RANCANGAN PENYELIDIKAN

PEMOHON: GOH EONG SHENG

PENYELIA: DR. YOON TIEM LEONG

PENYELIA BERSAMA: ASSOC. PROF. DR. ONG LYE HOCK

ALAMAT: SCHOOL OF PHYSICS, UNIVERSITI SAINS

MALAYSIA 11800 PULAU PINANG MALAYSIA

PENGAJIAN: MASTER OF SCIENCE (PHYSICS)

BIDANG: COMPUTATIONAL CONDENSED MATTER PHYSICS

TAJUK: FIRST-PRINCIPLES STUDY OF FERROELECTRIC

OXIDE

PENGESAHAN PENYELIA:

(DR. YOON TIEM LEONG)

School of PhysicsUniversity Sains Malaysia (USM)11800 Pulau Pinang, Malaysia.Email: tlyoon@usm.myTel: (604) 653-5314

RESEARCH TOPIC: FIRST-PRINCIPLES STUDY OF FERROELECTRIC OXIDE

NAME OF STUDENT: GOH EONG SHENG

NAME OF SUPERVISOR: DR. YOON TIEM LEONG

CO-SUPERVISOR: ASSOC. PROF. DR. ONG LYE HOCK

1.0 INTRODUCTION

Ferroelectrics oxides known as perovskites are very important functional materials

used in many technological applications [Smo84], such as transducers, gate dielectrics for

MOSFETs, EO modulators, IR detectors and non-volatile RAMs. The applications of

ferroelectrics rely on their special properties to display spontaneous polarisation and

switching under external electric fields. Due to the practical applications of ferroelectrics, the

physics of polarisation in ferroelectrics has been a very active research area since its

discovery by Valasek [Val21]. Good insight of the physical and thermodynamical properties

of ferroelectrics can be calculated using the well-known phenomenological Dovonshire-

Ginzburg-Landau (DGL) theory [AFD49][AFD51]. In DGL theory of ferroelectrics, the

parameters are phenomenological in nature, and have to be measured experimentally. This

approach used to be one of the most popular theoretical tools in the ferroelectrics research

community, and its application in describing ferroelectric effects has been very successful in

the past. However, to capture the atomistic origin of the ferroelectric effects of a chemically-

specific crystal, we need to go beyond the phenomenological theory. The research project

proposed here aims at investigating ferroelectric properties of crystals with an alternative,

powerful approach: the first-principles method.

In first-principles calculation, we can predict, at least in principle, many of the

relevant ferroelectric properties by supplying the crystal structure and bases of a ferroelectric

crystal [Van97]. The essential physical properties, in particular the electric dipole polarisation,

of these systems can be calculated by manipulating the DFT codes which takes care of the

relevant quantum mechanical interactions and the physics of polarisation in the crystal lattice.

A comprehensive review of first-principles calculation on ferroelectric oxides in bulk, thin

film, superlattices and nanostructures can be found in Ref. [Gho06]. In practice, supercells

mimicking the configurations of the ferroelectric crystal (e.g. a thin film) are built, and their

physical properties probed by cleverly manipulating the DFT codes. By building supercell

models representing these structures, we can calculate and obtain computationally the

ferroelectric properties of the materials represented by of these supercells. As such, the

ferroelectric effects of a chemically-specific perovskite can be understood at a more

fundamental level than that offered by DGL theory.

Comparatively, bulk perovskites are much easier to calculate, hence better

understood, than ferroelectric thin films. First-principles calculations on the latter form are

relatively scarce. The precise effects of the substrate, growth orientation, surface termination,

boundary conditions and thickness on the finite-temperature ferroelectric properties of

ultrathin films are not particularly well established [Kor06]. They vary from case to case. In

some cases thin films exhibit striking features that are quite unexpected from the bulk. A

possible avenue for further research is the ferroelectricity properties of superlattices.

Superlattices comprised of ferroelectric thin layers are artificial structures that offer a higher

level of complexity than the ferroelectric thin films. The research of ferroelectric properties of

superlattices is a frontier research topic. Other than being a very challenging condensed

matter system in which the interplay between the underlying atomistic interactions is yet to be

fully explored, superlattices also offers a highly promising way to purpose-design a functional

ferroelectric material.

This research proposes to make use of the DFT computational tools to investigate the

ferroelectric properties of some perovskite, ferroelectrics, in particular in the form of thin

film. Ultimately the insight gained from the first-principle modelling will help us in the

designing of more powerful functional ferroelectric materials.

2.0 LITERATURE REVIEW

Generically, the physical properties of a crystalline solid material are determined by

the electronic structure at the atomic scale. This is essentially a complex, many-body system

governed by the law of quantum mechanics. To determine the physical properties of a crystal

structure by computationally solving the Schrodinger equation from first-principles is a

numerically demanding task. A well-established scheme to calculate electronic properties of

solid crystal by first-principles is based on the Nobel-prize-winning Density Functional

Theory, DFT [Koh65] first proposed in the 1960s. It is a universal approach to the quantum

mechanical many-body problem, where the system of interacting electrons is mapped in a

unique manner onto an effective non-interacting system with the same total density. DFT has

made it a practical feasibility to carry out numerical computation to obtain realistic properties

of solid state systems [Mar04]. DFT has since been one of the most important tools in

understanding the physics and detailed atomistic mechanisms of condensed matter systems

developed on a sound theoretical foundation [Koh99]. Many numerical packages have been

developed since 1980s to implement DFT on computers, leading to many important

breakthroughs in condensed matter and quantum chemistry. Kohn and Pople were conferred

the Noble prize in 1998 because of their original work in developing first-principle

calculation methods.

Since the seminar paper that successfully elucidates the origin of ferroelectricity in

PbTiO3 and BaTiO3 by Cohen [Coh92] using first-principles method in 1990s, DFT has

enjoyed tremendous popularity due to its supreme power to address the physics of

ferroelectrics at the fundamental, atomistic level. It is to be stressed that density functional

theory software packages offer a powerful approach to investigate the ferroelectric system.

The astonishing achievements of first-principles method in ferroelectrics research, and its

future prospect, are well discussed in the review paper by one of the most important figures in

this field, Cohen [Coh00].

Ferroelectric thin films are still an active research area, ranging from exploring its

basis physics to discovering its new application in various areas. Recently, Syu Ou et al.

[OuS13] had studied perovskite BaTiO3 (BT) thin film as one of a promising candidate

material for Resistive RAM (ReRAM). An MOD-made (Metal-Organic-Decomposition) BT

thin film was prepared and fabricated as a stacked capacitor film for investigating the relation

between its ferroelectric properties and the behaviour of resultant resistive hysteresis. It is

revealed that a 110nmthickness BT film by two MOD layers shows ferroelectric hysteresis,

but a 60nmthickness BT film by one MOD layer becomes paraelectric.

External environmental effects and stimuli can influence the properties of a

ferroelectric. One of the recent related works by Wang and Ma [CDW13] investigates the

force induced phase transition of honeycomb-structured ferroelectric thin film. The external

force induced phase transition properties of a honeycomb-structured ferroelectric thin film

described by a spin-1/2 transverse Ising model were investigated by use of the effective field

theory with correlations (EFT). It is found that phase diagrams of the honeycomb ferroelectric

thin film depend sensitively on the force. Three different functions for the exchange

interaction under the external force are proposed, and force effects on pseudo-spin

polarization in 3D and 2D phase diagrams are revealed.

Mechanisms of dependence of the dielectric response of ferroelectrics on defect

types, particularly in the presence of interfaces imposing certain boundary conditions, are less

studied research area. One such research is made by Misirlioglu and Yildiz [eff13], who were

studying the thickness dependence of transition temperatures and dielectric response of

metal/BaTiO3/metal ferroelectric nanocapacitor structures grown on SrTiO3 using a

phenomenological approach accounting for the equations of electrostatics and

semiconductors. Relaxation of the misfit strain via misfit dislocations amplify the surface

effects in films below a critical thickness and favour electrical domains leading to very large

dielectric responses in this regime. A conclusion is made that control of the dislocation

density can lead to non-conventional functionalities in ferroelectric thin film capacitors.

3.0 OBJECTIVES

The following objectives of this project will be achievable by using the first

principles calculation approach.

1. To calculate the ferroelectric (FE) characteristics of perovskites in the forms

of bulk and thin film.2. To study the interfacial interaction effect at the film-substrate interface on the

FE properties of perovskites.

4.0 INSTRUMENT AND SOFTWARE

Given below are the instruments and software that would be employed in this work:

1. USM School of Physics computer cluster

2. DFT software packages: ABINIT [ABI]

5.0 METHODOLOGY

This is basically a computational research project which uses a computer cluster to

run computationally intensive parallel codes from readily available DFT software packages.

The DFT software packages chosen is the Abinit code [ABI], which is a common project of

the Université Catholique de Louvain, Corning Incorporated, and other contributors. The

computer cluster in School of Physics has in MPI capability to run parallel codes, which

enables Abinit code to be executed in parallel mode.

The planned procedures to investigate the ferroelectric properties of a generic

perovskites are as followed:

i. Initially the bulk structure of a prototypical ABO3 perovskite (PbTiO3, BaTiO3 etc.)

will be investigated. After a crystal structure has been constructed, relaxation and

optimization of structure are done using the built-in molecular dynamics functionality

in the DFT software package. Such structural optimization is sort of a routine

procedure in DFT calculations, usually done before actually carrying out the

abstraction of the physical properties.

ii. Ferroelectric properties (at zero temperature and zero pressure) of the bulk

prototypical ABO3 perovskite (PbTiO3, BaTiO3 etc.) are reproduced as reported by

Ghosez and Junquera [Gho06]. These ferroelectric properties, among others, include

the Born effective charges of the atoms in the ABO3 compound, the various phonon

modes and their dispersion relations, and also the range of ferroelectric instability as a

function of the geometry of the crystal structures.

iii. Once the bulk crystal has been reproduced, studies of perovskites structure in the

form of a free standing thin film are carried out. Supercells of isolated film in vacuum

with two free surfaces are constructed. The electronic and structural properties of

such a film can be calculated by the DFT software packages by simply supplying the

structure of the supercell mimicking the thin film.

iv. The properties of FE thin film are investigated; and these results are compared with

those published in the literature such as the work by Ghosez and Junquera [Gho06].

Once successful, ferroelectric properties of other perovskite films, particularly the

ferroelectric polarization along and perpendicular to the film surface, are to be

studied. The properties of FE thin film are investigated as a function of physical

parameters, such as its thickness, the free surface’s Miller index, the lattice constants,

as well as the shifting of the A, B atoms in the perovskites.

v. The next step involves the use of supercell method to construct an interface between a

bulk substrate (it could be a dielectric or a FE of different type) and a FE thin film.

Due to the thickness of the ferroelectric film, the strain induced by the two different

lattice structures at the interface will modify the ferroelectric properties of the film at

the free surface. The effects of such a strain coupling and charge accumulation at the

interface shall be investigated with DFT codes. Among the ferroelectric properties,

the polarisation of the thin film will be studied in depth.

vi. The effects of physical parameters of the thin film on its ferroelectric properties are

studied by constructing supercell models with varying thickness and relative surface

orientations between different combinations of substrate-thin film intermixing. In

particular, the method shall allow the investigation of the existence (or non-existence)

of critical thickness of a given perovskite film, below which the ferroelectricity of the

FE perovskite vanishes.

vii. Finally, the results calculated with first-principles method shall be checked against

those obtained via the phenomenological DGL theory. Such a consistency check will

be used as a benchmark for the reliability of the results obtained by the first-principle

calculation.

Begin

Configure computer cluster to run parallel codes. Install parallel-mode DFT packages. Test run.

Successful?

Troubleshooting

Prepare crystal structures of bulk FE perovskite. Optimise the bulk structures using the structural optimization function in DFT codes

Use the DFT software package functionalities (ABINIT) to abstract ferroelectric properties of the perovskite bulk structures.

Successfully reproduces the literature ferroelectric results of bulk perovskitesTroubleshooting

Choose a perovskite oxide and a Miller index of which surface is to be modelled. Build supercell model of an isolated slab to mimic the ferroelectric thin film.

Optimise the thin film structure using the structural optimization function in DFT codes. Obtain the surface energy of the slab surface corresponds to the chosen Miller index.

Is the surface energy minimized for the chosen Miller index?Change Miller index

The Miller surface with minimum energy is obtained. This corresponds to the most stable surface.

Use ABINIT functionalities to abstract ferroelectric properties of the perovskite free-standing thin film with optimum Miller surface. Vary the thin film thickness to investigate the coupling of the film’s thickness to the ferroelectricity of the perovskite.

Yes

No

No

Yes

No

Yes

6.0 FLOW CHART

Construct the supercell model of a bulk substrate/ ferroelectric thin film interface.

Optimise the surface energy, Miller index of the surface to model, and the resultant interface structure.

Investigate the effects on the ferroelectricity and other physical properties of the thin film by the strain induced at the interface.

Continue?Vary the interface structure

Construct free energy function of the thin film/substrate and superlattice systems within the framework of DGL theory. Abstract the relevant ferroelectric properties from the free energy.

Check the results calculated with the first-principles methodswith that inferred from DGL theory.

Results from GDL and DFT calculationsconsistent?

Troubleshooting

End

Yes

Yes

No

No

7.0 GANNT CHART

Project Duration

Activities

Year 1 Year 2

1 2 3 4 5 6 7 8 91

011 12 1 2 3 4 5 6 7 8 9 10 11 12

Activity

1Activity

2Activity

3Activity

4Activity

5Activity

6Activity

7Activity

8Activity

9

Activity 1: Literature review.

Activity 2: Study of properties of a constructed bulk structure of a prototypical ABO3 perovskite

Activity 3: Studies of perovskites structure in the form of a single thin film

Activity 4: Interplay between properties of perovskites thin film with its ferroelectric properties

is investigated

Activity 5: Study of interface between a bulk substrate and a perovskite thin film

Activity 6: Effects of physical parameters of the thin film (on substrate) on its ferroelectric

properties are studied

Activity 7: Compare calculated results with DGL theory

Activity 8: Compound report and prepare thesis.

Activity 9: Finalize on improvement of report and thesis, prepare for colloquium

8.0 EXPECTED OUTCOMES

A deeper understanding of the physics behind ferroelectric material. Provide insight towards proposing a new functional ferroelectric material. A computational method as a complimentary tool to supplement experimental results Findings about polarizations of ferroelectric thin film in terms of its critical thickness

9.0 CONTRIBUTIONS

Develop human resources in the area of computational condensed physics Bridging the gap between theoretical and experimental physics via computational physics Exploring the limits of functionality of perovskite materials.

10.0 References

[1] G. A. Smolenskiæi, Ferroelectrics and related materials (Vol. 3), New York: Gordon and Breach Science Publishers, 1984.

[2] J. Valasek, "Piezo-Electric and Allied Phenomena in Rochelle Salt," Phys. Rev., vol. 17, no. 4, pp. 475-481, Apr 1921.

[3] A. Devonshire, "XCVI. Theory of barium titanate," Philosophical Magazine Series 7, vol. 40, no. 309, pp. 1040-1063, 1949.

[4] A. Devonshire, "CIX. Theory of barium titanate—Part II," Philosophical Magazine Series 7, vol. 42, no. 333, pp. 1065-1079, 1951.

[5] D. Vanderbilt, "First-principles based modelling of ferroelectrics," Current Opinion in Solid State and Materials Science, vol. 2, no. 6, pp. 701--705, 1997.

[6] P. Ghosez and J. Junquera, "First-principles modeling of ferroelectric oxide nanostructures," eprint arXiv:cond-mat/0605299, 2006.

[7] I. A. a. F. H. a. B. L. Kornev, "Properties of ferroelectric ultrathin films from first principles," Journal of materials science, vol. 41, no. 1, pp. 137--145, 2006.

[8] W. Kohn and L. J. Sham, "Self-consistent equations including exchange and correlation effects," Physical Review, vol. 140, no. 4A, p. A1133, 1965.

[9] R. M. Martin, Electronic Structure: Basic Theory and Practical Methods, Cambridge university press, 2004.

[10] W. Kohn, "Nobel Lecture: Electronic structure of matter—wave functions and," Reviews of Modern Physics, vol. 71, no. 5, pp. 1253--1266, 1999.

[11] R. E. Cohen, "Origin of ferroelectricity in perovskite oxides," Nature, vol. 358, no. 6382, pp. 136--138, 1992.

[12] R. E. Cohen, "Theory of ferroelectrics: a vision for the next decade and beyond," Journal of Physics and Chemistry of Solids, vol. 61, no. 2, pp. 139--146, 2000.

[13] S. Ou, H. Kawahara, K. Yamashita and M. Noda, "Resistive hysteresis of MOD-made BaTiO 3 ferroelectric thin film dependent on film thickness," in Applications of Ferroelectric and Workshop on the Piezoresponse Force Microscopy (ISAF/PFM), 2013 IEEE International Symposium on the, 2013.

[14] C. W. a. R. Ma, "Force induced phase transition of honeycomb-structured ferroelectric thin film," Physica A: Statistical Mechanics and its Applications, vol. 392, no. 17, pp. 3570 - 3577,

2013.

[15] I. B. Misirlioglu and M. Yildiz, "Very large dielectric response from ferroelectric nanocapacitor films due to collective surface and strain relaxation effects," Journal of Applied Physics, vol. 114,no. 19, p. 194101, 2013.

[16] "ABINIT.ORG," The ABINIT Group, [Online]. Available: http://www.abinit.org/.