Materials Science
Chemistry,1970-2014-Chemistry-2014.jsonl.gz.gz
Chemistry Materials Science
6a5a22317059f9db4d15b26d8209e69442a63527
Theoretical study of the reaction mechanism Ba, Ti, O in the early growth of BTO thin films

s: We use the DMol program based on density functional theory(DFT) to clarify the processes of microcosmic reactions and the particle states in the early growth of BaTiO3 (BTO) thin films. This research is important for optimal preparation and structure control of BTO thin films. After designing and optimizing some possible intermediate states, we find that the molecules may serve as nucleation sites for BTO growth. This occurs by combining TiO2 with BaO molecules to form BaTiO3 with the G conformation, which is similar to a quarter of a BTO unit cell. By virtue of understanding these mechanisms, perovskite-structured BTO thin films are formed.


Introduction
A revolution is occurring in science and technology based on the recently developed ability to measure, manipulate, and organize matter on ferroelectric thin films. These thin films are widely exploited for microwave phase shifters and dynamic random access memory due to their advantageous physical properties (piezoelectricity, ferroelectricity, pyroelectricity, and photoelectricity-the latter is used in nonlinear optics). As a typical representative of the perovskite structure thin films, BaTiO 3 thin films are used not only to make microelectronic devices, but also to develop ferroelectric/superconductor devices by combining them with superconducting thin films [1][2][3]. As a result, progress in understanding BTO thin films will have a very far-reaching impact.
Currently, BaTiO 3 (BTO) and SrTiO 3 (STO) thin films are prepared primarily by Laser Molecular Beam Epitaxy (LMBE), not only because it allows in situ monitoring, but also because the chemical composition of thin films can be controlled. Using LMBE to prepare BTO and STO thin films, Li, et al [4][5][6] demonstrated the feasibility of unit cell migration with surface self-diffusion by in situ reflective high energy electron diffraction and atomic force microscopy. The experiments revealed "unit cell migration", which formed the basis for a growth model for films. In addition, they measured the activation energy of unit cell migration in BTO and STO thin films to be 0.29 ± 0.01 eV [4,5].
However, these experimental investigations are inadequate to describe physical chemistry data such as interface structure, adsorption, diffusivity, and particle trajectories in the growth of thin films. Additionally, experimental information is lacking regarding the formation of the BTO perovskite structure unit cell and the physicochemical processes involving Ba, Ti, and O atoms. Thus, developing a theoretical picture is very important for advancing research in this area. We had investigated possible reaction mechanisms in initial growth process of SrTiO 3 (STO) by a first-principles calculation in previous research [7]. To this end, we present a first-principles calculation using density functional theory (DFT) [8,9] to investigate both the possible combination reactions and the initial process of migration growth of BTO to the cell stage.
Regarding unit cell formation with Ba, Ti, and O microcosmic particles formed by flash evaporation in the unit cell migration growth of BTO thin films, we hypothesize two cases. The first is that Ba, Ti, and O atoms form intermediates (O 2 , BaO, BaO 2 , TiO, TiO 2 ) by colliding, after which the unit cell is formed. The second is the formation of a perovskite structure unit cell by direct deposition of Ba, Ti, and O atoms on the surface of the substrate. This paper is organized as follows, a brief introduction about the calculation method shows in section 2, the main results and discussion of the paper are described in section 3 and the end of the paper is conclusion.

Methodology
We use the local orbital density functional method DMol 3 program [10,11], which evolved from a gas phase molecular method to a method that allows for state-of-the-art calculations on non-conducting and metallic solids [12,13]. We used the PW91 function of the Generalized Gradient Approximation [14,15] and convergence conditions with a large basis set and high accuracy to optimize each structure of this system. During the calculations, the wave function of the valence electrons is expanded using the Double Numeric Polarization basis set in DFT, which is similar to 6-311++G** of Gaussian theory, but more precise. Its selfconsistent convergence precision is set above 10 -6 a.u. The energy convergence accuracy reaches 10 -5 a.u., and the convergence accuracy of grads and displacements surpassed 10 -4 a.u./nm and 5 × 10 -4 nm, respectively. In the DMol 3 program, all the electrons of atoms with atomic number less than 21 are involved in the calculation. Thus, all the electrons of O atoms and the valence electrons of Ba and Ti atoms are treated explicitly, but the core electrons of Ba and Ti atoms are replaced with effective core potential approximations [15]. Besides, we chose the most accurate transient state (TS) search methods to obtain the TS structure, namely the complete linear synchronous transit and the complete quadratic synchronous transit [17,18]. The activation energy of reactions can then be obtained after analyzing the energy difference between the intermediate state and the TS [19,20]. Incidentally, the TS can be confirmed easily if it has a higher energy than that of the reactants or intermediates and if it exists only at an imaginary frequency [21][22][23].

Results and Discussion
Generally, in an atmosphere containing Ba, Ti, and O atoms, Ba and Ti are easily oxidized by O atoms of higher activity, so that O 2 , BaO, BaO 2 , TiO, TiO 2 , and BaTiO 3 molecules are formed preferentially prior to formation of the unit cell. Based on our analysis, we present some reaction models and their initial conditions, assuming a vacuum and non-equilibrium states with high-density reactants.  Figure 1.

The Formation of Molecular BaO
The same analysis may be applied to Ba atoms, which are oxidized and form BaO molecules due to interactions with O atoms or O 2 molecules. Here, we likewise use two models, model IIA (IIB) where the Ba and O atoms (O 2 molecule) interact to form BaO. The reaction process is quite simple within model IIA-our calculation indicates that there is no energy barrier in this process. Using the energies given in Table 1, we find that the stabilization energy of the BaO molecule is 572.03 kJ/mol, which is consistent with values reported in the literature; i.e. E s ≥ 562.8 ± 14.6 kJ/mol [24]. In addition, the bond length of BaO is 0.2034 ± 0.0053 nm [24].
Within model IIB, two Ba atoms form coordination bonds with the lone-pair electrons of an O 2 molecule, instantly (on the time scale of interest) transforming into an M2 compound. The formation of the Ba-O bond weakens the O-O bond, and it is gradually broken resulting in the decomposition of M2 toward the BaO molecule via the transient TS2 state. By analyzed the transient TS2 state, we find that the stabilization energy of M2 is 424.74 kJ/mol and that the activation energy of the reaction is 55.01 kJ/mol. These results imply that the reaction always favors the formation of BaO molecules.

The Formation of Molecular BTO
After BaO and TiO 2 molecules are formed, they may interact to form BaTiO 3 . BaO, TiO 2 , and BaTiO 3 molecules, providing precursors for forming the BTO unit cell.
To be sure of the geometric conformations of BaTiO 3 , we built seven different possible structures according to the principle of molecular symmetry. As shown in Fig 5, after optimization of the seven structures, we find that the A, B, and C conformations are similar to the F conformation and that the D and E conformations are similar to the G conformation. Furthermore, the system energies of the F and G conformations are the lowest, at -813585.88 kJ/mol and -813587.18 kJ/mol, respectively, indicating that these conformations are more stable.
To study the components and structures of BTO thin film crystals, we create a 2×2 BTO super-cell with four BTO molecules, corresponding to BaTiO 3 molecules. The total energy of the super-cell is -3257201.00 kJ/mol, and the average energy of the BTO molecule is -814300.25 kJ/mol, making it 714.37 and 713.07 kJ/mol less than the F and G conformations, respectively. In addition, we note that the most stable conformation, G, is similar to a quarter-corner of the BTO unit cell, so that a BTO molecule with the G conformation, formed by BaO and TiO 2 molecules, will be shaped into the BTO unit cell with a perovskite structure. Put another way, the G conformation, which is a BTO molecule, may be regarded as one component of a BTO unit cell.
To form a BTO molecule (see Figs. 6 and 7), the F conformation is first formed by collision between BaO and TiO 2 molecules, which is a barrierless reaction. Immediately thereafter, the Ba atoms moves toward the center of the three O atoms until the G conformation is formed because of the attractive forces of the lone-pair electrons of the three O atoms. This process involves a barrier. Upon optimization and frequency analysis, we find a new transient state TS3. The characteristic parameters of TS3 are given in Table 2, and indicate that the reaction favors the G conformation and that it occurs easily due to the low activation energy (10.55 kJ/mol).
Our calculation and optimization indicate that there is little probability that Ba, Ti, and O atoms form a BTO unit cell directly but that some intermediates (such as BaO, TiO 2 , and BTO molecules) need to be formed beforehand. The activation energies for the formation processes of BaO, TiO 2 , and BTO are 55.01 kJ/mol, 11.81 kJ/mol, and 10.55 kJ/mol, respectively, with the lower value indicating that the reaction occurs more easily.

Analysis Using the Frontier Orbital Theory
The Frontier Orbital Theory considers that molecular orbitals (the highest occupied molecular orbital, or HOMO, and the lowest unoccupied molecular orbital, or LUMO) play a pivotal role during the chemical reaction. For lower E HOMO , the electronic capacity to offer molecules is lower because the electrons in the orbital are steadier. We use E LUMO to describe the ability of a molecule to accept electrons. The lower it is, the better electron-acceptor it is.
Our calculations indicate that the energy of the BaO HOMO is -288.44 kJ/mol and its LUMO energy is -154.02 kJ/mol. For TiO 2 the HOMO and LUMO energies are -558.31 kJ/mol and -352.97 kJ/mol, respectively, so that E HOMO (BaO) > E HOMO (TiO 2 ), and the E LUMO (BaO) > E LUMO (TiO 2 ). As a result, the LUMO of TiO 2 can react with the HOMO of BaO because BaO can offer electrons and TiO 2 can accept electrons. As shown in Figure 8, the main HOMO of BaO comes from the lone-pair electrons of the O 2p orbital, and the main part of the TiO 2 LUMO comes from the 3d orbital of the Ti atom, indicating that the O atoms of BaO molecules will combine with the Ti atoms of TiO 2 molecules. This conclusion is the same as the conclusion reached above. In addition, the calculated BTO HOMO and LUMO orbits are shown in Figure 8. The BTO HOMO distributed around the O atoms mainly form its lone-pair electrons in the 2p orbital, and the LUMO distributed around the Ba and Ti atoms mainly form their 5s and 3d orbital.

Conclusion
In our calculation, we find that BaO, TiO 2 , and BaTiO 3 molecules are the primary particle states in the early growth of BTO thin films by LMBE, with activation energies of 55.01 kJ/mol, 11.81 kJ/mol, and 10.55 kJ/mol, respectively. We find that TiO 2 molecules are formed first in vacuum where Ba, Ti, and O atoms coexist and become nucleation sites for BTO unit cell growth. Furthermore, the BaTiO 3 molecule, a part of the BTO unit cell, is formed by TiO 2 and BaO molecules. The BTO primary unit cell with a perovskite structure then evolves and grows with BTO unit cell migration growth on the substrate surface.