AIP Conference Proceedings 1875, 020017 (2017); https://doi.org/10.1063/1.4998371 1875, 020017
© 2017 Author(s).
A first principle study of band structure of tetragonal barium titanate
Cite as: AIP Conference Proceedings 1875, 020017 (2017); https://doi.org/10.1063/1.4998371 Published Online: 08 August 2017
Nurul Athirah Abd Razak, Noriza Ahmad Zabidi, and Ahmad Nazrul Rosli
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A First Principle Study of Band Structure of Tetragonal Barium Titanate
Nurul Athirah Abd Razak
1,b)Noriza Ahmad Zabidi
2,c)and Ahmad Nazrul Rosli
1, a)1Faculty of Sciences and Technology, Universiti Sains Islam Malaysia (USIM) Nilai, 71800 Negeri Sembilan, MALAYSIA.
2Department of Physics, Center for Defence Foundation Studies, Universiti Pertahanan Nasional Malaysia, 59200 Kuala Lumpur, MALAYSIA
a)Corresponding author: [email protected]
Abstract. Barium titanate (BaTiO3) is a perovskite crystal structure and it is well known to have many potential applications in microelectronic industry due to its high capabilities to enhance the performance of the capacitors and other energy storage devices. BaTiO3 has been reported to have a wide band gap around 3.4 eV from previous experimental studies. In theoretical studies, the analysis of the band structure of perovskite type of materials still under investigation due to high disagreement with the experimental result. The objective of this research is to investigate the band gap of the tetragonal BaTiO3 calculated using generalized gradient approximation (GGA) and hybrid functional (HSE03) with various pseudopotential methods performed by CASTEP module. The calculation using GGA show underestimation of energy band gap. However, the band gap calculated using HSE03 approximation shows an agreement with the experimental result.
INTRODUCTION
Perovskite barium titanate (BaTiO3) has been discovered for half of century and this material still attracted the whole world especially in microelectronic industry. This is due to their capability of high dielectric constant, low current lost and also known as superb piezoelectric and ferroelectric properties. In experimental study, the band gap of tetragonal BaTiO3 has been reported around 3.40 eV and can be categorized as an indirect band gap [1].
Perovskite has held the interest of crystallographer for a significant period of time due to the wide range of compositions and the existence variety of unique properties such as ferroelectricity. Ferroelectricity has been revealed by researchers since 1920s whereas in 1940s, perovskite barium titanate (BaTiଷሻ was discovered which exhibits this property [3]. In fact, perovskite was founded first in calcium titanate oxide (CaTiଷ). However, this perovskite has not been widely investigated and it is probably because of the higher tendency of other perovskites especially BaTiଷ which more promising in terms of their technology.
Since the last decade, BaTiଷ has become the most important material with excellent dielectric, ferroelectric and piezoelectric properties which make this kind of material have great capabilities that can be utilized widely in electronic devices manufacturing [4]. Barium titanate (A ions), which are large in size ( ̴158 pm), occupy the corner sites while the titanate ions (B ions) which are small in size ( ̴ 60 pm), locate in the centers of the cube and oxygen anions are on the face-centers. The sudden interest of BaTiଷ broadened gradually as it has four different phases such as cubic, tetragonal, orthorhombic and rhombohedra phase as these phases undergo ferroelectric transitions with growing temperature. In the past 20 years, several first-principles calculations on
BaTiଷ have been performed that focus more on the structural and electronic properties of the four phases (Sanna et al., 2011).
The theoretical investigation of this perovskite BaTiଷ is still need a further investigation as it does not show the same result when compare to the experimental investigation and still being an object of investigation until now.
From previous experimental study, the results had shown about 3.7 eV for the cubic phase and 3.9 eV for tetragonal phase [5]. Hence, in order to determine the band gap structure of perovskite BaTiଷ, the computational method called density functional theory (DFT) will be applied with different levels of approximation.
This method is well known to determine the waves function and allowed the energy state of the system which involves the time-independent Schrodinger equation. However, neither the local density approximation (LDA) nor generalized gradient approximation (GGA) is able to provide an accurate description of band structure as it could be underestimate and overestimate the experimental band gap values [6]. Besides, this particular problematic will be overcome by using hybrid exchange-correlation technique to improve the accuracy of band gap calculation and show a better result.
In this paper, we calculate the band gap of BaTiO3 for difference approximation. However, we only discuss the result from the hybrid HSE03 approximation since the GGA are underestimated the band gap value.
MEHTODOLOGY
This research of perovskite-type material barium titanate (BaTiܱଷሻ focused on the tetragonal structure and the corresponding space group is 99-P4mm while the calculated lattice constant for tetragonal BaTiO3 are a = 3.994 Ǻ and c = 4.034 Ǻ where a = b ≠ c. The size of atoms for this structure was different which Ba cation has larger size than Ti cation due to the Ba charge was smaller than Ti. Besides, the main atoms of this structure are (Ba, Ti, O) which have the electron configuration of [Kr] 4݀ଵ5ݏଶ5, [Ne] ͵ݏଶ͵͵݀ଶͶݏଶand ʹݏଶʹସ respectively. The core of the atoms was represented by the pseudopotentials of the respective atoms.
A density functional theory (DFT) has been used in the CASTEP software by BIOVIA to calculate the energy band gap of tetragonal BaTiO3. General gradient approximation, GGA and hybrid HSE03 has been used to treat the exchange-correlation potential from the Schrodinger equation.
RESULT AND DISCUSSION
The band structure of tetragonal perovskite BaTiଷhas been performed by using hybrid functional such as HSE03. The plane wave basic set cutoff energy was expanded up in plane waves to 600 eV and the k-point was set to 3x3x3 grid on the Brillioun zone. The norm-conserving method was used as pseudopotential for hybrid functional with the same valence states as in the GGA approximations. As a result, the band structure and density of state (DOS) graph were illustrated after the DFT calculation has been completely performed.
The minimum conduction band and maximum valence band as label in fig. 1 shows indirect band gap at A and G k-point of Brillouin zone. The wide band gap shows clearly at 3.412 eV
Figure 1 shows the band structure of BaTiଷ where the energy (eV) at y axis versus the high symmetry direction in the Brillouin zone in the x axis. This band structure was illustrated after the hybrid HSE03 functional was applied as the exchange correlation. The dotted line that separated the valence and conduction band at 0 eV was called as Fermi level energy.
The band gap of this material was about 3.412 eV after the DFT calculation has been successfully performed. In this graph, it was considered as indirect band gap due to the separation of wide band gap from A point of symmetry
in conduction band and G point in valence band. The indirect band gap was declared when the maximum valence band and minimum conduction band were distributed at different k space.
FIGURE 1. Band structure of BaTiଷ using hybrid HSE03 along the high symmetry directions in the Brillouin zone. The indirect band gap at A and G k-point with 3.412 eV.
FIGURE 2. The graph of density of state (DOS) of BaTiO3 using hybrid HSE03 exchange correlation.
Figure 2 shows the total density of state (DOS) of tetragonal BaTiଷ by using hybrid exchange correlation (B3LYP) functional versus energy (eV) ranges from -60 eV to 20 eV. Conduction and valence band edges in separation of wide energy gap via a common Fermi level shown as the vertical dotted line on the figure 4.18 above.
Maximum valence band
Minimum conduction band
The DOS peaks on the valence band at -10 and -17 eV respectively while in the conduction band, it appeared at the energy of about 3 to 17 eV.
Besides, the higher peak of DOS in the valence band was about -35 eV as the distribution of peaks are much more appeared in the valence band than in conduction band. The band gap of the tetragonal BaTiO3 is about 3.412 eV as band gap is the region of energy that separates the valence and conduction bands which contains no electronic state at all. It is consider as a wide band gap if the value of band gap is larger than 3eV.
CONCLUSION
This calculation has been done using DFT with HSE03 approximation of exchange-correlation potential at the ground state energy level. The calculated band structure of BaTiଷ shows a band gap 1.80 eV when using GGA.
However, hybrid HSE03 approximation shows better result at 3.412 eV which is an agreement with the experimental value of 3.40 eV. The comparison with the experimental result shown at table 1. It shows that HSE03 approximation can be used to deal with the perovskite type material and giving accurate result.
TABLE 1. The comparison of BaTiଷband gap with the experimental value calculated by DFT using hybrid exchange correlation (HSE03) functional.
Exchange
correlation Band gap (eV) Standard deviation
(%) Experimental (eV)
[1]
HSE03 3.412 0.35 3.400
ACKNOWLEDGMENTS
We would like to thanks Research Management Center of Universiti Sains Islam Malaysia (USIM) for providing research grant (PPP Short Term Grant) and also a financially support for attending ICAPE conference.
REFERENCES
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