriu, L. Mitoseriu, L. Padurariu, R. Truşcă, Dielectric and tunability properties of La-doped BaTiO3 ceramics, J. Alloys Compd. 509 (2011) 10040–10049. doi:10.1016/j.jallcom.2011.08.027.
18
[46] M.M. Vijatović, B.D. Stojanović, J.D. Bobić, T. Ramoska, P. Bowen, Properties of lanthanum doped BaTiO3 produced from nanopowders, Ceram. Int. 36 (2010) 1817–1824. doi:10.1016/j.ceramint.2010.03.010. [47] J. Li, S. Hao, D. Fu, W. Wang, T. Ma, C. Wang, Modification of Ag-doped BaTiO3 powders through La gaseous penetration route, J. Rare Earths 28 (2010) 154–157. doi:10.1016/S1002-0721(10)60288-8. [48] M. Menadakis, G. Maroulis, P.G. Koutsoukos, A quantum chemical study of doped CaCO3 (calcite), Comput. Mater. Sci. 38 (2007) 522–525. doi:10.1016/j.commatsci.2006.02.016. [49] A. Stashans, K. Rivera, Iron impurity in zircon by DFT computations, Mod. Phys. Lett. B 27 (2013) 1350145. doi:10.1142/S0217984913501455. [50] A. Stashans, J. Escobar, Effects of vanadium impurity on TiO2 properties, Int. J. Mod. Phys. B 29 (2015) 1550094. doi:10.1142/S0217979215500940. [51] R.D. Shannon, Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides, Acta Cryst. A 32 (1976) 751-767. doi: 10.1107/S0567739476001551. [52] R. F. W. Bader, The international series of monographs on chemistry, Vol. 22, Oxford University Press, Oxford, 1990. [53] H. Ikushima, S. Hayakawa, Electrical properties of Ag-doped barium titanate ceramics, Jpn. J. Appl. Phys. 4 (1965) 328. doi: 10.1143/JJAP.4.328.
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Highlights
Spin-polarized DFT+U study of Ag and La codoped BaTiO3 containing oxygen vacancies.
Indispensability of oxygen vacancy to produce n-type conductivity and magnetism.
Codoping advantage over single impurity doping to reduce resistivity in BaTiO3.
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