# Analyse:Kor

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 Bearbeitet: 26. April 2016, 21:30 Graf IsolanErstellt: 26. April 2016, 21:30 (Graf Isolan)

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In recent years, a large amount of research worldwide was focused on the growth and characterization of ferroelectric thin films. On one hand, their ferroelectric, dielectric, and piezoelectric properties were found to be promising for microelectronic and micromechanical applications [85]. On the other hand, the physical properties of ferroelectric thin films were found to be substantially different from those of bulk materials. The ferroelectric properties are known to degrade in thin films [86], and it is very important to understand the origin of this effect.

[85] J.F.Scott. Ferroelectrics, 183:51, 1996.

[86] Feng Tsai and J. M. Cowley. Thickness dependence of ferroelectric domains in thin crystalline films. Applied Physics Letters, 65(15):1906–1908, 1994.

In recent years, a large amount of research, worldwide was focused on the growth and characterization of ferroelectric thin films. On one hand, their ferroelectric, dielectric, and piezoelectric properties were found to be promising for microelectronic and micromechanical applications [1]. On the other hand, the physical properties of ferroelectric thin films were found to be substantially different from those of bulk materials. The ferroelectric properties are known to degrade in thin films [2], and it is very important to understand the origin of this effect.

1. J.F.Scott, Ferroelectrlcs 183, 51 (1996).

2. F.Tsai and M.Cowley, Appl.Phys.Lett. 65, 1906 (1994).

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 Bearbeitet: 26. April 2016, 21:49 Graf IsolanErstellt: 26. April 2016, 21:49 (Graf Isolan)

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At any surface the translational symmetry is broken, i.e. the surface can remain periodic in the plane, but the crystal is no more periodic in the direction perpendic[ular to the surface.] At any surface, the translational symmetry is broken: the surface can remain periodic in the plane, but the crystal is no more periodic in the direction perpendicular to the surface.
 Anmerkungen Not marked as a citation; continued on next page following. Sichter (Graf Isolan)

 Bearbeitet: 27. April 2016, 08:46 Graf IsolanErstellt: 26. April 2016, 22:13 (Graf Isolan)

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The atoms in the outermost layers (those which are closer to the surface) will feel the absence of neighboring atoms to interact with. These missing bonds affect the structural and electronic properties of the materials. In the particular case of ABO3 perovskite oxides, the hybridization between Ti 3d and O 2p orbitals, responsible for the giant effective charges and, ultimately, for the ferroelectric instability, is modified (see Sec. 4.2.3) The absence of some of the atoms leaves highly energetic and electronically active dangling bonds at the surface. In most cases this leads to structural relaxations, and in case of covalent bonding e.g. in semiconductors even reconstructions of the surface geometry to produce a more satisfactory bonding configuration, that might affect significantly the physical properties surface. The energy scale of the surface relaxations and reconstructions is orders of magnitude higher than the depth of the bulk ferroelectric double well, so it is expected to affect the ferroelectric ground state of the system.

The determination of electronic and structural properties is a delicate problem, that turns out to be strongly dependent on the nature of the material. Only changing one of the cations in a ABO3 perovskite surface can lead to very different qualitative and quantitative behavior. Even more, for a given material the results change also with the particular orientation and atomic termination i.e. AO or BO2 of the surface.

For studying of thin films or heterostructures, the first step is to choose an initial symmetry for the simulations and to define a reference ionic configuration that is obtained by cutting the bulk material along a particular direction. The reference configuration to which we will refer when discussing surface atomic relaxation is therefore the atomic arrangement of an unrelaxed truncated bulk structure. Usually, the bulk structure that is truncated is the theoretically relaxed bulk structure. In some cases, however, in order to include the effect of the epitaxial strain induced by a substrate, the reference configuration is defined by cutting a strained bulk phase, with the same strain constraints than those expected in the thin film. The three most important orientations for ABO3 surfaces (and also those which have been most investigated theoretically) are (001), (110) [91–93], and (111) [94–96]. In the (001) cut, the ABO3 perovskite structure can be considered as an alternating stack of AO and BO2 layers. For II-IV perovskites, where atoms A and B are divalent and tetravalent respectively, in the ionic limit, the structure is a sequence of neutral sheets (A2+O2-)0 and [B4+(O2-)2]0. The surface might have two possible different terminations, with the outermost layer being a AO layer or a BO2 layer. By contrast, both the (110) and the (111) orientations are polar irrespectively of the cation valence states. In the (110) cut, the perovskite structure is composed of (ABO)4+ and (O2)4- stacks, whereas the atomic planes in the (111) cut are AO3 and B, and they are both charged. The highly polar nature of the (110) and (111) surfaces makes them unstable and highly reactive in comparison to the (001) surface [97]. We will focus on the (001) orientation of the BaTiO3 and PbTiO3 structures.

In these system, bulk properties are recovered a few atomic layers away from the outermost surface layers. This allows the use of thin slabs of the order of ten layers thick. Typically (1 × 1) surface geometries are simulated.

[91] Alexie M. Kolpak, Dongbo Li, Rui Shao, Andrew M. Rappe, and Dawn A. Bonnell. Evolution of the structure and thermodynamic stability of the BaTiO3(001) surface. Physical Review Letters, 101(3):036102, 2008.

[92] R. I. Eglitis, S. Piskunov, E. Heifets, E. A. Kotomin, and G. Borstel. Ab initio study of the SrTiO3, BaTiO3 and PbTiO3(0 0 1) surfaces. Ceramics International, 30(7):1989 – 1992, 2004. 3rd Asian Meeting on Electroceramics.

[93] Fabio Bottin and Claudine Noguera. Stability and electronic structure of the (1×1) SrTiO3(110) polar. Phys. Rev. B, 68(3):035418, 2003.

[94] R. E. Cohen. Periodic slab lapw computations for ferroelectric batio3. Journal of Physics and Chemistry of Solids, 57(10):1393 – 1396, 1996. Proceeding of the 3rd Williamsburg Workshop on Fundamental Experiments on Ferroelectrics.

[95] Aravind Asthagiri, Christoph Niederberger, Andrew J. Francis, Lisa M. Porter, Paul A. Salvador, and David S. Sholl. Thin Pt films on the polar SrTiO3(1 1 1) surface: an experimental and theoretical study. Surface Science, 537(1-3):134–152, 2003.

[96] Aravind Asthagiri and David S. Sholl. DFT study of Pt adsorption on low index SrTiO3 surfaces: SrTiO3 (1 0 0), SrTiO3 (1 1 1) and SrTiO3 (1 1 0). Surface Science, 581(1):66–87, 2005.

[97] N. Mukunoki . Y.and Nakagawa, T. Susaki, and H. Y. Hwang. Atomically flat (110) SrTiO3 and heteroepitaxy. Applied Physics Letters, 86(17):171908, 2005.

[Page 43]

The atoms in the outermost layers (those which are closer to the surface) will feel the absence of neighboring atoms to interact with. These missing bonds affect the structural and electronic properties of the materials. In the particular case of ABO3 perovskite oxides, the hybridization between Ti 3d and O 2p orbitals, responsible for the giant effective charges and, ultimately, for the ferroelectric instability is modified (see Sec. 3) The absence of some of the atoms leaves highly energetic and electronically active dangling bonds at the surface. In most cases this leads to structural relaxations, and even reconstructions of the surface geometry to produce a more satisfactory bonding configuration, that might affect significantly the physical properties of the ferroelectric slab. The energy scale of the surface relaxations and reconstructions is orders of magnitude higher than the depth of the bulk ferroelectric double well, so it is expected to affect the ferroelectric ground state of the system.

The determination of electronic and structural properties is a delicate problem, that reveals strongly dependent on the nature of the material. Only changing one of the cations in a ABO3 perovskite surface can lead to very different qualitative and quantitative behaviour. Even more, for a given material the results change also with the particular orientation and atomic termination of the surface.

[Page 44]

In the first-principles study of thin films or heterostructures, the first step is to choose an initial symmetry for the simulations and to define a reference ionic configuration that is obtained by cutting the bulk material along a particular direction. The reference configuration to which we will refer when discussing surface atomic relaxation is therefore the atomic arrangement of an unrelaxed truncated bulk structure. Usually, the bulk structure that is truncated is the theoretically relaxed structure. In some cases, however, in order to include the effect of the epitaxial strain induced by a substrate, the reference configuration is defined by cutting a strained bulk phase, with the same strain contraints [sic] than those expected in the thin film.

The three most important orientations for ABO3 surfaces (and also those which have been most investigated theoretically) are (001), (110) [203, 217], and (111) [205, 206]. In the (001) cut, the ABO3 perovskite structure can be considered as an alternating stack of AO and BO2 layers. For II-IV perovskites, where atoms A and B are divalent and tetravalent respectively, in the ionic limit, the structure is a sequence of neutral sheets (A2+O2-)0 and [Ti4+(O2-)2]0. The surface might have two possible different terminations, with the outermost layer being a AO layer or a TiO2 layer. By contrast, both the (110) and the (111) orientations are polar irrespectively of the cation valence states. In the (110) cut, the perovskite structure is composed of (ABO)4+ and (O2)4- stacks, whereas the atomic planes in the (111) cut are AO3 and B, and they are both charged. The highly polar nature of the (110) and (111) cuts makes them unstable and highly reactive in comparison to the (001) surface [218]. In this review we will focus on the (001) orientation of the II-IV perovskite structures.

[Page 45]

Bulk properties are recovered a few atomic layers away from the outermost surface layers. This allows the use of thin slabs of the order of ten layers thick.

Typically (1 × 1) surface geometries are simulated.

[203] E. Heifets, E. A. Kotomin, and J. Maier, Surf. Sci. 462, 19 (2000).

[205] R. E. Cohen, J. Phys. Chem. Solids 57, 1393 (1996).

[206] R. E. Cohen, Ferroelectrics 194, 323 (1997).

[217] F. Bottin, F. Finocchi, and C. Noguera, Phys. Rev. B 68, 035418 (2003).

[218] Y. Mukunoki, N. Nakagawa, T. Susaki, and H. Y. Hwang, Appl. Phys. Lett. 86, 171908 (2005).

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 Bearbeitet: 13. October 2016, 22:13 Graf IsolanErstellt: 27. April 2016, 09:12 (Graf Isolan)

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Quelle: Meyer and Vanderbilt 2001
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In addition to the microscopic quantities ρ(r) and ν(r), we assume the slabs to be thick enough that macroscopic quantities like the macroscopic electric field E, the dielectric displacement field D, and the polarization P are also well defined inside the slab. In practice, these fields may be calculated, for example, from unit cell averages of the electrostatic potential and the charge density.

In the case of an applied external electric field Eext perpendicular to the surfaces, the dielectric displacement field D inside the slab is oriented parallel to the z axis and is equal to Eext. The boundary condition of a vanishing external electric field is therefore equivalent to a vanishing dielectric displacement field D inside the slab. fig. [sic] 5.1(a) shows a schematic picture of the planar-averaged potential ν(r) for this situation.

The potential is constant outside the slab, but due to the slab dipole moment m the potential drops by 4πem when going from one side of the slab to the other. At the same time, the polarization P leads to surface charges σ = P ⋅ $\hat n$, which give rise to a huge depolarization field E = D - 4πP = -4πP inside the slab. (Notice, that E does not depend on the thickness of the slab). The contribution of the depolarization field to the total energy is large enough to completely destabilize the bulk FE state. Therefore, relaxing a polarized slab under the boundary condition of a vanishing external electric field will inevitably result in a paraelectric cubic structure [111].

[111] B. Meyer and David Vanderbilt. Ab initio study of BaTiO3 and PbTiO3 surfaces in external electric fields. Phys. Rev. B, 63(20):205426, May 2001.

In addition to the microscopic quantities ρ(r) and ν(r), we assume the slabs to be thick enough that macroscopic quantities like the macroscopic electric field E, the dielectric displacement field D, and the polarization P are also well defined inside the slab. In practice, these fields may be calculated, for example, from unit cell averages of the electrostatic potential and the charge density.6 [...]

In the case of an applied external electric field Eext perpendicular to the surfaces, the dielectric displacement field D inside the slab is oriented parallel to the z axis and is equal to Eext. The boundary condition of a vanishing external electric field is therefore equivalent to a vanishing dielectric displacement field D inside the slab. Figure 1(a) shows a schematic picture of the planar-averaged potential ν(z) for this situation.

The potential is constant outside the slab, but due to the slab dipole moment m the potential jumps by 4πem when going from one side of the slab to the other. At the same time, the polarization P leads to surface charges σ = P·<hat>n</hat>, which give rise to a huge depolarization field E=D-4πPP inside the slab (notice that E does not depend on the thickness of the slab). The contribution of the depolarization field to the total energy is large enough to completely destabilize the bulk FE state.15,16 Therefore, relaxing a polarized slab under the boundary condition of a vanishing external electric field will inevitably result in a paraelectric cubic structure.

6L. Fu, W. Yaschenko, L. Resca, and R. Resta, Phys. Rev. B 60, 2697 (1999).

15M. E. Lines and A. M. Glass, Principles and Applications of Ferroelectrics and Related Materials (Clarendon Press, Oxford, 1977).

16W. Zhong, R. D. King-Smith, and D. Vanderbilt, Phys. Rev. Lett. 72, 3618 (1994).

 Anmerkungen At the end of the first two paragraphs and in the legend of figure 5.1.a the original paper is given. But nothing hinds at Kor's text being a nearly exact copy of the original one. Mark that the original ν(z) becomes ν(r) in Kor. Sichter (Graf Isolan)

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