The Pennsylvania State University

The Graduate School

College of Earth and Mineral Sciences

GROWTH OF NANOSCALE BaTiO3/SrTiO3 SUPERLATTICES BY

MOLECULAR-BEAM EPITAXY

A Thesis in

Materials Science and Engineering

by

Arsen Soukiassian

© 2007 Arsen Soukiassian

Submitted in Partial Fulfillment

of the Requirements

for the Degree of

Doctor of Philosophy

December 2007

The thesis of Arsen Soukiassian was reviewed and approved∗ by the following:

Xiaoxing Xi Professor of Physics and Materials Science and Engineering Thesis Co-Adviser Co-Chair of Committee Darrell G. Schlom Professor of Materials Science and Engineering Thesis Co-Adviser Co-chair of Committee Mark Horn Associate Professor of Engineering Science and Mechanics Long-Qing Chen Professor of Materials Science and Engineering Venkatraman Gopalan Professor of Materials Science and Engineering James P. Runt Professor of Polymer Science Associate Head for Graduate Studies Department of Materials Science and Engineering

∗Signatures are on file in the Graduate School.

ABSTRACT

The well known ferroelectric BaTiO3 was confined within nanoscale

BaTiO3/SrTiO3 superlattices to investigate the importance of finite size and strain on its

ferroelectric properties, especially the paraelectric-to-ferroelectric transition temperature

(TC). The BaTiO3/SrTiO3 superlattices were grown by reactive molecular-beam epitaxy

(MBE) on three different substrates: TiO2-terminated (001) SrTiO3, (101) DyScO3, and

(101) GdScO3. With the aid of reflection high-energy electron diffraction (RHEED),

precise single-monolayer doses of BaO, SrO, and TiO2 were deposited sequentially to

create commensurate BaTiO3/SrTiO3 superlattices with a variety of periodicities. X-ray

diffraction (XRD) measurements exhibit clear superlattice peaks at the expected positions

for the targeted superlattices. XRD rocking curve measurements of the BaTiO3/SrTiO3

superlattices grown on (101) DyScO3 and (101) GdScO3 substrates exhibit full width at

half maximum (FWHM) of 9 and 7 arc sec, respectively, the narrowest ever reported for

any oxide superlattices grown by any technique. High-resolution transmission electron

microscopy (HRTEM) reveals nearly atomically abrupt BaTiO3/SrTiO3 interfaces.

Temperature-dependent ultraviolet (UV) Raman and XRD reveal the TC in these

superlattices. Ferroelectricity was observed in BaTiO3/SrTiO3 superlattices containing as

few as one BaTiO3 layer in the repeated superlattice structural unit, i.e., a BaTiO3 layer

just 4 Å thick. The combination of finite size and strain effects was seen to shift the TC

over a 500 K range. Unstrained SrTiO3 layers in commensurate BaTiO3/SrTiO3

superlattices grown on SrTiO3 substrate are poled by the neighboring ferroelectric

BaTiO3 layers, while strained SrTiO3 layers in BaTiO3/SrTiO3 superlattices grown on

DyScO3 and GdScO3 substrates are not only polar, but also exhibit strain-induced

iii

ferroelectricity.

In addition to probing finite size and strain effects, these heterostructures may be

relevant for novel phonon devices, including mirrors, filters, and cavities for coherent

phonon generation and control. The concept and design of acoustic Bragg mirrors and

cavities made of BaTiO3/SrTiO3 superlattices with superior acoustic performance and

potential applications in electronic and optical THz modulators are described. We have

observed folded acoustic phonons at the expected frequencies using UV Raman

spectroscopy. Our results demonstrate the feasibility to design, fabricate, and characterize

oxide acoustic devices and may be considered as a first step towards a phonon “laser.”

iv

TABLE OF CONTENTS List of Tables…………………………………………………………………………….vi List of Figures…………………………………………………………………………vii Acknowledgements……………………………………………………………………xvii Chapter 1: Introduction…………………………………………………………………1 Chapter 2: Background.…………………………………………………………………3

2.1 Ferroelectric BaTiO3/SrTiO3 superlattices..............................................................3 2.2 Molecular-Beam Epitaxy.......................................................................................15 2.3 Raman Spectroscopy..............................................................................................19 2.4 Phonon “laser”.......................................................................................................25

References..............................................................................................................29 Chapter 3: Epitaxial growth of BaTiO3/SrTiO3 superlattices by MBE......................33

3.1 Introduction……………………………………………………………………....36 3.2 Experimental……………………………………………………………………38 3.3 Results and discussion…………………………………………………………43 3.4 Conclusions………………………………………………………………………53

References….……………………………………………………………….....…55 Chapter 4: Acoustic Bragg mirrors and cavities made using piezoelectric oxides....83

References……………………………………………………………………………96 Chapter 5: Conclusions and Future Work..……..……………………………………99

Conclusions..................................................................................................................99 Future work................................................................................................................101 References..................................................................................................................105

Appendix A. Practical aspects of the growth of BaTiO3/SrTiO3 superlattices by reactive MBE..................................................................................................................106

A.1. Substrate preparation..........................................................................................106 A.2. Structural characterization of BaTiO3/SrTiO3 superlattices by four-circle x-ray diffraction...................................................................................................................108 A.3. Mathematica code for the calculation of the lattice parameters and error bars.............................................................................................................................117 References..................................................................................................................121

Appendix B. Details on the growth attempts of BaO/SrTiO3 superlattices..............122

v

List of Tables

Table I. Structural parameters and TC of [(BaTiO3)n/(SrTiO3)m]p superlattices studied in

this work. Here n is the BaTiO3 thickness in unit cells, m is the SrTiO3 thickness in unit

cells, and p is the number of periods. For the samples grown on (101) DyScO3 and (101)

GdScO3 substrates, the measured pseudocubic lattice constant ap is shown in

parentheses.........................................................................................................................59

vi

List of Figures

Fig. 2.1.1 Phase transitions in bulk BaTiO3 and direction of the polarization vector P......4

Fig. 2.1.2 Temperature and frequency dependence of dielectric permittivity of

BaxSr1-xTiO3 single crystals for x = 0.05, 0.10, 0.20, 0.35, and 0.50. The maximums of

dielectric permittivity are near TC. (From Ref. 8)................................................................5

Fig. 2.1.3. Phase diagram of the BaTiO3 film as a function of temperature and substrate

in-plane strain. The letters T, O, and M indicate tetragonal, orthorhombic, and monoclinic

phases, respectively. Superscripts P and F indicate paraelectric and ferroelectric nature of

the phases, respectively. M + O implies a mixture of M and O phases. The

components of the polarization vector P corresponding to the phases (along the

crystallographic directions of pseudocubic BaTiO

F1

F2

F1

F2

3) are indicated within the parentheses

following the phase notation (from Ref. 38)........................................................................9

Fig. 2.1.4. Phase diagram of the single-domain SrTiO3 film as a function of temperature

and substrate in-plane strain. Nomenclature identical to that of Figure 2.1.3 is used to

describe the crystallographic symmetry of the phases and order parameters (from Ref.

38)......................................................................................................................................10

Fig. 2.1.5. Polarization enhancement computed from first principles as a function of

α = ℓSr/ℓBa for each BaTiO3/SrTiO3 superlattice (filled circles), where ℓSr and ℓBa are the

number of layers of SrTiO3 and BaTiO3, respectively (from Ref. 39)..............................12

Fig. 2.1.6. Variations of [001] and [110] components and magnitude of local polarization

Plocal in BaTiO3/SrTiO3 superlattices (from Ref. 40).........................................................13

Fig. 2.2.1 Schematic of reactive MBE system devoted to the growth of oxides (from A.

Schmehl)............................................................................................................................18

vii

Fig. 2.3.1. Schematic diagram of the Raman scattering process. .....................................19

Fig. 2.3.2. Forward scattering (a) and backscattering (b) geometry of the Raman

measurements.....................................................................................................................20

Fig. 2.3.3. Temperature evolution of Raman spectra of the BaTiO3 single crystal

measured in parallel polarization geometry. Red arrows are guides to eye. (from Ref.

61)......................................................................................................................................22

Fig. 2.3.4. Schematic of the band structure, light absorption, and penetration depth of

light in SrTiO3 as compared to the energies of the visible and UV photons. Strong

absorption, small penetration depth, and strong resonance enhancement make UV Raman

spectroscopy ideal for studying very thin ferroelectric films (from D.

Tenne)................................................................................................................................24

Fig. 2.4.1 Scheme of an acoustic cavity within an optical cavity (from reference 76). Here

layers of two materials having different optical refractive indices (e.g. AlAs/Al0.8Ga0.2As)

are arranged to form Bragg mirrors for photons separated by mλlight/2 thick layer forming

an optical Fabry-Perot resonator. Inside the optical cavity, an acoustic cavity is placed,

consisting of two superlattices designed to make Bragg reflectors for acoustic phonons,

separated by mλsound/2 thick layer......................................................................................28

Fig. 3.1. Timing diagram of the sequential deposition of barium, strontium, and titanium

during the growth of two periods of a (BaTiO3)8/(SrTiO3)4 superlattice (sample #14).

Oxygen is provided continuously during the growth.........................................................60

Fig. 3.2. RHEED patterns during the growth of a [(BaTiO3)8/(SrTiO3)4]40 superlattice

(sample #14) on a TiO2-terminated (001) SrTiO3 substrate. RHEED patterns viewed

along the [100] azimuth (a) with the substrate at room temperature prior to growth and (c)

viii

at Tsub = 650 ºC during the growth (end of the titanium dose during a SrTiO3 layer).

RHEED patterns along the [110] azimuth (b) with the substrate at room temperature prior

to the growth and (d) at Tsub = 650 ºC during the growth (end of the strontium dose during

a SrTiO3 layer). The white boxes show the region containing the 00 and 01 streaks that

was monitored during growth to establish the time evolution of the RHEED streaks

(shuttered RHEED oscillations).........................................................................................61

Fig. 3.3. Shuttered RHEED intensity oscillations observed during the growth of a

[(BaTiO3)8/(SrTiO3)4]40 superlattice (sample #14). The RHEED beam was incident along

the [110] azimuth during growth. Three periods of [(BaTiO3)8/(SrTiO3)4]40 superlattice

growth are shown. The average diffracted intensity in the regions shown in Fig. 2(d) of

the 00 streak (top) and 01 streak (bottom) were recorded simultaneously. Dashed lines

show the boundaries of the (BaTiO3)8 and (SrTiO3)4 sections of the superlattice.............62

Fig. 3.4. (a) An AFM image of a TiO2-terminated (001) SrTiO3 substrate prepared using

the method described in Ref. 15. The AFM scan extends over 4×4 µm with a height range

of 0.5 nm from black to white. (b) A horizontal line-scan across (a) reveals well-defined

single-layer steps each ~0.39 nm in height........................................................................63

Fig. 3.5. The shuttered RHEED intensity oscillation observed from the beginning of the

growth of a [(BaTiO3)4/(SrTiO3)2]40 superlattice (sample #14) on a non-terminated (001)

SrTiO3 substrate. The intensity of the 01 RHEED streak along the [110] azimuth for the

first three superlattice periods is shown.............................................................................64

Fig. 3.6. The shuttered RHEED intensity oscillation observed from the beginning of the

growth of a [(BaTiO3)6/(SrTiO3)13]15 superlattice (sample #12) on a TiO2-terminated

(001) SrTiO3 substrate. The intensity of the 01 RHEED streak along the [110] azimuth of

ix

the first superlattice period is shown.................................................................................65

Fig. 3.7. The shuttered RHEED intensity oscillation observed from the beginning of the

growth of a [(BaTiO3)8/(SrTiO3)4]40 superlattice (sample #17) on a (101) GdScO3

substrate. The intensity of the 01 RHEED streak along the [110] azimuth for the first two

superlattice periods is shown.............................................................................................66

Fig. 3.8. RHEED patterns during the growth of a [(BaTiO3)8/(SrTiO3)4]40 superlattice

(sample #17) on a (101) GdScO3 substrate at Tsub = 650 ºC. RHEED patterns viewed

along the [100] pseudocubic azimuth (a) of the bare substrate prior to growth and (c)

during the growth (end of the titanium dose during a SrTiO3 layer). RHEED patterns

along the [110] pseudocubic azimuth (b) of the bare substrate prior to the growth and (d)

during the growth (end of the titanium dose during a SrTiO3 layer). The white boxes

show the recorded area of the 01 superlattice streak.........................................................67

Fig. 3.9. RHEED patterns of bare (101) DyScO3 substrates at Tsub = 650 ºC prior to

growth. RHEED patterns viewed along the [100] pseudocubic azimuth (a) of a non-

terminated substrate and (c) a terminated substrate. RHEED patterns along the [110]

pseudocubic azimuth (b) of a non-terminated substrate and (d) a terminated substrate....68

Fig. 3.10. The shuttered RHEED intensity oscillation observed from the beginning of the

growth of a [(BaTiO3)8/(SrTiO3)4]40 superlattice on a non-terminated (a) and terminated

(b) (101) DyScO3 substrate. The intensity of the 01 RHEED streak along the [110]

azimuth of the first superlattice period is shown...............................................................69

Fig. 3.11. θ – 2θ x-ray diffraction scans of the [(BaTiO3)n/(SrTiO3)m]p superlattices using

Cu Kα radiation for m = 4 and n = 1, 2, 3, 4, 5, 6, and 8 (samples #1−7). Substrate peaks

are marked with asterisks (*). Nearly all superlattice peaks are present for 2θ < 55°,

x

indicating atomically sharp interfaces between the BaTiO3 and SrTiO3 layers and

accurate superlattice periodicity........................................................................................70

Fig. 3.12. θ – 2θ x-ray diffraction scans of the [(BaTiO3)n/(SrTiO3)m]p superlattices using

Cu Kα radiation for m = 13 and n = 1, 2, and 3 (samples #8−10). Substrate peaks are

marked with asterisks (*). Nearly all superlattice peaks are present for 2θ < 55°,

indicating atomically sharp interfaces between the BaTiO3 and SrTiO3 layers and

accurate superlattice periodicity........................................................................................71

Fig. 3.13. An x-ray diffraction φ scan at χ = 44.3º of the 1012 peak of the

[(BaTiO3)8/(SrTiO3)4]40 superlattice (sample #14) grown on a (001) SrTiO3 substrate.

χ = 90º aligns the diffraction vector to be perpendicular to the plane of the substrate.

φ = 0° corresponds to when the in-plane component of the diffraction vector is parallel to

the [100] in-plain direction of the substrate. This scan shows that the superlattice is

epitaxial with the expected ([100] superlattice || [100] substrate) in-plane alignment with

the substrate.......................................................................................................................72

Fig. 3.14. (a) Rocking curves of the [(BaTiO3)3/(SrTiO3)4]35 superlattice 0014 peak and

the underlying SrTiO3 substrate 002 peak (sample #3). The FWHM is 21 arc sec

(0.0058°) for the superlattice peak as compared to 20 arc sec (0.0055°) for the substrate

peak. The sharp rocking curve indicates the high structural perfection of the superlattice.

(b) Rocking curves of the [(BaTiO3)2/(SrTiO3)4]40 superlattice 0012 peak and the

underlying SrTiO3 substrate 002 peak (sample #2). The FWHM is 62 arc sec (0.0172°)

for the superlattice peak as compared to 61 arc sec (0.0169°) for the substrate peak

having a strongly mosaic feature.......................................................................................73

Fig. 3.15. (a) A cross-sectional HRTEM image of the partially relaxed

xi

[(BaTiO3)8/(SrTiO3)4]40 superlattice grown on a (001) SrTiO3 substrate (sample #14)

showing threading dislocation. (b) Z-contrast TEM over a larger area of the same

[(BaTiO3)8/(SrTiO3)4]40 superlattice (sample #14). The threading dislocations are the light

vertical defects, some of which are labeled with arrows...................................................75

Fig. 3.16. (a) A cross-sectional HRTEM image of the [(BaTiO3)1/(SrTiO3)13]20

superlattice (sample #8). It shows alternating layers of 1 unit cell of BaTiO3 and 13 unit

cells of SrTiO3, confirming the intended superlattice periodicity and the XRD result. (b)

Z-contrast HRTEM image of the [(BaTiO3)1/(SrTiO3)4]50 superlattice (sample #1). The

interfaces are abrupt and no misfit dislocations were seen................................................76

Fig. 3.17. XRD scans of the [(BaTiO3)8/(SrTiO3)4]40 superlattice grown on (101) DyScO3

substrate (sample #16) (a) shows a θ – 2θ scan. Substrate peaks are marked with asterisks

(*). Nearly all superlattice peaks are present for 2θ < 55°, indicating atomically sharp

interfaces between BaTiO3 and SrTiO3 layers and accurate periodicity. (b) The in-plane

orientation relationship between the [(BaTiO3)8/(SrTiO3)4]40 superlattice and the (101)

DyScO3 substrate was determined by a φ-scan at χ = 45° of the 1012 superlattice peak.

φ = 0° corresponds to when the in-plane component of the diffraction vector is parallel is

aligned parallel to the [010] in-plane direction of the DyScO3 substrate. (c) Rocking

curves of the same [(BaTiO3)8/(SrTiO3)4]40 superlattice and the underlying DyScO3

substrate FWHM of 9 arc sec (0.0024°) for the superlattice 0024 peak and FWHM of 8

arc sec (0.0022°) for the 202 peak of the DyScO3 substrate were measured....................77

Fig. 3.18. XRD scans of the [(BaTiO3)8/(SrTiO3)4]40 superlattice grown on (101) GdScO3

substrate (sample #17) (a) shows a θ – 2θ scan. Substrate peaks are marked with asterisks

(*). Nearly all superlattice peaks are present for 2θ < 55°, indicating atomically sharp

xii

interfaces between BaTiO3 and SrTiO3 layers and accurate periodicity. (b) The in-plane

orientation relationship between the [(BaTiO3)8/(SrTiO3)4]40 superlattice and the (101)

GdScO3 substrate was determined by a φ-scan at χ = 42.09º of the 1011 superlattice

peak. φ = 0° corresponds to when the in-plane component of the diffraction vector is

parallel to the [010] in-plain direction of the GdScO3 substrate. (c) Rocking curves of the

[(BaTiO3)8/(SrTiO3)4]40 superlattice. FWHM of 7 arc sec (0.0020°) for the superlattice

0024 peak and FWHM of 7 arc sec (0.0019°) for the 202 peak of the GdScO3 substrate

were measured...................................................................................................................79

Fig. 3.19. Temperature dependence of the lattice constants of the (a) commensurate

[(BaTiO3)8/(SrTiO3)4]10 superlattice (sample #7), (b) partially relaxed

[(BaTiO3)8/(SrTiO3)4]40 superlattice (sample #14), and SrTiO3 substrate, measured by

XRD...................................................................................................................................81

Fig. 3.20. A summary plot of the TC obtained from UV Raman measurements. (a) Shows

the dependence of TC on n and m in [(BaTiO3)n/(SrTiO3)m]p superlattices grown on (001)

SrTiO3 substrates. Solid triangles are for m = 4, solid squares are for m = 13, and the open

diamond symbol is for m = 30. Open circles are from temperature-dependent XRD

measurements. Lines are from three-dimensional phase-field model calculations for m = 4

and m = 13 and the horizontal dash-dotted line shows the TC of bulk (unstrained) BaTiO3.

(b) dependence of TC on the mismatch strain ε on the BaTiO3 layers in the superlattices

with the same [(BaTiO3)8/(SrTiO3)4]p structure grown on (001) SrTiO3, (101) DyScO3,

and (101) GdScO3 substrates (samples #7, 16, 17)...........................................................82

Fig. 4.1. Top: Calculated acoustic reflectivity as a function of phonon energy (left) and

square of phonon displacement along the growth axis z as a function of the distance into

xiii

the mirror (right) for phonon mirrors consisting of a superlattice of (001)-oriented

BaTiO3/SrTiO3 layers repeated 10 times. Bottom: Calculated acoustic reflectivity as a

function of phonon energy (left) and square of phonon displacement along the growth

axis z as a function of the distance from the surface of the top mirror (right) for 2λ

acoustic cavities enclosed by the superlattice phonon mirrors with 10 repeats shown in

the top panel. The increasing curve thicknesses correspond to BaO/SrTiO3,

BaTiO3/SrTiO3, and GaAs/AlAs, respectively. A schematic of the structure for the

specific case of BaTiO3/SrTiO3 is shown..........................................................................88

Fig. 4.2. X-ray diffraction scans of a [(BaTiO3)8/(SrTiO3)4]40 superlattice. (a) θ-2θ x-ray

diffraction scan. Substrate peaks are marked by asterisks (*). (b) X-ray diffraction φ-scan

of the 1012 peak [(BaTiO3)8/(SrTiO3)4]40 superlattice taken at χ = 44.3°. In this scan φ

= 0° is aligned parallel to the [100] in-plane direction of the substrate and χ = 90° aligns

the diffraction vector to be perpendicular to the plane of the substrate.............................91

Fig. 4.3. Cross-sectional HRTEM image of a [(BaTiO3)8/(SrTiO3)4]40 superlattice grown

on a (001) SrTiO3 substrate................................................................................................92

Fig. 4.4. Bottom: Folded acoustic phonon modes measured by uv Raman scattering (E) in

comparison with a photoelastic model calculation of the Raman efficiency (T). Top:

Folded acoustic phonon dispersion obtained with a continuum Rytov model. The

horizontal dashed line indicates the wavevector q transferred in the Raman scattering

process................................................................................................................................95

Fig. A.2.1. Schematic of Bragg condition. If the difference in the path length of each

wave is equal to an integer multiple n of the wavelength λ, the reflected waves remain in

phase and will interfere constructively. The path difference ABC is equal to 2dsinθ, thus

xiv

diffraction maxima will appear if nλ = 2dsinθ (from www.bmsc.washington.edu)........112

Fig. A.2.2. Calculation of the out-of-plane superlattice parameter dS and error bar from

the Nelson-Riley plot for the two [(BaTiO3)1/(SrTiO3)4]50 superlattices grown on (001)-

oriented SrTiO3 substrate (samples A128 and A132). (a) Combined θ – 2θ plot of

samples A128 (blue line) and A132 (red line). (b) Combined Nelson-Riley plot of A128

(blue squares) and A132 (red circles) samples................................................................113

Fig. A.2.3. Lorenzian fit used for more accurate determination of the 2θ value of the 006

peak of sample A132, a [(BaTiO3)1/(SrTiO3)4]50 superlattice.........................................114

Fig. A.2.4. Rocking curves of the [(BaTiO3)8/(SrTiO3)4]40 superlattice grown on a (101)-

oriented SmScO3 substrate revealing the asymmetry in the FWHM of the peaks in ω for

rocking curves taken along the in-plane [010] (φ = 90º) and [ 1 01] (φ = 0º)

directions..........................................................................................................................115

Fig. A.2.5. Off-axis θ – 2θ scan at χ = 45º of the [(BaTiO3)8/(SrTiO3)4]40 superlattice

grown on a (101) SmScO3 substrate. The 121 SmScO3 substrate peak is marked with an

asterisk (*)........................................................................................................................116

Fig. B.1. θ – 2θ scan of a [(BaTiO3)2/SrTiO3)13]20 superlattice grown on a (001) SrTiO3

substrate with the shuttered growth sequence shown on the right...................................124

Fig. B. 2. (a) A cross-sectional HRTEM image of the sample A69 showing that

superlattice have alternating layers of 2 unit cells of BaTiO3 and 13 unit cells of SrTiO3.

(b) A cross-sectional HRTEM image of the sample A49 showing that superlattice have

layers consisting of a mixture of rack-salt BaO and perovskite BaTiO3 separated by 13

unit cells of SrTiO3..........................................................................................................125

xv

Fig.B.2 θ – 2θ scan of a [(BaTiO3)2+(BaO)1ML/SrTiO3)13]20 superlattice grown on a (001)

SrTiO3 substrate with the shuttered growth sequence shown on the right......................126

Fig. B.3. RHEED patterns along the [110] azimuth after the deposition of four

monolayers of BaO (a) and that observed after adding one monolayer of TiO2 on top of

the BaO (b). The decrease in the RHEED intensity and the presence of the 3D spots

indicate the roughening of the surface.............................................................................127

Fig. B.4. combined plot of θ – 2θ scans of [(BaO)2ML/SrTiO3)13]20,

[(BaO)3ML/SrTiO3)13]20, and [(BaO)4ML/SrTiO3)13]20 superlattices grown on (001) SrTiO3

substrate with the shuttered growth sequence shown on the right...................................128

xvi

Acknowledgements

This work would not have been possible without love and support from my family

and friends. Especially I would like to thank Deborah Van Vechten and Armen Gulian

for helping me to begin my work at Penn State University. Their trust and support was

very important for me.

I would like to thank my advisers, Xiaoxing Xi and Darrell G. Schlom, for giving

me the unique opportunity to study and work in one of the world’s leading research

groups in the field of epitaxial thin film synthesis and characterization. Their constant

support and guidance was a key factor in the progress of my work.

During my stay at Penn State University I have strongly benefited working with

and learning from many exceptional people. Particularly I would like to thank Dmitri

Tenne for mentoring me and introducing me to the Raman spectroscopy, Ruyan Guo for

introducing me to the ferroelectric ceramic synthesis and single crystal laser heated

pedestal growth technique during my work in her lab, Xianghui Zeng for sharing with me

his vast experience in pulsed laser deposition technique, James Lettieri for introducing

me to the structural characterization of the thin films by x-ray diffraction, as well as Mike

Biegalski, Jeff Haeni, Venugopalan Vaithyanatan, Jürgen Schubert, Wei Tian, Tassilo

Heeg, and Andreas Schmehl for sharing their experience and helping me during my work

on the reactive molecular-beam epitaxy system. I should thank all the members of our

group for creating a relaxing and friendly atmosphere in the lab which made my work

and study at Penn State University enjoyable.

The work presented in this thesis is a result of successful collaborations with a

large number of research groups from many countries. These collaborators are listed as

xvii

coauthors on the papers in this thesis. I am grateful to them for their vital contribution to

my thesis. In particular I would like to thank Prof. Alex Fainstein from Argentina, who

inspired us with the idea of using oxide ferroelectric superlattices for novel acoustic

phonon devices. His group calculated the structures for all THz acoustic Bragg mirrors

and cavities presented in this thesis. In addition, they measured Raman spectra on the

superlattices that I grew, along with Dmitri Tenne. I also thank Prof. Andres Cantarero

from Spain and Prof. Ram Katiyar from Puerto Rico for providing their UV Raman

systems and helping during the Raman measurements. I am grateful to Prof. Long-Qing

Chen’s group at Penn State University and Karin Rabe’s group at Rutgers University that

made the thermodynamic and first principle calculations, respectively. I thank Prof.

Xiaoqing Pan's group at the University of Michigan for doing all of the TEM work

presented in this thesis. I thank Prof. Chang-Beom Eom’s group at University of

Wisconsin for temperature-dependence x-ray diffraction measurements and Prof. Randall

Feenstra’s group at Carnegie Mellon University for the AFM measurements.

I also thank the NSF for financial support of this work.

xviii

Chapter 1

Introduction

Oxides, in particular those of perovskite structure, exhibit a large variety of

electronic properties such as: dielectric, ferroelectric, ferromagnetic, semiconducting,

superconducting, and colossal magneto-resistive behavior. Perovskites are important

materials for electronic devices and have a huge potential for new device applications.

Bulk properties of ferroelectric perovskites were extensively studied since the discovery

of ferroelectricity in BaTiO3 in 1940’s, the beginning of the “Perovskite Era”. However,

the constant research efforts to improve the performance and efficiency of ferroelectric

devices move the forefront to the ferroelectrics at nanoscale. During the last decade the

large number of theoretical and experimental research publications on thin-film

ferroelectrics revealed that the boundary conditions applied on thin commensurate films

are responsible for the drastic differences in the properties of thin ferroelectric films

compared to those in the bulk. Heterostructures, such as BaTiO3/SrTiO3 superlattices, are

particularly interesting both for their applications and for probing the ferroelectricity.

Theoretical studies of the BaTiO3/SrTiO3 superlattices predict that these superlattices can

have improved physical properties compared to its bulk constituents. However, testing

these predictions requires growth of commensurate BaTiO3/SrTiO3 superlattices with

high degree of structural perfection and interface abruptness at atomic scale.

This thesis is focused on the growth of nanoscale BaTiO3/SrTiO3 superlattices by

means of molecular-beam epitaxy (MBE) with sufficiently high quality in terms of

crystallinity and interface abruptness required both for probing the ferroelectricity and for

using these superlattices in novel phonon devices. Effects of strain, size, and interface on

1

ferroelectric properties, as well as information on lattice dynamics of BaTiO3/SrTiO3

superlattices are primary interest in this work.

The organization of this thesis is described as follows: Chapter 2 is a background

chapter and contains four sections. The first section is a review of experimental and

theoretical studies of BaTiO3/SrTiO3 superlattices. The second section describes the

reactive MBE, the deposition technique used for the growth of nanoscale BaTiO3/SrTiO3

superlattices in this work. In the third section I give a background on Raman

spectroscopy, an important characterization tool used both for probing the ferroelectricity

and for testing acoustic phonon devices. The last section of Chapter 2 is a review of

research efforts made towards a phonon “laser.” Chapter 3 describes in detail the growth

of nanoscale BaTiO3/SrTiO3 superlattices by reactive MBE and discusses the obtained

results from temperature-dependent ultraviolet Raman spectroscopy and X-ray

diffraction. In addition to the probing of ferroelectricity, BaTiO3/SrTiO3 superlattices

may be relevant for novel phonon devices operating at terahertz frequencies with superior

acoustic performance. The design and important material parameters of acoustic Bragg

mirrors and cavities made of BaTiO3/SrTiO3 and BaO/SrTiO3 superlattices are described

in Chapter 4. Chapter 5 concludes this work with the summary of the results and

describes the future work that could be performed to further improve the understanding

of the fundamental properties of ferroelectric BaTiO3/SrTiO3 superlattices and to move

on to the next step toward a phonon “laser.”

2

Chapter 2

Background

2.1 Ferroelectric BaTiO3/SrTiO3 superlattices.

A ferroelectric BaTiO3/SrTiO3 superlattice is an artificially synthesized multilayer

structure that consists of alternating layers of BaTiO3 and SrTiO3. Here BaTiO3 is a

ferroelectric material, while SrTiO3 is an incipient ferroelectric. By definition

ferroelectrics are polar materials that have at least two equilibrium orientations of the

spontaneous polarization switchable by an external electric field. In ferroelectrics electric

dipoles form domains, regions of homogeneous polarizations that differ only in the

direction of the polarization. These domains can be reoriented by the electric field and are

separated by domain walls, which can be atomically thin. Most ferroelectrics undergo a

structural phase transition from the ferroelectric phase into a paraelectric phase, and the

transition temperature is called the Curie point, (TC). BaTiO3 has a simple cubic

perovskite structure Pm3m (space group # 221) and lattice constant a = 4.05 Å. It

undergoes three phase transitions as shown in Figure 2.1.1. The Ba2+ ions (blue balls) are

located at the corners of the unit cell, the O2- ions (red balls) are at the centers of the six

planes of the unit cell, and Ti4+ ion (green ball) is in the center of the unit cell. The

paraelectric-to-ferroelectric transition occurs at TC around 403 K, when its perovskite

structure changes from the cubic paraelectric phase to a ferroelectric tetragonal phase. A

permanent ionic dipole moment in ferroelectric phases results from the displacement of

the O2- and Ti4+ ions from their symmetrical positions. The magnitude and direction of

the spontaneous polarization is a result of interactions between adjacent permanent

3

dipoles in BaTiO3.

Cubic Tetragonal Orthorhombic RhombohedralT > 403 K 403 K > T > 278 K 278K > T > 183 K T < 183 K

P ll ⟨001⟩ P ll ⟨011⟩ P ll ⟨111⟩ P = 0

Fig. 2.1.1 Phase transitions in bulk BaTiO3 and direction of the polarization vector P.

The SrTiO3 is an insipient ferroelectric that undergoes a structural phase transition

from cubic to tetragonal at 105 K. In tetragonal phase the O2- ions rotated around Ti4+ ion

which doubles the periodicity of the lattice, since the O2- ions rotate in opposite directions

in the neighboring cells. However SrTiO3 has no TC at any temperature since the

ferroelectric transition is completely suppressed by the quantum fluctuations. 1

Chemical2,3 or isotopic4 substitution, applied electric fields,5,6 as well as strain7 can make

SrTiO3 ferroelectric.

The temperature dependence of dielectric constant in ferroelectrics described by

the Curie-Weiss Law: ε(T) = C/(T-TC), where C is the Curie-Weiss constant. At T = TC

one can expect a very large dielectric permittivity. The large dielectric permittivity near

TC is important for thin film devices. Furthermore, by applying the electric fields one can

reduce the dielectric constant, known as the dielectric nonlinearity, which is important for

tunable microwave devices.

4

One of the most common methods to achieve the large dielectric permittivity at

desired temperature is the BaxSr1-xTiO3 solid solution. By changing the ratio of Ba and Sr

one can change the TC of the BaxSr1-xTiO3 from 0 to 403 K. As an example, Figure 2.1.2

shows the temperature and frequency dependence of dielectric permittivity of (110)-

oriented BaxSr1-xTiO3 single crystal fibers for x = 0.05, 0.10, 0.20, 0.35, and 0.50.8

50 100 150 200 250 3000

5000

10000

15000

20000

0.50

0.35

0.20

0.10

ε/ε o

Temperature (K)

100Hz 1kHz 10kHz 100kHz 1MHz

0.05

Fig. 2.1.2 Temperature and frequency dependence of dielectric permittivity of

BaxSr1-xTiO3 single crystals for x = 0.05, 0.10, 0.20, 0.35, and 0.50. The maximums of

dielectric permittivity are near TC. (From Ref. 8)

Both BaTiO3 and SrTiO3 are members of perovskite family and have in-plane

lattice constant at room temperature of 3.992 Å and 3.905 Å, respectively, indicating that

5

a very high homogeneous mismatch strain of about ~2.3% can be realized in

commensurate BaTiO3/SrTiO3 superlattices grown on (001) SrTiO3 substrate. Relaxation

via misfit dislocations may occur if the critical thicknesses of the BaTiO3/SrTiO3

superlattice or individual BaTiO3 layers are exceeded. Defects and misfit dislocations in

starting-to-relax BaTiO3/SrTiO3 superlattices produce inhomogeneous strain that can

affect the properties of thicker superlattices. In order to preserve the homogeneous high-

strain state the BaTiO3/SrTiO3 superlattice must be grown on SrTiO3 substrate below its

critical thickness for relaxation and have BaTiO3 layer thickness less than 10 unit cells,

since the critical thickness for commensurate single BaTiO3 film grown on SrTiO3

substrate is about 10 unit cells (~40 Å).9 Decreasing the mismatch strain applied by the

underlying substrate will allow growing thicker homogeneously strained BaTiO3/SrTiO3

superlattices as in the case of BaTiO3/SrTiO3 superlattices grown on DyScO3 and

GdScO3 substrates described in Chapter 3.

In commensurate thin films and superlattices the boundary conditions in form of

effects of strain, size and interface play a crucial role in the property changes, which can

be used to manipulate the ferroelectric properties.10 For example, ferroelectricity in

BaTiO3 can be enhanced and SrTiO3 can become ferroelectric at room temperature in

thin films under ~1% strain,11, ,12 13 thin PbTiO3 films can remain ferroelectric down to 3

unit cells (~1.2 nm), 14 interface-induced changes in electronic structures can make

insulating layers of LaTiO3 and SrTiO3 metallic in nanoscale LaTiO3/SrTiO3

superlattices.15 Combinations of various important oxide materials such as superlattices

of PbTiO3/PbZrO3, 16 PbTiO3/SrTiO3, 17 KNbO3/KTaO3, 18 , ,19 20 CaMnO3/CaRuO3, 21

LaMnO3/SrMnO3, 22 , 23 LaAlO3/SrTiO324 , 25 as well as “tricolor” superlattices of

6

CaTiO3 3 3/SrTiO /BaTiO ,26,27 were studied and in all cases the boundary conditions play

important role in property changes.

Commensurate nanoscale BaTiO3/SrTiO3 superlattices can be a perfect prototype

for probing ferroelectricity and were extensively studied both theoretically and

experimentally over the last decade. In 1992, Iijima et al. were first to report the growth

of BaTiO3/SrTiO3 superlattices by reactive molecular beam epitaxy and the use of

RHEED intensity oscillations to monitor the growth.28 A rapidly growing number of

experimental studies of BaTiO3/SrTiO3 superlattices reported the enhancements of

dielectric constant, polarization, and dielectric nonlinearity, compared to the bulk

constituents and (Ba,Sr)TiO3 solid solution films.29-32 However, such reports must be

carefully evaluated since the enhancement of dielectric constant and polarization could

also be an artifact produced by carrier migration to interfaces and may be attributed to the

Maxwell–Wagner effect.33

Besides these experimental reports, theoretical studies first on BaTiO3 thin films

and later on BaTiO3 confined in BaTiO3/SrTiO3 superlattices have also been reported. In

1998, Pertsev et al. calculated the temperature-misfit strain phase diagrams of epitaxial

single-domain BaTiO3 and PbTiO3 films, two classical perovskite ferroelectrics.34 They

predicted drastic differences in thermodynamic properties of thin epitaxial films and bulk

crystals due to the effect of boundary conditions. In 2002, Zembilgotov et al. reported

theoretical studies of the mean polarization as a function of film thickness, temperature,

and misfit strain in BaTiO3 and PbTiO3 films.35 They predicted that TC can be shifted

from its bulk value both to higher and lower temperatures and it is governed by the

competing finite size and misfit strain effects. The most recent theoretical study on the

7

effect of biaxial strain on phase transitions and domain stability in BaTiO3 thin films by

phase-field simulation were reported by Li at al. 36 They constructed a phase-strain

diagram of BaTiO3 thin film based on their simulation results, adapted version of which

is shown in Figure 2.1.3.

A strain-phase diagram derived from thermodynamic analysis for single-domain

SrTiO3 thin films were reported by Li at. al.37 This diagram is shown in Figure 2.1.4,

indicating that room-temperature ferroelectricity in SrTiO3 thin films can be achieved if

sufficiently large tensile strain is applied. A more detailed review of various theoretical

approaches, including first-principle, thermodynamic analysis, and phase-field models

applied to the biaxially strained BaTiO3 and SrTiO3 films can be found in recent report

by Schlom at. al.38

8

Fig. 2.1.3. Phase diagram of the BaTiO3 film as a function of temperature and substrate

in-plane strain. The letters T, O, and M indicate tetragonal, orthorhombic, and monoclinic

phases, respectively. Superscripts P and F indicate paraelectric and ferroelectric nature of

the phases, respectively. M + O implies a mixture of M and O phases. The

components of the polarization vector P corresponding to the phases (along the

crystallographic directions of pseudocubic BaTiO

F1

F2

F1

F2

3) are indicated within the parentheses

following the phase notation (from Ref. 38).

9

Fig. 2.1.4. Phase diagram of the single-domain SrTiO3 film as a function of temperature

and substrate in-plane strain. Nomenclature identical to that of Figure 2.1.3 is used to

describe the crystallographic symmetry of the phases and order parameters (from Ref.

38).

10

In 2003, Neaton and Rabe studied the spontaneous polarization as a function of

composition in epitaxial nanoscale BaTiO3/SrTiO3 superlattices using first-principles

density functional theory. 39 They predicted that epitaxial nanoscale BaTiO3/SrTiO3

superlattices can have a polarization larger than bulk BaTiO3 due to the compressive

biaxial mismatch strain of ~2.2% applied by the underlying SrTiO3 substrate on the

BaTiO3 layers. Polarization enhancement in BaTiO3/SrTiO3 superlattices can be achieved

by maximizing the BaTiO3 layer thickness while preserving strain (Fig. 2.1.5.). They

predicted that BaTiO3/SrTiO3 superlattices having BaTiO3 layers as thin as one unit cell

(~4Å) can be ferroelectric. Also they found that unstrained SrTiO3 layers in

BaTiO3/SrTiO3 superlattices are tetragonal and polar and have a polarization nearly same

as BaTiO3 layers. In 2005, Johnston et al. reported similar theoretical calculations of

nanoscale BaTiO3/SrTiO3 superlattices, but with a mismatch strain of ~1% implying that

SrTiO3 layers are under tensile in-plane strain and BaTiO3 layers are under compressive

in-plane strain.40 They predicted that the value of polarization depends on the structure of

the superlattice and increases with increasing the BaTiO3 layer thickness. Meanwhile,

tensile strained SrTiO3 layers that are polarized by adjacent ferroelectric BaTiO3 layers

have also a polarization component along the [110] in-plane direction that increases with

increasing SrTiO3 layer thickness (Fig. 2.1.6). These theoretical studies shed light on the

ferroelectric properties of epitaxial BaTiO3/SrTiO3 superlattices and inspired us to test

these predictions experimentally.

11

Fig. 2.1.5. Polarization enhancement computed from first principles as a function of

α = ℓSr/ℓBa for each BaTiO3/SrTiO3 superlattice (filled circles), where ℓSr and ℓBa are the

number of layers of SrTiO3 and BaTiO3, respectively (from Ref. 39).

12

Fig. 2.1.6. Variations of [001] and [110] components and magnitude of local polarization

Plocal in BaTiO3/SrTiO3 superlattices (from Ref. 40).

13

In the experimental reports mentioned above various deposition techniques such

as MBE, pulsed laser deposition, metal organic chemical vapor deposition, and thermal

evaporation were used to grow BaTiO3/SrTiO3 superlattices claiming good structural

quality. However, lack of convincing evidence on high degree of structural perfection and

interface abruptness made accuracy of most reports of measured BaTiO3/SrTiO3

superlattice properties questionable. In order to better understand the changes in the

fundamental properties of BaTiO3/SrTiO3 superlattices and measure more accurately

effects of strain, size and interface, one will need to grow high quality commensurate

superlattices free of defects and dislocations with abrupt interfaces at the atomic scale.

This remains a challenging task since for the growth of high quality superlattices not only

the stoichiometry of the film must be controlled but also exact monolayers of each

material must be deposited in sequential manner in order to maintain the interface

abruptness at the atomic scale. Nevertheless, remarkably high quality commensurate

nanoscale BaTiO3/SrTiO3 superlattices with atomically abrupt interfaces can be

synthesized by means of reactive MBE and were recently reported.41 Encouraged by

these results and eager to test the theoretical predictions of strain-induced polarization

enhancement, we began to study epitaxial nanoscale BaTiO3/SrTiO3 superlattices grown

on SrTiO3 substrate by ultraviolet (UV) Raman spectroscopy.42 We have observed that

one-unit-cell-thick BaTiO3 layer is ferroelectric and SrTiO3 becomes polar in

BaTiO3/SrTiO3 superlattices as theoretically predicted. Also TC in commensurate

nanoscale BaTiO3/SrTiO3 superlattices can be tuned by ~500 K by just varying the

BaTiO3 and SrTiO3 layer thicknesses.42 The summary of these results as well as the data

obtained on BaTiO3/SrTiO3 superlattices grown on DyScO3 and GdScO3 substrates can

14

be found in Chapter 3.

2.2 Molecular-Beam Epitaxy.

In this thesis reactive molecular-beam epitaxy (MBE) was used to deposit

nanoscale BaTiO3/SrTiO3 superlattices. The main advantage of MBE lies in the

capability to control the deposition of films on an atomic scale, unsurpassed by any other

thin film growth techniques. MBE was initially developed for the growth of compound

semiconductor structures of GaAs and GaAs/AlGaAs in the end of 1960’s.43,44 It uses

thermal evaporation of high purity elemental sources in a high-vacuum environment to

generate atomic or molecular fluxes of constituent materials (molecular beams) that react

at the substrate to form an ordered overlayer (epitaxy). The composition of the growing

epilayers depends on the relative arrival rates of constituent materials. Shutters located in

front of the sources are used to interrupt the molecular beams resulting in abrupt changes

in composition on an atomic scale. Since MBE deposition takes place in the high-

vacuum environment, the growth can be carried out far from thermodynamic equilibrium

at relatively low growth temperatures, which allows synthesizing layered metastable

materials and superlattices. The MBE high-vacuum growth environment permits the

simultaneous use of surface sensitive characterization techniques such as reflection high-

energy electron diffraction (RHEED), Auger electron spectroscopy (AES), x-ray

photoemission spectroscopy (XPS), scanning electron microscopy (SEM), ellipsometry,

and so on. The instrumental development over last decades made MBE a powerful and

versatile growth technique for wide variety of materials. The major milestones in the

development of MBE that directly impacted my growth of BaTiO3/SrTiO3 superlattices

15

include the use of MBE for growth of high temperature superconducting oxide films, the

beginning of oxide MBE era,45,46 as well as the first use of RHEED to establish the

growth conditions47 and first observation of RHEED intensity oscillations during growth

of GaAs.48

There are several differences between oxide MBE systems and conventional ones.

First, the high temperature components (e.g. heater filaments, crucibles, and substrate

holders) must be made of materials that are resistive to the oxidant. Second, the oxidizing

agent must be introduced in a way to prevent its degradation. Third, adequate pumping is

required in order to handle the oxidant gas load. A major problem in the growth of oxides

by reactive MBE is to provide sufficient oxygen during the growth to form the desired

structure. The typical distance between the substrate and the source in MBE is ~20 cm.

To maintain such a long mean free path the O2 pressure must be lower than 2×10-4 Torr.

Thus utilization of more reactive oxidant species such as ozone and atomic oxygen can be

vital to reduce the minimum O2 pressure required to form the desired structure. 49

However, ozone is highly toxic and flammable and extra care is required to operate such

system. Moreover, the use of cryogenic pumps becomes a serious hazard, since ozone

may detonate during regeneration of the pump.

An Applied Epi 930 MBE chamber50 dedicated to the growth of oxides was used

for deposition of BaTiO3/SrTiO3 superlattices. Fig. 2.4.1 (from A. Schmehl) shows the

basic scheme of the oxide MBE system and its main components. The high-vacuum was

maintained by Balzers TPH 2200 turbo-molecular pump, 51 Cryo-Torr 8 cryogenic

pump,52 and VacIon 150 ion pump.53 The available in situ characterization techniques in

the chamber included quartz crystal microbalance (QCM), RHEED, multi-beam optical

16

sensor (MOS), atomic absorption spectroscopy (AA), and real-time wafer temperature

sensing kSA BandiT.53 The oxidant gas was molecular oxygen of 99.994% purity as well

as an ozone-oxygen mixture containing ~10% of O3 that was produced by an ASTeX

AX8401 ozone generator. 54 The barium and strontium sources were Veeco low

temperature effusion cells containing high-purity (99.99%) premelted metallic barium

and strontium in titanium crucibles.55 The titanium source was the Ti-Ball5 3 sublimation

pump.56 The BaTiO3/SrTiO3 superlattices can be grown either by co-deposition, where

constituent materials are deposited simultaneously, or by shuttered deposition method. In

this work I have grown BaTiO3/SrTiO3 superlattices in shuttered manner by sequential

deposition of constituent monolayers of BaO, SrO, and TiO2. During growth the substrate

temperature was ~650 °C and the background pressure was ~5×10-7 Torr of molecular

oxygen. The barium, strontium, and titanium fluxes were adjusted to be ~3×1013

atoms/cm2, yielding an average growth rate of ~0.1 Å/sec. The shuttered RHEED

intensity oscillation technique was used to control stoichiometry and monolayer doses of

the constituent materials. This shuttered growth technique is similar to migration

enhanced epitaxy of GaAs57 and recently was reported for the growth of SrTiO3 films,58

demonstrating that film stoichiometry control within 1% can be achieved by monitoring

the shuttered RHEED intensity oscillations during the growth. We found that this

technique can be successfully used also for the growth of BaTiO3 films. The details on

the use of this method for the growth of BaTiO3/SrTiO3 superlattices can be found in

Chapter 3.

17

Pump RHEED camera

Fig. 2.2.1 Schematic of reactive MBE system devoted to the growth of oxides (from A.

Schmehl).

RHEED gun

Shutters

Effusion cells

Ti-BallTM

Shutters

Substrate heater

O2/O3 nozzle

18

2.3 Raman Spectroscopy

Raman spectroscopy is a measurement of the inelastic light scattering resulting

from the excitation of vibrations in molecular and crystalline materials. It was named

after C. V. Raman, who discovered the phenomenon in 1928. Gradual improvements of

the various Raman instrumentations make this technique a powerful and versatile

characterization tool at these days. It is a non-destructive and non-contact technique that

can provide information on most elementary excitations in materials, symmetry and

crystal ordering, atomic and molecular bonds, chemical fingerprinting, phase transition

behavior, as well as strain, size, and interface effects. In Raman spectroscopy the sample

is irradiated by an intense laser beam in the ultraviolet-visible region. The scattered light

has two components: the elastic (Rayleigh) scattering that is strong and has the same

frequency as the incident beam and the inelastic (Raman) scattering that is very weak

~10-5 of the intensity of incident beam (Fig. 1).

β ћΩ α

Fig. 2.3.1. Schematic diagram of the Raman scattering process.

0

α ћΩ β

ħωiħωs

Stokes

0

ħωi

Rayleigh

ħωs Anti-

Stokes

19

Raman scattering can be described by conservation of energy as: ħωi = ħωs ± ħΩ,

where ħωi is the incident photon and ħωs is the scattered photon energy. Here ħΩ is the

energy of phonons created (Stokes) or annihilated (anti-Stokes) during the scattering

process. The frequency Ω of phonons measured in Raman experiments is called Raman

shift and the spectra are most commonly shown as a function of wavenumber (in cm-1).

The first order Raman scattering process can be described via the conservation of

momentum as: ks = ki ± q, where ks is the wave vector of the scattered light, ki is the

wave vector of the incident light, and q is the quasi-momentum of the phonon. The

direction and magnitude of the wave vector q depends on the scattering geometry (Fig. 2)

and is ranging from 0 to 2ki.

Fig. 2.3.2. Forward scattering (a) and backscattering (b) geometry of the Raman

measurements.

Sincei

ink

λπ2

= , we can obtaini

nqλπ40 ≤≤ , where λi is the wavelength of the

incident light, which is typically ~5000 Å. If we compare the scattered wave vector q to

the wave vector of the Brillouin zone 0a

π , where a0 ~4 Å, we can see that it is much

k

k i

s qk k

i s 0q ≈(a)

2q k≈ i(b)

kks i

20

smaller0a

q π<< , indicating that only zone-center phonons are seen in first order Raman

spectra of bulk crystals. Cubic perovskite crystals, such as BaTiO3 and SrTiO3, are

centrosymmetric with every atom at the center of inversion indicating that all optical

phonons are of odd symmetry, therefore Raman inactive. Hence, only second-order (two-

phonon) features will be observed. Ferroelectric phase transition breaks the inversion

symmetry and first-order peaks become Raman active.

In crystals there are three acoustic and 3N-3 optical modes, where N is the number

of atoms per formula per unit cell (for perovskites N = 5). The enlarged superlattice unit

cell will increase the number of optical modes in the superlattice. Also due to the

enhancement of the superlattice parameter d along the z direction d = d1 + d2, where d1 =

n1a1 and d2 = n2a2 are the layer thicknesses of two constituents, the Brillouin zone must

be folded into a smaller superlattice Brillouin zone in order to stay within the reduced

zone scheme. After folding, new modes appear in the superlattice Brillouin zone that can

be Raman active. The acoustic modes are folded and doublet peaks of folded acoustic

phonons appear in Raman spectra, while the optical modes become confined in either one

or the other material, decaying rapidly beyond the interfaces.59

In this thesis, we are using Raman spectroscopy for lattice dynamics studies of

ferroelectric nanoscale BaTiO3/SrTiO3 superlattices. Lattice dynamical studies are

essential to understand the properties of ferroelectrics since the zone-center optical

phonon frequencies are connected to the static dielectric constant via the Liddane-Sachs-

Teller relation. The lowest frequency transverse optical phonon (the soft mode) is of

particular importance as it involves the same ionic displacements as those causing the

ferroelectric phase transition. The frequency of soft phonon exhibits strong temperature

21

dependence, tending to zero when the temperature approaches the Curie point.60 As an

example Figure 2.3.3 shows the temperature-dependent Raman spectra of a BaTiO3

single crystal.61 The changes in the Raman spectra are due to the low temperature phase

transitions in the crystal.

tetragonal

rhombohedral

orthorhombic

293 K285 K275 K250 K225 K200 K190 K

185 K175 K150 K125 K100 K

50 K

10 K

Fig. 2.3.3. Temperature evolution of Raman spectra of the BaTiO3 single crystal

measured in parallel polarization geometry. Red arrows are guides to eye (from Ref. 61).

Although conventional visible Raman spectroscopy was successfully applied for

studies of thick ferroelectric films (from 150 nm to 2 µm) of SrTiO3,62 BaTiO3,61 and

BaTiO3/SrTiO3 superlattices,63 it works poorly on thin ferroelectric films of thicknesses

less than ~100nm. The difficulty of using visible Raman spectroscopy arises from the

transparency in the visible range of oxides allowing the laser light to penetrate into the

substrate, which generates an overwhelming substrate contribution to the Raman spectra.

22

However, in the UV range the phonon energy is above the band gap indicating a stronger

absorption and smaller penetration depth as shown in the Fig. 2.3.4 (from D. Tenne). This

will prevent the UV light from entering the substrate, therefore the main contribution in

the Raman spectra will come from the film. Recently, we have demonstrated the use of

UV Raman spectroscopy as an effective technique to study ferroelectric films and

superlattices as thin as 10 nm.64 We have used UV Raman to measure the ferroelectric

transition temperature (TC) of nanoscale BaTiO3/SrTiO3 superlattices and the obtained

results are presented in the Chapter 3. We have also used UV Raman spectroscopy to

investigate the acoustic phonon modes of particular [(BaTiO3)8/(SrTiO3)4]40 superlattice

designed as an acoustic phonon Bragg mirror and observed the folded longitudinal

acoustic phonons at the expected energies (Chapter 4).

23

Fig. 2.3.4. Schematic of the band structure, light absorption, and penetration depth of

light in SrTiO365 as compared to the energies of the visible and UV photons. Strong

absorption, small penetration depth, and strong resonance enhancement make UV Raman

spectroscopy ideal for studying very thin ferroelectric films (from D. Tenne).

24

2.4 Phonon “laser”.

A particularly interesting application of ferroelectric BaTiO3/SrTiO3 superlattices

would be its possible use in a THz acoustic phonon generation (phonon “laser”). A THz

source of coherent acoustic phonons can significantly increase the resolution of acoustic

imaging or can be used in high-speed electronic and optoelectronic devices to break the

“phonon bottleneck” and reduce carrier scattering by enhancing the decay rate of

longitudinal optical (LO) phonons.66, 67 Due to the similarities between phonons and

photons one can transfer the ideas that lead to laser to build a phonon “laser”. For

example, an optical Bragg reflector consists of two materials with different refractive

indices of λlight/4-thick layer. Similarly an acoustic phonon Bragg reflector consists of two

materials of same λsound/4-thick layer but with different acoustic impedances. 68

Furthermore, an acoustic phonon cavity in analogy to optical cavity can be build by

enclosing a spacer of mλsound/2-thick layer, where λsound is the acoustic phonon

wavelength.

The first observation of phonon amplification to the best of our knowledge was

reported in 1961 by Tucker in a ruby rod.69 He demonstrated amplification of 9.3 GHz

ultrasonic waves generated by spin-phonon interaction in a 3700 gauss magnetic field.

The observation of stimulated emission of 10 – 100 GHz acoustic phonons resonant with

Zeeman-split doublets in ruby was reported in 1997 by Fokker at al.70 and later by Tilstra

et al.71 The population inversion was obtained by selective pulsed optical pumping and a

cavity for acoustic phonons was formed by the crystal surfaces. In 1999, Bartels at al.

reported the observation of 0.4 - 0.6 THz coherent zone-folded acoustic phonons excited

in GaAs/AlAs superlattices by resonant impulsive Raman scattering.72 In 2001, Camps

25

at al. reported theoretical studies of GaAs/AlGaAs double-barrier heterostructures

designed for emission of coherent phonons.73 Their calculations showed that applied

external bias produces longitudinal optical (LO) phonons at high rate, which decay into

secondary LO and transverse acoustic (TA) phonons. In 2003, Stanton et al. observed the

generation of monochromatic ~0.6 THz longitudinal acoustic (LA) phonons in

GaAs/AlAs superlattice structures by resonant photoexcitation by femtosecond laser

pulses.74 During the same year, Chen et al. studied the feasibility of reducing the lifetime

of LO phonons in InP by externally injecting coherent LA phonons.6 7 The proposed a

scheme in which LO phonons decay into LA and TO phonons that can lead to phonon

laser if proper feedback is provided. In 2004, Bragas et al. reported femtosecond optical

generation of coherent phonons in CdTe1-xSex quantum dots embedded in a glass

matrix. 75 In 2006, Kent et al. reported measurements of terahertz acoustic phonon

emission from a weakly coupled GaAs/AlAs superlattice under vertical electron transport

and suggested that such a superlattice may form a basis for phonon “laser”.76 Despite the

various approaches described above the realization of phonon “laser” hampered due to

the several obstacles. One of the main obstacles for attaining coherent acoustic phonon

generation is the very short wavelength (in a range of few nm) of phonons that have also

a shorter mean free path and a slower velocity of sound compared to photons.77 This will

imply that the requirements for the structural quality of acoustic phonon devices such as

mirrors, filters, and cavities are much higher than for optical ones. Recently a combined

optical and acoustic cavity approach for coherent phonon generation was proposed.78,79

The basis of this approach is a device that has a resonant cavity for acoustic phonons

embedded inside an optical cavity (Fig. 2.4.1). The feasibility of this approach was

26

shown first on compound semiconductor materials reporting an enhancement of

interaction between light and sound more than five orders of magnitude.80 We have

recently reported that further enhancement of the performance of acoustic phonon

devices can be achieved by replacing compound semiconductor materials with oxide

piezoelectric and ferroelectric materials such as BaTiO3 and SrTiO3.81 Advantages of

oxide materials over compound semiconductor materials are in larger acoustic impedance

mismatches, stronger sound-light coupling due to piezoelectricity and the capability of

electrical tuning of acoustic cavity wavelengths.81 Acoustic phonon Bragg mirrors and

cavities made of BaTiO3/SrTiO3 superlattices are described in Chapter 4.

27

Fig. 2.4.1 Scheme of an acoustic cavity within an optical cavity (from reference 79). Here

layers of two materials having different optical refractive indices (e.g. AlAs/Al0.8Ga0.2As)

are arranged to form Bragg mirrors for photons separated by mλlight/2 thick layer forming

an optical Fabry-Perot resonator. Inside the optical cavity, an acoustic cavity is placed,

consisting of two superlattices designed to make Bragg reflectors for acoustic phonons,

separated by mλsound/2 thick layer.

28

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32

Chapter 3

Growth of nanoscale BaTiO3/SrTiO3 superlattices

by molecular-beam epitaxy

(To be submitted to Journal of Materials Research)

33

Growth of nanoscale BaTiO3/SrTiO3 superlattices by molecular-beam epitaxy

A. Soukiassian, W. Tian,a) V. Vaithyanathan,a) J. H. Haeni,b) L. Q. Chen, X. X. Xi, and D. G. Schlom

Materials Research Institute, The Pennsylvania State University, University Park, Pennsylvania 16802-5005

D. A. Tenne

Department of Physics, Boise State University, Boise, Idaho 83725

N. D. Lanzillotti-Kimura, A. Bruchhausen, and A. Fainstein Centro Atómico Bariloche & Instituto Balseiro, C.N.E.A., 8400 S. C. de Bariloche, R.N.,

Argentina

H. P. Sun and X. Q. Pan Department of Materials Science and Engineering, University of Michigan, Ann Arbor,

Michigan 48109

K. J. Choi and C. B. Eom Department of Materials Science and Engineering, University of Wisconsin, Madison,

Wisconsin 53706

Y. L. Li and Q. X. Jia Materials Science and Technology Division, Los Alamos National Laboratory, Los

Alamos, NM 87545

R. S. Katiyar Department of Physics, University of Puerto Rico, Rio Piedras Campus, San Juan,

Puerto Rico 00931

A. Cros and A. Cantarero Materials Science Institute, University of Valencia, P.O. Box 22085, E-46071 Valencia,

Spain

C. Constantin and R. M. Feenstra Department of Physics, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213

M. Bernhagen, P. Reiche, and R. Uecker

Institute for Crystal Growth, Max-Born-Straße 2, D-12489 Berlin, Germany

a) Present address: Seagate Technology, Bloomington, MN 55437 b) Present address: USAID, Washington, DC

34

ABSTRACT

Commensurate BaTiO3/SrTiO3 superlattices were grown by reactive molecular-

beam epitaxy on three different substrates: TiO2-terminated (001) SrTiO3, (101) DyScO3,

and (101) GdScO3. With the aid of reflection high-energy electron diffraction (RHEED),

precise single-monolayer doses of BaO, SrO, and TiO2 were deposited sequentially to

create commensurate BaTiO3/SrTiO3 superlattices with a variety of periodicities. X-ray

diffraction (XRD) measurements exhibit clear superlattice peaks at the expected

positions. The rocking curve full width at half maximum of the superlattices was as

narrow as 7 arc sec (0.002º). High-resolution transmission electron microscopy reveals

nearly atomically abrupt interfaces. Temperature-dependent ultra violet Raman and XRD

were used to reveal the paraelectric-to-ferroelectric transition temperature (TC). Our

results demonstrate the importance of finite size and strain effects on the TC of

BaTiO3/SrTiO3 superlattices. In addition to probing finite size and strain effects, these

heterostructures may be relevant for novel phonon devices, including mirrors, filters, and

cavities for coherent phonon generation and control.

35

I. INTRODUCTION

Well ordered BaTiO3/SrTiO3 superlattices with BaTiO3 and SrTiO3 layer

thicknesses in the nanometer range are of interest to probe fundamental issues in

ferroelectricity as well as for potential devices. For example, recent theoretical studies

predict that (1) the SrTiO3 layers in BaTiO3/SrTiO3 superlattices grown commensurately

on cubic (100) SrTiO3 substrates are themselves tetragonal and poled by internal electric

fields, (2) the polarization of such superlattices can be enhanced beyond that achievable

in unstrained BaTiO3 due to the biaxial compressive strain state of the BaTiO3 layers

within the superlattice, and (3) that ferroelectricity will persist in such superlattices for

BaTiO3 layers as thin as the thickness of a single BaTiO3 unit cell (0.4 nm).1,2

We have begun to experimentally test these predictions 3 and assess oxide

heterostructures for phonon confinement 4 by growing commensurate BaTiO3/SrTiO3

superlattices with a high degree of structural perfection and abrupt interfaces. The

thicknesses of the BaTiO3 and SrTiO3 layers (an n unit cell thick BaTiO3 layer followed

by an m unit cell thick SrTiO3 layer) making up the BaTiO3/SrTiO3 superlattice repeat

unit as well as the number of times p these layers are repeated to form a

[(BaTiO3)n/(SrTiO3)m]p superlattice must be such to prevent relaxation by the formation

of misfit dislocations. Since the critical thickness of a single BaTiO3 film grown on a

(001) SrTiO3 substrate is about 4 nm (10 unit cells) for our growth conditions, 5

commensurate [(BaTiO3)n/(SrTiO3)m]p superlattices grown on (001) SrTiO3 are limited to

n < 10 to preserve the high-strain state, 3

33

BaTiO

BaTiOSrTiO

aaa −

= −2.5% for the BaTiO3 film at a

growth temperature of 650 ºC,6 and prevent their relaxation. The allowed thickness of the

36

BaTiO3 layers (n unit cells thick) decreases as the number of superlattice repeats p

increases.

High quality [(BaTiO3)n/(SrTiO3)m]p superlattices with abrupt interfaces are also

of interest for novel acoustic phonon devices including mirrors, filters, and cavities for

coherent acoustic phonon generation and control (phonon “laser”).4 The structure of these

devices is determined by the acoustic phonon wavelength, which is typically in the range

of a few nanometers, indicating that structural quality and interface abruptness is crucial

for device performance.

In this paper we focus on the growth of high quality nanoscale

[(BaTiO3)n/(SrTiO3)m]p superlattices with atomically abrupt interfaces that are vital for

the performance of acoustic phonon devices as well as the study of fundamental

properties of ferroelectric superlattices. We describe the shuttered reflection high-energy

electron diffraction (RHEED) intensity oscillations used in our reactive molecular-beam

epitaxy (MBE) process to control film stoichiometry and the n and m unit cell layer

thicknesses of the BaTiO3 and SrTiO3 layers comprising the [(BaTiO3)n/(SrTiO3)m]p

superlattices. The structural properties of the superlattices grown are described in detail.

The improvement of the structural quality of [(BaTiO3)n/(SrTiO3)m]p superlattices grown

on (101) GdScO3 and (101) DyScO3 substrates7-9 is also shown. Using these superlattices

we demonstrate the importance of strain and finite size effects on the TC of

[(BaTiO3)n/(SrTiO3)m]p superlattices with a variety of superlattice thicknesses, constituent

layer thicknesses n and m, and strains.

37

II. EXPERIMENTAL

Epitaxial [(BaTiO3)n/(SrTiO3)m]p superlattices were grown on (001) SrTiO3, (101)

DyScO3, and (101) GdScO3 substrates by reactive MBE. The strontium and barium

fluxes were produced by sublimating elemental strontium and barium contained in

titanium crucibles using low-temperature effusion cells. The titanium flux was supplied

by a Ti-Ball10 titanium sublimation pump.11 The [(BaTiO3)n/(SrTiO3)m]p superlattices

were grown by sequential shuttered deposition of the constituent monolayers,12-14 in a

background pressure of 5×10-7 Torr of molecular oxygen and a substrate temperature of

~650 °C, as measured by an optical pyrometer. The shuttering timing sequence used to

grow a [(BaTiO3)8/(SrTiO3)4]40 superlattice is shown in Fig. 1. A quartz crystal

microbalance (QCM) located directly in front of the substrate was used to get a rough

(±5%) idea of the barium, strontium, and titanium molecular beam fluxes. Based on these

QCM values, the shuttering times for the deposition of one monolayer of SrO, BaO, and

TiO2 were calculated. These values were used as the starting point for growth on a

calibration sample. In order to determine the shutter opening times more accurately to

deposit precise monolayer doses of SrO, BaO, and TiO2, RHEED was monitored during

epitaxial growth on the calibration sample.

Typical RHEED patterns along the [100] and [110] azimuths before and during

the growth of a [(BaTiO3)n/(SrTiO3)m]p superlattice on a TiO2-terminated (001) SrTiO3

substrate15 are shown in Fig. 2. Here white boxes show the area monitored in the analysis

of the time evolution of the 00 and 01 streaks. (001) SrTiO3 can have a wide variety of

surface reconstructions depending on stoichiometry, temperature, and oxygen partial

pressure.12,15-17 The RHEED patterns on the TiO2-terminated (001) SrTiO3 substrates15

38

used in this work show additional spots (not visible in the zeroth Laue zone). The spots

can be seen clearly in the [100] azimuth RHEED pattern (Fig. 2(a)) at room temperature.

As the substrate temperature begins to increase, the intensity of the extra spots starts to

fade and disappears after about 10 min during heating to the ~650 °C growth temperature

in ultra high vacuum in the MBE chamber.

By monitoring the changes in the shuttered RHEED intensity oscillations during

deposition, film stoichiometry control within ~1% can be achieved for SrTiO3.18 We

found this method to also work for BaTiO3. An example of typical shuttered RHEED

oscillations during the growth of a [(BaTiO3)n/(SrTiO3)m]p superlattice is shown in Fig. 3.

The shuttered RHEED oscillations shown in Fig. 3 were recorded simultaneously along

the 00 streak (top) and the 01 streak (bottom) during the growth of three periods of a

[(BaTiO3)8/(SrTiO3)4]40 superlattice (sample #14). Deposition starts when the barium

shutter is opened. The RHEED intensity increases until one monolayer of BaO is

deposited. The barium shutter was then closed and the titanium shutter opened causing

the RHEED intensity to decrease until one monolayer of TiO2 was deposited, completing

one unit cell of BaTiO3. Shuttered RHEED oscillations for the growth of unit cells of

SrTiO3 are similar to those of BaTiO3. Each peak in Fig. 3 corresponds to the deposition

of one unit cell of BaTiO3 or SrTiO3. The deposition rates of SrO, BaO, and TiO2 were

about 15-20 s for each monolayer, corresponding to an average growth rate of about 0.1

Å/s.

The total time to deposit the 40 repeats of the [(BaTiO3)8/(SrTiO3)4]40 superlattice

(sample #14) was more than 5 hours. During such a long deposition, fluxes can drift

resulting in changes in film stoichiometry. Therefore, monitoring the shuttered RHEED

39

oscillations during the growth of the [(BaTiO3)n/(SrTiO3)m]p superlattices and

periodically adjusting the shutter timing was vital to maintaining stoichiometry and

accurate monolayer doses during superlattice growth.

An atomically flat substrate surface with a well-defined single termination is

required for the reproducible growth of high quality [(BaTiO3)n/(SrTiO3)m]p superlattices

with atomically abrupt interfaces. Knowledge of the surface termination is particularly

important for our sequential monolayer deposition conditions in which we need to know

which species to begin with as we deposit well calibrated monolayer doses of SrO, BaO,

and TiO2. A well terminated substrate allows starting with the right material (SrO or BaO

in our case) in order to maintain stoichiometry and grow exact monolayers of SrTiO3 or

BaTiO3 from the very beginning, which is important to obtain atomically abrupt

interfaces. For this reason we have used the method developed by Koster et. al.15 to

prepare TiO2-terminated (001) SrTiO3 substrates. An AFM image of a typical TiO2-

terminated SrTiO3 substrate surface prepared by us using this method is shown in Fig.

4(a). The surface has an atomically flat step-terrace structure. Figure 4(b) is a line-cut

through the data revealing a height of 0.37±0.03 nm, in agreement with the expected

0.3905 nm unit cell step height of SrTiO3.19

The nearly ideal TiO2-termination of the etched and annealed SrTiO3 substrates

can be seen by the RHEED behavior of the shuttered oscillations during the growth of the

first several unit cells of the [(BaTiO3)n/(SrTiO3)m]p superlattice. If the substrate surface

is not fully terminated with TiO2, the RHEED intensity behavior of the first monolayers

of BaTiO3 and SrTiO3 will differ from the steady state shuttered RHEED intensity

oscillations shown in Fig. 3. This difference is seen in Fig. 5 where shuttered RHEED

40

intensity oscillations during the first three periods of a [(BaTiO3)n/(SrTiO3)m]p

superlattice recorded from the beginning of growth on a non-terminated (001) SrTiO3

substrate in its as-received state from the substrate supplier.20 Since the initial (001)

SrTiO3 surface is not fully TiO2-terminated, during the deposition of exactly one

monolayer of BaO, only part of the BaO will form BaTiO3 and the excess BaO will leave

the film surface BaO-rich. The subsequent deposition of exactly one monolayer of TiO2

will again partially form BaTiO3 and leave the surface TiO2-rich. As a result, the

shuttered RHEED intensity oscillation does not vary monotonically during the doses of

the constituent monolayers as it does in the case of stoichiometric growth (Fig. 3)

resulting in the double peaks seen in the initial oscillations in Fig. 5.18 This RHEED

behavior continues until a fully terminated surface is attained at the end of each

deposition cycle due to diffusion of the excess BaO, SrO, and TiO2 into the film. Thus

the deposition of several unit cells of BaTiO3 and SrTiO3 at the beginning of growth

takes place before the surface eventually becomes singly terminated in steady state

(Fig. 5).

For comparison shuttered RHEED oscillations from the very beginning of the

growth of a [(BaTiO3)6/(SrTiO3)13]15 superlattice (sample #12) on a TiO2-terminated

SrTiO3 substrate15 are shown in Fig. 6. The RHEED intensity varies monotonically

during each shuttered dose and no double peaks are observed. This indicates that the

growth proceeds via the growth of fully terminated constituent monolayers and is

stoichiometric from the very beginning.

The phase shift that a (100) SrTiO3 surface of mixed termination can lead to is

likely responsible for the contradictory RHEED intensity behavior for the growth of

41

SrTiO3 layers21 or BaTiO3/SrTiO3 superlattices12,13 reported in the literature. Iijima et

al.12 reported the RHEED intensity to increase during the deposition of barium and

strontium and to decrease during the deposition of titanium. Tsurumi et al.13 reported

exactly the opposite behavior. Our observations on substrates of controlled termination

are in agreement with the results of Iijima et al.,12 where the intensity RHEED intensity

increases during the deposition of barium and strontium and decreases during titanium.18

Shuttered RHEED intensity oscillations during the growth of

[(BaTiO3)n/(SrTiO3)m]p superlattices on (101) GdScO3 and (101) DyScO3 substrates are

similar to those grown on (001) SrTiO3 substrates. Unfortunately no termination method

has been developed for GdScO3 substrates so far. An alternative method to improve the

substrate surface and achieve a single termination could be via the deposition of a

homoepitaxial GdScO3 buffer layer that ends at a chosen monolayer prior to the growth

of the [(BaTiO3)n/(SrTiO3)m]p superlattice. We have not used such an approach, however,

in this study. Thus the shuttered RHEED intensity oscillation behavior for the

superlattices grown on (101) GdScO3 are similar to those grown on non-terminated (001)

SrTiO3 substrates (Fig. 7). The RHEED patterns along [100] and [110] azimuths of the

superlattice before and during the growth of a [(BaTiO3)8/(SrTiO3)4]40 superlattice

(sample #17) on a (101) GdScO3 substrate are shown in Fig. 8. White boxes show the

recorded area of the 01 streak for the shuttered RHEED intensity oscillations shown in

Fig. 7.

Blank et al.22 have developed a method to terminate the surface of (101) DyScO3

substrates. This treatment improves the smoothness of the DyScO3 substrate surface as

can be seen from comparisons of RHEED patterns of non-terminated and terminated ones

42

(Fig. 9). A comparison of the shuttered RHEED intensity oscillations during the growth

of the first several unit cells of a [(BaTiO3)8/(SrTiO3)4]40 superlattice (sample #16) on

non-terminated and terminated DyScO3 substrates are shown in Fig. 10. Although the

termination method does not provide a fully ScO2-terminated DyScO3 substrate, it

significantly reduces the number of BaTiO3 and SrTiO3 monolayers prior to the onset of

steady-state shuttered RHEED intensity oscillations.

Structural characterization of all [(BaTiO3)n/(SrTiO3)m]p superlattices was made

by four-circle X-ray diffraction (XRD) with Cu Kα radiation using a Picker low-

resolution XRD and with monochromated Cu Kα1 radiation on a Philips X’Pert PRO

high-resolution system. For θ –2θ and φ-scans on the Philips X’Pert PRO system a hybrid

monochromator was used on the incident beam side and a 0.27° parallel plate collimator

was used on the diffracted beam side. For high-resolution rocking curve measurements a

hybrid monochromator on the incident beam side and a triple axis arrangement with a

220 Ge analyzer crystal on the diffracted beam side was used. High-resolution

transmission electron microscopy (HRTEM) measurements on selected samples were

performed in JEOL 3011 and JEOL 2010F transmission electron microscopes operated at

400 kV. The TC of all of the [(BaTiO3)n/(SrTiO3)m]p superlattices presented in this paper

were obtained from UV Raman studies3 and from temperature-dependent XRD

measurements23-28 on selected samples.

III. RESULTS AND DISCUSSION.

The results of the structural characterization by four-circle XRD of the

[(BaTiO3)n/(SrTiO3)m]p superlattices are listed in Table I. All samples were grown

43

sequentially with BaTiO3 being the first layer deposited and SrTiO3 the last layer of the

superlattice, with the SrTiO3 ending at the TiO2 monolayer. We grew

[(BaTiO3)n/(SrTiO3)m]p superlattices with various periodicities including a series with the

thickness of the SrTiO3 layer fixed to m = 4, 13, and 30 unit cells while the thickness of

the BaTiO3 layer was varied from n = 1 to 8 unit cells. θ – 2θ X-ray diffraction scans of

all of the [(BaTiO3)n/(SrTiO3)m]p superlattices were measured and the out-of-plane lattice

parameter d of all of the superlattices were obtained from a Nelson-Riley analysis.29 The

measured out-of-plane lattice parameters of the superlattices indicated that all

superlattices reported in this work have the targeted number of BaTiO3 and SrTiO3 unit

cells in their superlattice units (Table I).

θ – 2θ X-ray diffraction scans of the [(BaTiO3)n/(SrTiO3)m]p superlattices with

m = 4 and n = 1, 2, 3, 4, 5, 6, and 8 are shown in Fig. 11. Similarly θ − 2θ X-ray

diffraction scans of the [(BaTiO3)n/(SrTiO3)m]p superlattices with m = 13 and n = 1, 2,

and 3 are shown in Fig. 12. Nearly all superlattice peaks are present for 2θ < 55°, which

is an indication of atomically sharp interfaces between the BaTiO3 and SrTiO3 layers.

The in-plane orientation relationship between the [(BaTiO3)n/(SrTiO3)m]p superlattices

and the underlying substrates was determined by an XRD φ-scan. A typical φ-scan of the

10ℓ peak of a [(BaTiO3)n/(SrTiO3)m]p superlattice grown on a (001) SrTiO3 substrate is

shown in Fig. 13 (sample #14, [(BaTiO3)8/(SrTiO3)4]40). Here φ = 0° corresponds to when

the in-plane component of the diffraction vector is parallel to the [100] in-plain direction

of the substrate. It shows that the superlattice is epitaxial with the expected cube-on-cube

in-plane alignment with the substrate ([100] of the superlattice is parallel to the [100] of

the substrate). The 2θ positions of the 10ℓ superlattice reflections in combination with

44

the measured out-of-plane lattice parameters were used to calculate the in-plane lattice

parameters of the superlattices. All [(BaTiO3)n/(SrTiO3)m]p superlattices (except sample

#14, [(BaTiO3)8/(SrTiO3)4]40) grown on SrTiO3 substrates are commensurate and have

measured in-plane lattice constants that are the same (within the experimental error of our

measurements) as that of the SrTiO3 substrate (a = 3.905 Å, Table I).

Rocking curves of the [(BaTiO3)n/(SrTiO3)m]p superlattices were measured on the

strongest superlattice 00ℓ peaks that were well separated from the substrate peaks.

Rocking curves of the underlying substrates were measured on the 002 SrTiO3, 202

GdScO3, and 202 DyScO3 peaks. The rocking curve (ω-scans) full widths at half

maximum (FWHM) of the superlattices and underlying substrates are shown in Table I.

The rocking curve measurements on SrTiO3 substrates reveal that nearly all of them

exhibit mosaic features (subgrain boundaries) resulting in a large spread in measured ω

FWHM values from as low as 20 arc sec (0.0055°) to 162 arc sec (0.0451°) for the (001)

SrTiO3 substrates used in this work20 (Table I). Moreover, different regions of the SrTiO3

substrate may also have different ω FWHM due to the highly inhomogeneous mosaic

spread of commercial SrTiO3 single crystals. 30 For this reason, rocking curve

comparisons between the [(BaTiO3)n/(SrTiO3)m]p superlattices and the substrates on

which they were grown were always measured on the same region of the substrate.

As an example, rocking curves of two [(BaTiO3)n/(SrTiO3)m]p superlattices grown

on (001) SrTiO3 substrates with a one single narrow peak (sample #3,

[(BaTiO3)3/(SrTiO3)4]35) and another with a strongly mosaic peak (sample #2,

[(BaTiO3)2/(SrTiO3)4]40), are shown in Fig. 14. Rocking curves of the

[(BaTiO3)3/(SrTiO3)4]35 superlattice 0014 peak (sample #3) and the underlying SrTiO3

45

substrate 002 peak (at the same position on the substrate) are shown in Fig. 14(a). The ω

FWHM is 21 arc sec (0.0058°) for the superlattice peak as compared to 20 arc sec

(0.0055°) for the substrate peak. The sharp rocking curve indicates the high structural

perfection of the superlattice. For comparison, the rocking curves of the

[(BaTiO3)2/(SrTiO3)4]40 superlattice 0012 peak (sample #2) and the underlying SrTiO3

substrate 002 peak are shown in Fig. 14(b). The ω FWHM is 62 arc sec (0.0172°) for the

superlattice peak as compared to 61 arc sec (0.0169°) for the substrate peak with multiple

mosaic features. Both samples in Fig. 14 are commensurate as indicated from the in-

plane lattice parameters.

We noticed that the ω FWHM of all commensurate samples had similar ω

FWHM values as their underlying substrates, showing that the crystalline quality of the

superlattices is limited by that of the underlying substrates. Sample #6, the

[(BaTiO3)6/(SrTiO3)4]20 superlattice, grown on a SrTiO3 substrate with poor crystallinity

(ω FWHM = 162 arc sec (0.0451°)) shows a large ω FWHM = 320 arc sec (0.0890°). We

suspect that the increase in the ω FWHM of this superlattice is due to an increase in its

dislocation density, which can result in the lowering of TC. Relaxation may occur also if

the critical thickness of the superlattice is exceeded. A ~1930 Å thick

[(BaTiO3)8/(SrTiO3)4]40 superlattice grown on a (001) SrTiO3 substrate (sample #14) is

not commensurate and has an in-plane lattice parameter of a = 3.945±0.01 Å. This

indicates that the [(BaTiO3)8/(SrTiO3)4]40 superlattice is partially relaxed and is only

strained by ε = −1.05%, rather than the ε = −2.3% biaxial compressive strain that it would

be under if it were still commensurate. As a result the ferroelectric phase transition

temperature is significantly decreased (TC ~440 K) as compared to the commensurate

46

sample #7 (TC ~640 K), which has a similar [(BaTiO3)8/(SrTiO3)4]10 structure, but is

thinner (~500 Å).3

The mechanism of superlattice relaxation has been studied by TEM and is found

to be the introduction of misfit dislocations, which form dislocation half loops with

threading dislocation segments that extend through the entire film. Figure 15(a) is a

cross-sectional HRTEM image showing a threading dislocation in this partially relaxed

[(BaTiO3)8/(SrTiO3)4]40 superlattice (sample #14) that extends through the film. These

threading dislocations may also be seen in the Z-contrast TEM image from a larger area

of the same [(BaTiO3)8/(SrTiO3)4]40 superlattice, Fig. 15(b), where they show up as the

lighter regions (see arrows). The [(BaTiO3)8/(SrTiO3)4]40 superlattice (sample #14) has a

large ω FWHM of 214 arc sec (0.0595°) as compared to the substrate ω FWHM of 118

arc sec (0.0328°), consistent with the superlattice having a high density of misfit

dislocations. Unlike the partially relaxed [(BaTiO3)8/(SrTiO3)4]40 superlattice, no

threading dislocations were observed in the commensurate [(BaTiO3)n/(SrTiO3)m]p

superlattices studied by HRTEM. Figure 16 shows two cross-sectional HRTEM examples

from commensurate [(BaTiO3)n/(SrTiO3)m]p superlattices (samples #1 and #8). The TEM

(both HRTEM and Z-contrast TEM) reveal superlattices with nearly atomically abrupt

interfaces and no observable dislocations.

The last two rows of Table I contain data from [(BaTiO3)8/(SrTiO3)4]40

superlattices grown on (101) DyScO3 (sample #16) and (101) GdScO3 (sample #17).

Both samples are commensurate with the underlying substrates despite the fact that the

thickness and structure of these samples are the same as the partially relaxed sample #14

grown on SrTiO3, i.e., all are [(BaTiO3)8/(SrTiO3)4]40 superlattices. The measured in-

47

plane lattice parameter of sample #16 is a = 3.945±0.05 Å as compared to the measured

pseudocubic lattice parameter of the underlying DyScO3 substrate ap = 3.945 Å (shown in

Table I in brackets). This is due to BaTiO3 undergoing a smaller compressive strain,

ε ≈ −1.7%, when grown on (101) DyScO3 than on (001) SrTiO3. Thus the critical

thicknesses of individual BaTiO3 layers and of the whole [(BaTiO3)n/(SrTiO3)m]p

superlattice are much larger.23 The SrTiO3 layers of this superlattice are under biaxial

tension, ε ≈ 1%. Similarly the [(BaTiO3)8/(SrTiO3)4]40 grown on (101) GdScO3 (sample

#17) is also found to be commensurate. Here the BaTiO3 layers are under an even smaller

compressive strain ~1%, while the SrTiO3 layers are under biaxial tensile strain of

~1.7%.23 In superlattices grown commensurately on SrTiO3 substrates, the unstrained

SrTiO3 layers are polar because of the presence of neighboring ferroelectric BaTiO3

layers,3 while in superlattices grown on DyScO3 and GdScO3 substrates the SrTiO3 layers

are strained and exhibit strain-induced ferroelectricity31,32 in addition to the polarization

induced by the BaTiO3.

Structural characterization of the [(BaTiO3)8/(SrTiO3)4]40 superlattices grown on

(101) DyScO3 and (101) GdScO3 substrates reveals a significant improvement in the

superlattice crystalline perfection. The XRD scans of the [(BaTiO3)8/(SrTiO3)4]40

superlattice grown on (101) DyScO3 substrate (sample #16) are shown in Fig. 17. Nearly

all superlattice peaks show up in the θ – 2θ XRD scan (Fig. 17(a)). The in-plane

orientation relationship between the [(BaTiO3)8/(SrTiO3)4]40 superlattice and the (101)

DyScO3 substrate was determined by a φ-scan of the 1012 superlattice peak (Fig. 17(b)).

In this scan φ = 0° corresponds to when the in-plane component of the diffraction vector

is aligned parallel to the [010] in-plain direction of the DyScO3 substrate. It shows that

48

the superlattice is epitaxial with the expected ([100] superlattice || [010] substrate) in-

plane alignment with the substrate. Rocking curves of the [(BaTiO3)8/(SrTiO3)4]40

superlattice and the underlying DyScO3 substrate are shown on Fig. 17(c). The FWHM in

ω of the superlattice 0024 peak and of the 202 peak of the underlying DyScO3 substrate

were found to be 9 arc sec (0.0024°) and 8 arc sec (0.0022°), respectively.

Similar XRD scans of the [(BaTiO3)8/(SrTiO3)4]40 superlattice grown on (101)

GdScO3 substrate (sample #17) are shown in Fig. 18. Again nearly all superlattice peaks

are seen in the θ – 2θ XRD scan (Fig. 18(a)). Since the compressive mismatch strain

imposed by the GdScO3 substrate on BaTiO3 is smaller and tensile strain on SrTiO3 is

larger than in sample #16, the out-of-plane lattice parameter d = 48.0±0.5 Å is smaller

than d = 48.2±0.5 Å for sample #16 and even smaller than d = 48.8±0.2 Å in sample #7

with the largest mismatch strain. The in-plane orientation relationship between the

[(BaTiO3)8/(SrTiO3)4]40 superlattice (sample #17) and the (101) GdScO3 substrate was

determined by a φ-scan of the 1011 superlattice peak (Fig. 18(b)). This φ-scan shows that

the superlattice is epitaxial with the same in-plane alignment with the substrate as the

superlattice grown on DyScO3 ([100] superlattice || [010] substrate). Rocking curves of

the [(BaTiO3)8/(SrTiO3)4]40 superlattice and the underlying GdScO3 substrate are shown

in Fig. 18(c). The rocking curve FWHM in ω of the superlattice 0024 peak was 7 arc sec

(0.0020°) and that of the 202 peak of the underlying GdScO3 substrate was 7 arc sec

(0.0019°).

Our results indicate that the structural perfection of the [(BaTiO3)n/(SrTiO3)m]p

superlattices depend on the structural perfection of the substrate they are grown on. When

the underlying substrates have very high structural perfection, i.e., DyScO3 and GdScO3,

49

the commensurate [(BaTiO3)8/(SrTiO3)4]40 superlattices have very high structural

perfection. This indicates that [(BaTiO3)n/(SrTiO3)m]p superlattices, if grown on high

quality DyScO3 and GdScO3 substrates, can have better structural perfection than any

commercially available SrTiO3 substrate33-35 or films grown on such substrates. The

rocking curves of our [(BaTiO3)8/(SrTiO3)4]40 superlattices grown on DyScO3 and

GdScO3 substrates are by far the narrowest ever reported for oxide superlattices.

An important advantage of using DyScO3 and GdScO3 substrates is that as

DyScO3 and GdScO3 have pseudocubic lattice constants lying between SrTiO3 and

BaTiO3, commensurate [(BaTiO3)n/(SrTiO3)m]p superlattices of arbitrary thickness may

be grown by the same principles as strained layer superlattices of conventional

semiconductors.36 This enables the growth of much thicker commensurate superlattice

structures free of high densities of dislocations. A particular application in need of thick

high quality [(BaTiO3)n/(SrTiO3)m]p superlattices is novel phonon devices including

mirrors, filters, and cavities that are part of a phonon “laser” architecture.4 Moreover, the

fact that DyScO3 and GdScO3 have large band gaps (>5.5eV)37,38 indicates that these

substrates are transparent in the UV range allowing forward scattering UV Raman

measurements to be carried out. Such experiments are difficult with SrTiO3 substrates

due to its low bandgap (3.2 eV).39

The TC of all superlattices shown in the last column of Table I was obtained from

UV Raman measurements.3 For several samples, the TC was also determined by

temperature-dependent XRD and compared with the UV Raman results. Figure 19 shows

the temperature-dependent in-plane and out-of-plane parameters measured by XRD on

commensurate sample #7 and partially relaxed sample #14. Both of these samples have

50

similar [(BaTiO3)8/(SrTiO3)4]p structures, but differ in their thicknesses: p = 10 and 40,

respectively. The in-plane lattice parameters of the underlying SrTiO3 substrates were

measured as well and are shown in the plot as open circles. The solid squares and

triangles are the measured out-of plane d and in-plane a lattice parameters of the

corresponding superlattices. The plot in Fig. 19(a) shows the temperature-dependent

XRD of commensurate sample #7, a [(BaTiO3)8/(SrTiO3)4]10 superlattice. The TC

~400 °C of this sample was determined from the change in slop of the out-of-plane

superlattice parameter d as a function of temperature23-28 and its position is shown by the

arrow. For the partially relaxed [(BaTiO3)8/(SrTiO3)4]40 superlattice (sample #14) shown

in the Fig. 19(b) the in-plane lattice parameters of the superlattice do not overlap with

those of the underlying SrTiO3 substrate, indicating that the superlattice has partially

relaxed. The TC of the partially relaxed sample cannot be determined by the temperature-

dependent XRD due to absence of a clear change in the slope of d(T). It is possible,

however, to determine the TC of this partially relaxed sample from UV Raman

measurements.3

Figure 20 summarizes the TC of the [(BaTiO3)n/(SrTiO3)m]p superlattices

measured by UV Raman and in some cases by temperature-dependent XRD. Figure 20(a)

shows the dependence of TC on n and m in [(BaTiO3)n/(SrTiO3)m]p superlattices grown on

(001) SrTiO3 substrates. The horizontal dash-dotted line shows the TC of bulk

(unstrained) BaTiO3. The data in Fig. 20(a) shows that in nanoscale commensurate

[(BaTiO3)n/(SrTiO3)m]p superlattices grown on (001) SrTiO3 substrates the TC strongly

depend on the superlattice structure and thickness n of individual BaTiO3 layers. The

large variation of TC from ~170 K (sample #15) to ~640 K (sample #7) is a result of

51

competing finite size effects in these superlattices. It can be seen that TC increases with n

and decreases with m.3 The curves in Fig. 20(a) are from three-dimensional phase field

calculations that allow the [(BaTiO3)n/(SrTiO3)m]p superlattice to break up into small

domains (their lowest energy configuration). These calculations that utilize the physical

properties of BaTiO3 and SrTiO3 single crystals (i.e., are not fit to the experimental data

in Fig. 20(a)) are described in detail elsewhere.3,40

Figure 20(b) shows the dependence of TC on the mismatch strain ε in the BaTiO3

layers for superlattices with the same [(BaTiO3)8/(SrTiO3)4]p structure grown on (001)

SrTiO3, (101) DyScO3, and (101) GdScO3 substrates. This plot emphasizes the influence

of mismatch strain on TC. The highest TC is observed in the [(BaTiO3)8/(SrTiO3)4]p

superlattice subjected to the largest compressive strain (~2.3%). As the strain decreases,

the TC decreases towards its value in unstrained bulk BaTiO3. The horizontal dash-dotted

line in this plot shows the TC of bulk BaTiO3 for comparison. Thus DyScO3 and GdScO3

substrates not only significantly improve the crystallinity of the [(BaTiO3)n/(SrTiO3)m]p

superlattices but also can be used to tune the TC via strain. Detailed UV Raman

measurements on these [(BaTiO3)n/(SrTiO3)m]p superlattices in combination with first-

principles calculations have shown that unstrained SrTiO3 layers in commensurate

BaTiO3/SrTiO3 superlattices grown on SrTiO3 substrate are poled by the neighboring

ferroelectric BaTiO3 layers, while strained SrTiO3 layers in BaTiO3/SrTiO3 superlattices

grown on DyScO3 and GdScO3 substrates are not only polar, but also exhibit strain-

induced ferroelectricity.3,41

52

IV. CONCLUSIONS

We have used shuttered RHEED intensity oscillations to precisely grow a series

of [(BaTiO3)n/(SrTiO3)m]p superlattices by reactive MBE on (001) SrTiO3, (101) DyScO3,

and (101) GdScO3 substrates. Structural characterization by XRD and HRTEM

demonstrate the synthesis of commensurate nanoscale superlattices with excellent

crystalline quality and atomically abrupt interfaces. The mosaic spread of superlattices

depends not only on the growth parameters and mismatch strain, but also on the structural

perfection of the underlying substrate. By using new DyScO3 and GdScO3 substrates we

have shown that the structural perfection of [(BaTiO3)n/(SrTiO3)m]p superlattices can be

drastically improved. Ferroelectricity was observed in BaTiO3/SrTiO3 superlattices

containing as few as one BaTiO3 layer in the repeated superlattice structural unit, i.e., a

BaTiO3 layer just 4 Å thick. The combination of finite size and strain effects was seen to

shift the TC of commensurate [(BaTiO3)n/(SrTiO3)m]p superlattices over a 500 K range.

ACKNOWLEGMENTS

We gratefully acknowledge D. H. A. Blank for informing us of his termination

method for (101) DyScO3 substrates. This work was supported by the Office of Naval

Research under grants N00014-03-1-0721 (D.G.S.), N00014-04-1-0426 (D.G.S.),

N00014-03-1-0534 P0005 (A.F.), and N00014-05-1-0559 (C.B.E.) monitored by Dr.

Colin Wood; by the National Science Foundation (NSF) under grants DMR-0507146

(D.G.S., L.Q.C., X.Q.P., C.B.E., and X.X.X.), DMR-0122638 (L.Q.C.), DMR-0213623

(L.Q.C.), DMR-0313764 (C.B.E.), ECS-0210449 (C.B.E.), and DMR-0315633 (X.Q.P.);

by the U.S. Department of Energy (DOE) under grant DE-FG02-01ER45907 (X.X.X.);

53

by a Guggenheim fellowship (L.Q.C.); and by NASA under grant NASA3-NCC1034

(R.S.K.).

54

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56

26 H.-M. Christen, E. D. Specht, D. P. Norton, M. F. Chisholm, and L. A. Boatner: Long-range ferroelectric interactions in KTaO3/KNbO3 superlattice structures. Appl. Phys. Lett. 72, 2535 (1998). 27 M. Sepliarsky, S. R. Phillpot, M. G. Stachiotti, and R. L. Migoni: Ferroelectric phase transitions and dynamical behavior in KNbO3/KTaO3 superlattices by molecular-dynamics simulation. J. Appl. Phys. 91, 3165 (2002). 28 D. G. Schlom, L. Q. Chen, C. B. Eom, K. M. Rabe, S. K. Streiffer, and J. M. Triscone: Strain Tuning of Ferroelectric Thin Films. Annu. Rev. Mater. Res. 37, 589 (2007). 29 J. B. Nelson, and D. P. Riley: An experimental investigation of extrapolation methods in the derivation of accurate unit-cell dimensions of crystals. Proc. Phys. Soc. London 57, 160 (1945). 30 C. Brooks, W. Tian, and D. G. Schlom, unpublished. 31 J. H. Haeni, P. Irvin, W. Chang, R. Uecker, P. Reiche, Y. L. Li, S. Choudhury, W. Tian, M. E. Hawley, B. Craigo, A. K. Tagantsev, X. Q. Pan, S. K. Streiffer, L. Q. Chen, S. W. Kirchoefer, J. Levy, and D. G. Schlom: Room-temperature ferroelectricity in strained SrTiO3. Nature 430, 758 (2004). 32 M. D. Biegalski, Y. Jia, D. G. Schlom, S. Trolier-McKinstry, S. K. Streiffer, V. Sherman, R. Uecker, and P. Reiche: Relaxor ferroelectricity in strained epitaxial SrTiO3 thin films on DyScO3 substrates. Appl. Phys. Lett. 88, 192907 (2006). 33 H. J. Scheel, J. G. Bednorz, and P. Dill: Crystal growth of strontium titanate SrTiO3. Ferroelectrics 13, 507 (1976). 34 S. B. Qadri, J. S. Horwitz, D. B. Chrisey, R. C. Y. Auyeung, and K. S. Grabowski: X-ray characterization of extremely high-quality (Sr,Ba)TiO3 films grown by pulsed-laser deposition. Appl. Phys. Lett. 66, 1605 (1995). 35 P. I. Nabokin, D. Souptel, and A. M. Balbashov: Floating zone growth of high-quality SrTiO3 single crystals. J. Cryst. Growth 250, 397 (2003). 36 J. W. Mathews: Epitaxial growth, edited by J. W. Mathews, (Academic Press, New York 1975), Vol. 2. 37 D.G. Schlom and J.H. Haeni: A thermodynamic approach to selecting alternative gate dielectrics. MRS Bull. 27, 198 (2002). 38 S.G. Lim, S. Kriventsov, T.N. Jackson, J.H. Haeni, D.G. Schlom, A.M. Balbashov, R. Uecker, P. Reiche, J.L. Freeouf, and G. Lucovsky: Dielectric functions and optical bandgaps of high-K dielectrics for metal-oxide-semiconductor field-effect transistors by far ultraviolet spectroscopic ellipsometry. J. Appl. Phys. 91, 4500 (2002). 39 M. Cardona: Optical properties and band structure of SrTiO3 and BaTiO3. Phys. Rev.

57

140, 651 (1965). 40 Y. L. Lee, S. Y. Hu, D. Tenne, A. Soukiassian, D. G. Schlom, X. X. Xi, K. J. Choi, C. B. Eom, A. Saxena, T. Lookman, Q. X. Jia, and L. Q. Chen: Prediction of ferroelectricity in BaTiO3/SrTiO3 superlattices with domains. Appl. Phys. Lett. 91, 112914 (2007). 41 D. Tenne, et al., unpublished.

58

TABLE

Table I. Structural parameters and TC of [(BaTiO3)n/(SrTiO3)m]p superlattices studied in

this work. Here n is the BaTiO3 thickness in unit cells, m is the SrTiO3 thickness in unit

cells, and p is the number of periods. For the samples grown on (101) DyScO3 and (101)

GdScO3 substrates, the measured pseudocubic lattice constant ap is shown in parentheses.

Sample number

n m p d (Å)

(superlattice wavelength)

a (Å) (in-plane spacing)

Film FWHM ω(arc sec)

Substrate FWHM ω (arc sec)

Thickness (Å)

TC from UV

Raman (K)

1 1 4 50 19.7±0.1 3.905±0.01 45 50 ~1000 250±20 2 2 4 40 23.8±0.1 3.905±0.01 62 61 ~950 320±28 3 3 4 35 28.1±0.1 3.905±0.01 21 20 ~980 350±20 4 4 4 25 32.3±0.5 3.90±0.05 87 79 ~800 560±21 5 5 4 25 36.3±0.1 3.91±0.01 90 86 ~900 530±18 6 6 4 20 40.5±0.5 3.91±0.05 320 162 ~800 510±25 7 8 4 10 48.8±0.2 3.90±0.02 109 96 ~500 640±17 8 1 13 20 54.9±0.1 3.905±0.01 38 43 ~1100 170±23 9 2 13 20 59.1±0.1 3.905±0.01 33 35 ~1200 230±25 10 3 13 20 63.3±0.5 3.905±0.05 55 55 ~1250 280±19 11 4 13 20 67.6±0.5 3.905±0.05 108 104 ~1350 380±30 12 6 13 15 75.6±0.5 3.91±0.05 110 118 ~1130 500±21 13 8 13 15 83.6±0.5 3.90±0.05 55 29 ~1250 540±24 14 8 4 40 48.3±0.1 3.945±0.01 214 118 ~1930 440±19 15 1 30 20 121.4±0.5 3.91±0.05 113 139 ~2430 170±15 16 3.95±0.05

(DyScO3) 8 4 40 48.2±0.5

(3.945) 9 8 ~1930 580±17

17 3.97±0.05 (GdScO3)

8 4 40 48.0±0.5 (3.973)

7 7 ~1930 470±20

59

SrTiO3 BaTiO3

Fig. 3.1. Timing diagram of the sequential deposition of barium, strontium, and titanium

during the growth of two periods of a (BaTiO3)8/(SrTiO3)4 superlattice (sample #14).

Oxygen is provided continuously during the growth.

O2

Ba Ti Sr

Time

BaTiO3 SrTiO3

60

010010

(a) (b)

(c) (d)

Fig. 3.2. RHEED patterns during the growth of a [(BaTiO3)8/(SrTiO3)4]40 superlattice

(sample #14) on a TiO2-terminated (001) SrTiO3 substrate. RHEED patterns viewed

along the [100] azimuth (a) with the substrate at room temperature prior to growth and (c)

at Tsub = 650 ºC during the growth (end of the titanium dose during a SrTiO3 layer).

RHEED patterns along the [110] azimuth (b) with the substrate at room temperature prior

to the growth and (d) at Tsub = 650 ºC during the growth (end of the strontium dose during

a SrTiO3 layer). The white boxes show the region containing the 00 and 01 streaks that

was monitored during growth to establish the time evolution of the RHEED streaks

(shuttered RHEED oscillations).

61

0 200 400 600 800 1000 1200 1400

Ba shutter open Sr shutter open

Ti shutter open

(BaTiO3)

8

(SrTiO3)

4

(BaTiO3)

8(BaTiO

3)

8

(SrTiO3)

4(SrTiO

3)

4

RH

EED

Inte

nsity

(arb

. uni

ts)

T im e (sec.)

Fig. 3.3. Shuttered RHEED intensity oscillations observed during the growth of a

[(BaTiO3)8/(SrTiO3)4]40 superlattice (sample #14). The RHEED beam was incident along

the [110] azimuth during growth. Three periods of [(BaTiO3)8/(SrTiO3)4]40 superlattice

growth are shown. The average diffracted intensity in the regions shown in Fig. 3.2(d) of

the 00 streak (top) and 01 streak (bottom) were recorded simultaneously. Dashed lines

show the boundaries of the (BaTiO3)8 and (SrTiO3)4 sections of the superlattice.

62

0 1 2 3 4

-10

-5

0

5

10

Sca

n he

ight

(Å)

Scan distance (µm)

(b)

Fig. 3.4. (a) An AFM image of a TiO2-terminated (001) SrTiO3 substrate prepared using

the method described in Ref. 15. The AFM scan extends over 4x4 µm with a height range

of 0.5 nm from black to white. (b) A horizontal line-scan across (a) reveals well-defined

single-layer steps each ~0.39 nm in height.

63

0 100 200 300 400 500 600 700

Ba shutter open Sr shutter open

T i shutter open

T im e (sec.)

RH

EED

Inte

nsity

(arb

. uni

ts) (BaT iO

3)

4(BaTiO

3)

4(BaT iO

3)

4(S rT iO

3)

2(S rTiO

3)

2(S rT iO

3)

2

Fig. 3.5. The shuttered RHEED intensity oscillation observed from the beginning of the

growth of a [(BaTiO3)4/(SrTiO3)2]40 superlattice (sample #14) on a non-terminated (001)

SrTiO3 substrate. The intensity of the 01 RHEED streak along the [110] azimuth for the

first three superlattice periods is shown.

64

0 100 200 300 400 500 600 700

Ba shutter open

Ti shutter open

Sr shutter openRH

EE

D In

tens

ity (a

rb. u

nits

)

Time (sec.)

Fig. 3.6. The shuttered RHEED intensity oscillation observed from the beginning of the

growth of a [(BaTiO3)6/(SrTiO3)13]15 superlattice (sample #12) on a TiO2-terminated

(001) SrTiO3 substrate. The intensity of the 01 RHEED streak along the [110] azimuth of

the first superlattice period is shown.

65

0 200 400 600 800

RH

EE

D In

tens

ity (a

rb. u

nits

)

T ime (sec.)

Ba shutter open Sr shutter open

Ti shutter open

(BaTiO3)

8(BaTiO

3)

8(SrTiO

3)4

(SrTiO3)

4

Fig. 3.7. The shuttered RHEED intensity oscillation observed from the beginning of the

growth of a [(BaTiO3)8/(SrTiO3)4]40 superlattice (sample #17) on a (101) GdScO3

substrate. The intensity of the 01 RHEED streak along the [110] azimuth for the first two

superlattice periods is shown.

66

Fig. 3.8. RHEED patterns during the growth of a [(BaTiO3)8/(SrTiO3)4]40 superlattice

(sample #17) on a (101) GdScO3 substrate at Tsub = 650 ºC. RHEED patterns viewed

along the [100] pseudocubic azimuth (a) of the bare substrate prior to growth and (c)

during the growth (end of the titanium dose during a SrTiO3 layer). RHEED patterns

along the [110] pseudocubic azimuth (b) of the bare substrate prior to the growth and (d)

during the growth (end of the titanium dose during a SrTiO3 layer). The white boxes

show the recorded area of the 01 superlattice streak.

(a)

(d)

(b)

(c)

67

(a) (b)

(c) (d)

Fig. 3.9. RHEED patterns of bare (101) DyScO3 substrates at Tsub = 650 ºC prior to

growth. RHEED patterns viewed along the [100] pseudocubic azimuth (a) of a non-

terminated substrate and (c) a terminated substrate. RHEED patterns along the [110]

pseudocubic azimuth (b) of a non-terminated substrate and (d) a terminated substrate.

68

0 100 200 300 400

RH

EED

Inte

nsity

(arb

. uni

ts)

Time (sec.)

Ba shutter open Sr shutter open

Ti shutter open

(BaTiO3)8

(SrTiO3)4

0 100 200 300 400 500

RH

EED

Inte

nsity

(arb

. uni

ts)

Time (sec.)

Ba shutter open Sr shutter open

Ti shutter open

(BaTiO3)8

(SrTiO3)4

Fig. 3.10. The shuttered RHEED intensity oscillation observed from the beginning of the

growth of a [(BaTiO3)8/(SrTiO3)4]40 superlattice on a non-terminated (a) and terminated

(b) (101) DyScO3 substrate. The intensity of the 01 RHEED streak along the [110]

azimuth of the first superlattice period is shown.

69

0 10 20 30 40 50

n

0021

* *

* *

* *

**

**

**00

1

Inte

nsity

(arb

. uni

ts)

2θ (degrees)

0015

0014

**

0020 00

270022

0020

0026

0024

0023

0022

0020

0019

0018

001700

16

0013

0012

0011

0010

009

008

00700

6

005

004

003

002

001

0011

0010

009

008

007

006

005

004

003

002

0013

0012

001

0010

009

008

007

006

005

00400

3002

0015

0014

0013

0012

001

0011

0010

009

008

007

00600

5

004

003

002

0016

0018

0017

0016

0015

0014

0013

0012

001

0011

0010

009

008

007006

005

004

003

0018

0017

0016

0019

0014

0013

0012

001

0011

0010

009

00800

7

00600

4003

002

001800

170016

0015

0014

0013

0012

0011

0010

009

008

00500

4

002

1

2

3

5

6

8

4

Fig. 3.11. θ – 2θ x-ray diffraction scans of the [(BaTiO3)n/(SrTiO3)m]p superlattices using

Cu Kα radiation for m = 4 and n = 1, 2, 3, 4, 5, 6, and 8 (samples #1−7). Substrate peaks

are marked with asterisks (*). Nearly all superlattice peaks are present for 2θ < 55°,

indicating atomically sharp interfaces between the BaTiO3 and SrTiO3 layers and

accurate superlattice periodicity.

70

0 10 20 30 40 50

n* *

*

**

0034

0033

Inte

nsity

(arb

. uni

ts)

2θ (degrees)

0031

0015

0014

0030

0029

0028

0027

0026

0025

0024

0023

0022

0021

002000

19001800

170016

0013

0012

0011

0010

009

008

00700

6005

004

003

002

0032

0035

0015

0014

0030

0029

0028

0027

0026

0025

0024

0023

002200

21002000

19001800

170016

0013

0012

0011

0010

009

008

00700

600

500

400

300

2

0034

0033

0032

0031

0015

0014 00

3000

2900

2800

2700

2600

2500

2400

2300

220020

0019

001800

1700

16

0013

0012

0011

001000

9008

007

00600

500

400

300

2

1

2

3*

Fig. 3.12. θ – 2θ x-ray diffraction scans of the [(BaTiO3)n/(SrTiO3)m]p superlattices using

Cu Kα radiation for m = 13 and n = 1, 2, and 3 (samples #8−10). Substrate peaks are

marked with asterisks (*). Nearly all superlattice peaks are present for 2θ < 55°,

indicating atomically sharp interfaces between the BaTiO3 and SrTiO3 layers and

accurate superlattice periodicity.

71

0 90 180 270 360

101

102

103

104

105

Inte

nsity

(arb

. uni

ts)

φ (degrees)

Fig. 3.13. An x-ray diffraction φ scan at χ = 44.3º of the 1012 peak of the

[(BaTiO3)8/(SrTiO3)4]40 superlattice (sample #14) grown on a (001) SrTiO3 substrate.

χ = 90º aligns the diffraction vector to be perpendicular to the plane of the substrate.

φ = 0° corresponds to when the in-plane component of the diffraction vector is parallel to

the [100] in-plain direction of the substrate. This scan shows that the superlattice is

epitaxial with the expected ([100] superlattice || [100] substrate) in-plane alignment with

the substrate.

72

Fig. 3.14. (a) Rocking curves of the [(BaTiO3)3/(SrTiO3)4]35 superlattice 0014 peak and

the underlying SrTiO3 substrate 002 peak (sample #3). The FWHM is 21 arc sec

(0.0058°) for the superlattice peak as compared to 20 arc sec (0.0055°) for the substrate

peak. The sharp rocking curve indicates the high structural perfection of the superlattice.

(b) Rocking curves of the [(BaTiO3)2/(SrTiO3)4]40 superlattice 0012 peak and the

-0.2 -0.1 0.0 0.1 0.2

Inte

nsity

(arb

. un.

)

ω (degrees)

SrTiO3

substrate

Film

Inte

nsity

(arb

. uni

ts)

Film

(a)

SrTiO3 substrate

(b)

73

underlying SrTiO3 substrate 002 peak (sample #2). The FWHM is 62 arc sec (0.0172°)

for the superlattice peak as compared to 61 arc sec (0.0169°) for the substrate peak

having a strongly mosaic feature.

74

Threading

Fig. 3.15. (a) A cross-sectional HRTEM image of the partially relaxed

[(BaTiO3)8/(SrTiO3)4]40 superlattice grown on a (001) SrTiO3 substrate (sample #14)

showing threading dislocation. (b) Z-contrast TEM over a larger area of the same

[(BaTiO3)8/(SrTiO3)4]40 superlattice (sample #14). The threading dislocations are the light

vertical defects, some of which are labeled with arrows.

75

Fig. 3.16. (a) A cross-sectional HRTEM image of the [(BaTiO3)1/(SrTiO3)13]20

superlattice (sample #8). It shows alternating layers of 1 unit cell of BaTiO3 and 13 unit

cells of SrTiO3, confirming the intended superlattice periodicity and the XRD result. (b)

Z-contrast HRTEM image of the [(BaTiO3)1/(SrTiO3)4]50 superlattice (sample #1). The

interfaces are abrupt and no misfit dislocations were seen.

76

Fig. 17. XRD scans of the [(BaTiO3)8/(SrTiO3)4]40 superlattice grown on (101) DyScO3

substrate (sample #16) (a) shows a θ – 2θ scan. Substrate peaks are marked with asterisks

(*). Nearly all superlattice peaks are present for 2θ < 55°, indicating atomically sharp

interfaces between BaTiO3 and SrTiO3 layers and accurate periodicity. (b) The in-plane

orientation relationship between the [(BaTiO3)8/(SrTiO3)4]40 superlattice and the (101)

DyScO3 substrate was determined by a φ-scan at χ = 45° of the 1012 superlattice peak.

φ = 0° corresponds to when the in-plane component of the diffraction vector is parallel is

aligned parallel to the [010] in-plane direction of the DyScO3 substrate. (c) Rocking

curves of the same [(BaTiO3)8/(SrTiO3)4]40 superlattice and the underlying DyScO3

substrate FWHM of 9 arc sec (0.0024°) for the superlattice 0024 peak and FWHM of 8

arc sec (0.0022°) for the 202 peak of the DyScO3 substrate were measured.

77

0 10 20 30 40 50102

103

104

105

Inte

nsity

(arb

. uni

ts)

2θ (degrees)

0025

003

0019

0018

*

0022

0027

0026

0024

0023

0021

0020

001700

1600

1500

140013

0012

0011

0010

009

008

007

006

005

004

002

*

-0.2 -0.1 0.0 0.1 0.2101

102

103

104

105

106

107

Inte

nsity

(arb

. uni

ts)

ω (degrees)

(a)

DyScO3

substrate

Film

0 90 180 270 360100

101

102

103

104

Inte

nsity

(arb

. uni

ts)

φ (degrees)

(b)

(c)

78

Fig. 18. XRD scans of the [(BaTiO3)8/(SrTiO3)4]40 superlattice grown on (101) GdScO3

substrate (sample #17) (a) shows a θ – 2θ scan. Substrate peaks are marked with asterisks

(*). Nearly all superlattice peaks are present for 2θ < 55°, indicating atomically sharp

interfaces between BaTiO3 and SrTiO3 layers and accurate periodicity. (b) The in-plane

orientation relationship between the [(BaTiO3)8/(SrTiO3)4]40 superlattice and the (101)

GdScO3 substrate was determined by a φ-scan at χ = 42.09º of the 1011 superlattice

peak. φ = 0° corresponds to when the in-plane component of the diffraction vector is

parallel to the [010] in-plain direction of the GdScO3 substrate. (c) Rocking curves of the

[(BaTiO3)8/(SrTiO3)4]40 superlattice. FWHM of 7 arc sec (0.0020°) for the superlattice

0024 peak and FWHM of 7 arc sec (0.0019°) for the 202 peak of the GdScO3 substrate

were measured.

79

0 10 20 30 40 50102

103

104

105

003

Inte

nsity

(arb

. uni

ts)

2θ (degrees)

0025

0019

0018

*

0022

0027

0026

0024

0023

0021

0020

001700

1600

1500

1400

1300

1200

1100

1000

900

800

700

500

4

002

*

-0.2 -0.1 0.0 0.1 0.2100

101

102

103

104

105

106

107

108

Inte

nsity

(arb

. uni

ts)

ω (degrees)

(a)

GdScO3

substrate Film

0 90 180 270 360100

101

102

103

φ (degrees)

Inte

nsity

(arb

. uni

ts) (b)

(c)

80

0 100 200 300 400 500 600 700 8003.8

3.9

48.7

48.8

48.9

49.0

49.1 d (superlattice) a (superlattice) a (substrate)

Temperature (°C)

Latti

ce P

aram

eter

s (Å

)

TC ~400 °C

0 100 200 300 400 500 600 700 8003.8

3.9

48.3

48.4

48.5

48.6

48.7

48.8

Temperature (°C)

d (superlattice) a (superlattice) a (substrate)

(a) (b)

Fig. 3.19. Temperature dependence of the lattice constants of the (a) commensurate

[(BaTiO3)8/(SrTiO3)4]10 superlattice (sample #7), (b) partially relaxed

[(BaTiO3)8/(SrTiO3)4]40 superlattice (sample #14), and SrTiO3 substrate, measured by

XRD.

81

1 2 3 4 5 6 7 8 90

100

200

300

400

500

600

m = 4

Fig. 3.20. A summary plot of the TC obtained from UV Raman measurements. (a) Shows

the dependence of TC on n and m in [(BaTiO3)n/(SrTiO3)m]p superlattices grown on (001)

SrTiO3 substrates. Solid triangles are for m = 4, solid squares are for m = 13, and the open

diamond symbol is for m = 30. Open circles are from temperature-dependent XRD

measurements. Lines are from three-dimensional phase-field model calculations for m = 4

and m = 13 and the horizontal dash-dotted line shows the TC of bulk (unstrained) BaTiO3.

(b) dependence of TC on the mismatch strain ε on the BaTiO3 layers in the superlattices

with the same [(BaTiO3)8/(SrTiO3)4]p structure grown on (001) SrTiO3, (101) DyScO3,

and (101) GdScO3 substrates (samples #7, 16, 17).

m = 13

Tc (K)

n in (BaTiO3)n/(SrTiO3)m

bulk BaTiO3

-2 -1 0

400

500

600

on SrTiO3

partially relaxed

Bulk BaTiO3

Tc (K)

Mismatch strain ε (%)

on GdScO3

on DyScO3

on SrTiO3(a) (b)

82

Chapter 4

Acoustic Bragg mirrors and cavities made using piezoelectric oxides

Applied Physics Letters 90, 042909 (2007)

83

Acoustic Bragg mirrors and cavities made using piezoelectric oxides

A. Soukiassian, W. Tian, D. A. Tenne,a) X. X. Xi, and D. G. Schlom

Materials Research Institute, The Pennsylvania State University, University Park,

Pennsylvania 16802

N. D. Lanzillotti-Kimura, A. Bruchhausen, and A. Fainstein

Centro Atómico Bariloche & Instituto Balseiro, C.N.E.A., 8400 S. C. de Bariloche, R.N.,

Argentina

H. P. Sun and X. Q. Pan

Department of Materials Science and Engineering, University of Michigan, Ann Arbor,

Michigan 48109

A. Cros and A. Cantarero

Materials Science Institute, University of Valencia, P.O. Box 22085, E-46071 Valencia,

Spain

(Received

84

Abstract

The concept and design of acoustic Bragg mirrors and cavities made of

multilayers of piezoelectric oxides with superior acoustic performance and

potential applications in electronic and optical THz modulators are described.

With these applications in mind we have grown phonon mirrors consisting of

BaTiO3/SrTiO3 superlattices on SrTiO3 substrates by reactive molecular-beam

epitaxy and investigated their properties. Characterization of the superlattices by

x-ray diffraction and high-resolution transmission electron microscopy reveals

high structural quality with nearly atomically abrupt interfaces. We have observed

folded acoustic phonons at the expected frequencies using uv Raman

spectroscopy.

a) Currently at Department of Physics, Boise State University, Boise, Idaho 83725

85

Tailoring acoustic phonon properties is important for THz frequency phonon

devices including the generation and amplification of coherent phonons.1-6 Recently, THz

acoustic cavities have been demonstrated with enormously amplified acoustic phonon-

photon interaction,2,7 leading to the possibility of modifying the lifetime of optical

phonons through tailored anharmonic processes.8 Acoustic cavities could also provide the

required feedback mechanism of a phonon laser.4,8 These and other important

developments in THz acoustics are based mainly on compound semiconductors using

mature epitaxial growth techniques like molecular-beam epitaxy (MBE) that enable the

construction of heterostructures with atomically flat interfaces by design.

Heterostructures of oxide materials such as BaTiO3 and SrTiO3, with strong

coupling between sound, charge, and light, offer a nearly unexplored, but rich terrain of

versatile compounds with superior acoustic properties. They provide a range of acoustic

impedances that can exceed the acoustic impedance mismatches in semiconductor

heterostructures. In addition, they can be strongly piezoelectric, providing additional

mechanisms that can significantly enhance sound-light coupling9 and allowing electrical

tuning of acoustic cavity wavelengths. Recently, room temperature ferroelectricity was

observed in SrTiO3 thin films under ~1% biaxial tensile strain.10-12 Such strain could be

attained at THz frequencies through coherent phonon generation using ultrafast laser

excitation.9 Because the light-sound interaction is greatly amplified in piezoelectric and

ferroelectric materials,13 including strain-enhanced heterostructures of ferroelectric

SrTiO3 and BaTiO3,12,14,15 these are very attractive for efficient phonon devices operating

at THz frequencies.

86

In the present paper we propose acoustic Bragg mirrors and cavities made of

BaTiO3/SrTiO3 heterostructures. Figure 1 shows their schematics, calculated acoustic

reflectivity, and phonon field distribution.16,17 The BaTiO3/SrTiO3 structures are

compared with equivalent ones made of GaAs/AlAs, the materials system previously

used for these acoustic structures,2,7 and of BaO/SrTiO3, another multilayer that can be

grown by reactive MBE. A superlattice with a basic building block formed by two

acoustic impedance-mismatched materials with respective layer thicknesses λ/4 and 3λ/4

acts as an acoustic phonon Bragg mirror with stop-band centered at ω = v/λ. Here λ and v

are the (material dependent) phonon wavelength and sound velocity, respectively.2 The

acoustic impedance mismatch Z = (v1ρ1)/(v2ρ2) < 1,7 where vj and ρj are the sound

velocity and density of material j, respectively. For BaTiO3/SrTiO3 Z = 0.75, whereas

Z = 0.84 for GaAs/AlAs and Z = 0.66 for BaO/SrTiO3.16 This difference in Z leads to

enormous differences in device performance, as shown in Fig. 4.1. A (001)-oriented

BaTiO3/SrTiO3 superlattice with a building block made of 4 unit cells of SrTiO3 and 8

unit cells of BaTiO3 is close to having the ideal (λ/4, 3λ/4) stacking. The mirror

reflectivities R for superlattices with 10 repeats are 0.878 for GaAs/AlAs, 0.987 for

BaTiO3/SrTiO3, and 0.999 for BaO/SrTiO3.16 A BaTiO3/SrTiO3 phonon cavity may be

constructed by enclosing a 21 unit-cell-thick (001) BaTiO3 spacer, which is close to 2λ,

between two [(BaTiO3)8/(SrTiO3)4)]10 phonon mirrors leading to a well centered cavity

mode. Here the subscript 4 and 8 indicate the thickness of the (001)-oriented SrTiO3 and

BaTiO3 layers in unit cells and the subscript 10 indicates the number of times the

BaTiO3/SrTiO3 bilayer is repeated.

87

Fig. 4.1. Top: Calculated acoustic reflectivity as a function of phonon energy (left) and

square of phonon displacement along the growth axis z as a function of the distance into

the mirror (right) for phonon mirrors consisting of a superlattice of (001)-oriented

BaTiO3/SrTiO3 layers repeated 10 times. Bottom: Calculated acoustic reflectivity as a

function of phonon energy (left) and square of phonon displacement along the growth

axis z as a function of the distance from the surface of the top mirror (right) for 2λ

acoustic cavities enclosed by the superlattice phonon mirrors with 10 repeats shown in

the top panel. The increasing curve thicknesses correspond to BaO/SrTiO3,

BaTiO3/SrTiO3, and GaAs/AlAs, respectively. A schematic of the structure for the

specific case of BaTiO3/SrTiO3 is shown.

88

As is evident from the plot in Fig. 4.1, a higher R results in a better cavity finesse.

A consequence of the better finesse is a larger number of transit times of a phonon in the

cavity before tunneling out through the mirrors. For the cavities shown, this corresponds

to 8 for the GaAs/AlAs structure, 80 for BaTiO3/SrTiO3, and 1000 for BaO/SrTiO3.16

Concomitant with this increase in finesse, the square of the phonon displacement at the

cavity center (indicative of the cavity Q-factor and related to the acoustic energy

deposited at the resonator) grows from ~12, to ~120, to ~1500 (given in relative units, for

an incident phonon wave of amplitude equal to 1).16 The latter, corresponding to

BaO/SrTiO3, is not shown in Fig. 4.1 for clarity.

The most important problem related to the growth of the heterosturctures

described above is the abruptness of the many ideally planar heterointerfaces on the

atomic scale. Due to the extremely short phonon wavelength targeted for these structures

(λ ~5 nm for 4 unit cells SrTiO3 and 8 unit cells BaTiO3 phonon mirrors), the quality of

the heterointerfaces plays a crucial role in the device performance. MBE has been used to

create outstanding oxide superlattices with interface flatness and abruptness rivaling that

of compound semiconductor superlattices grown by the same technique.18

Epitaxial BaTiO3/SrTiO3 superlattices were grown on TiO2-terminated (001)

SrTiO3 substrates19 by reactive MBE. The BaTiO3/SrTiO3 superlattices were grown by

sequential deposition of the constituent monolayers at a background pressure of

5×10-7 Torr of molecular oxygen and a substrate temperature of 650-700° C, as measured

by an optical pyrometer. Additional details on the sample preparation are given

elsewhere.20

Four-circle x-ray diffraction with Cu Kα radiation and high-resolution

89

transmission electron microscopy (HRTEM) were used to structurally characterize the

[(BaTiO3)8/(SrTiO3)4]40 superlattice. A θ-2θ x-ray diffraction scan is shown in Fig. 4.2.

Nearly all superlattice peaks are present for 2θ < 55°, which is an indication of atomically

sharp interfaces between BaTiO3 and SrTiO3 layers. The superlattice period,

dSL = 48.25 ± 0.01 Å, was obtained from a Nelson-Riley analysis21 of these peaks. The

in-plane orientation relationship between the [(BaTiO3)8/(SrTiO3)4]40 superlattice and the

(001) SrTiO3 substrate was determined by a φ-scan of the 1012 superlattice peak. The

result is that the [100] superlattice direction is aligned parallel to the [100] SrTiO3

substrate direction.20 From the position of the 1012 superlattice peak and the out-of-plain

lattice parameter, the in-plane lattice parameter a = 3.946 ± 0.003 Å was determined.

This in-plane lattice constant lies between that of SrTiO3 and BaTiO3, as expected for a

partially relaxed [(BaTiO3)8/(SrTiO3)4]40 superlattice that is no longer commensurately

strained to the underlying (001) SrTiO3 substrate. An analogous phonon mirror with

fewer repeats i.e., [(BaTiO3)8/(SrTiO3)4]10 was fully commensurate with the underlying

(001) SrTiO3 substrate.22 The full width at half maximum (FWHM) of the rocking curve

of the 0023 peak of the [(BaTiO3)8/(SrTiO3)4]40 superlattice was 0.06°. A cross-sectional

HRTEM image of the same superlattice is shown in Fig. 4.3. It reveals that the

superlattice has nearly atomically abrupt interfaces. The interface roughness determined

between the BaTiO3 and SrTiO3 layers is within 1 unit cell.

Raman scattering is a powerful technique to monitor the phonon properties of

acoustic devices.2,7,8 The challenge with oxide heterostructures lies in the large optical

gaps, implying that Raman experiments with visible lasers are hindered by the small

photoelastic constants, and the overwhelming contribution of the SrTiO3 substrate. It has

90

10 20 30 40 50

102

103

104

105

2θ (degrees)

Inte

nsity

(arb

. uni

ts)

004

0019

0018

*

0022

0027

0026

0025

0024

0023

0021

0020

001700

1600

1500

1400

1300

1200

1100

1000

9008

007

006

005

003

002

*

Fig. 4.2. θ-2θ x-ray diffraction scan of a [(BaTiO3)8/(SrTiO3)4]40 superlattice. Substrate

peaks are marked by asterisks (*).

91

Fig. 4.3. Cross-sectional HRTEM image of a [(BaTiO3)8/(SrTiO3)4]40 superlattice grown

on a (001) SrTiO3 substrate.

92

been recently shown that uv Raman spectroscopy can be used for ferroelectric thin films

and superlattices.22 We used a uv-optimized Jobin-Yvon T64000 triple spectrometer with

a N2-cooled multichannel coupled-charge-device detector and the λ = 351.1 nm line of an

Ar-laser for excitation. A measured room temperature Raman spectrum for the same

[(BaTiO3)8/(SrTiO3)4)]40 superlattice in the low frequency region, obtained with

polarizations parallel to [100] in backscattering along the growth c-axis, is shown in Fig.

4. A clear doublet due to the folded longitudinal acoustic (LA) phonon modes is

observed. The expected energy of the LA doublet can be derived by evaluating the

acoustic modes of the superlattice with a Rytov continuum-model23 and using the

wavevector transferred in the Raman scattering process, q = 4πn/λ. To evaluate the latter,

shown with the horizontal dashed line in the top panel of Fig. 4.4, the index of refraction

of the superlattice at 351.1 nm (n = 2.88) was measured using variable-angle

ellipsometry. The folded phonon dispersion, calculated using the c-axis phonon velocities

vSrTiO3 = 7848.5 m/s and vBaTiO3 = 5420 m/s is displayed in the top panel of Fig. 4.4.24,25

The predicted Raman doublet energies, corresponding to the intersection between the

phonon dispersion and the transferred wavevector q, match precisely the experimental

peaks. We also show in Fig. 4.4 the Raman spectrum obtained with a photoelastic model

for the Raman efficiency.23 The calculated curve was Gaussian convoluted to account for

the spectrometer resolution (2σ = 3 cm-1). The agreement between the measured and

calculated spectra is extremely good, both for the position and relative intensity of the

peaks.

In conclusion, we propose THz acoustic mirrors and cavities based on multilayers

of BaTiO3, SrTiO3, and BaO. These structures exploit the acoustic and ferroelectric

93

properties of oxides for superior performance. Our results demonstrate the feasibility to

design, fabricate, and characterize oxide piezoelectric acoustic devices.

This work is partially supported by ONR under grant Nos. N00014-03-1-0721

(AS, WT, and DGS) and N00014-04-1-0426 (AS, WT, and DGS) monitored by Dr. Colin

Wood, by NSF under grant No. DMR-0507146 (AS, DGS, HPS, XQP, and XXX), and

by DOE under grant No. DE-FG02-01ER45907 (DAT and XXX). AF acknowledges

supports from ONR (US) and CONICET (Argentina).

94

30 34 38 42 46 50

T

E

Ram

an In

t. (a

rb. u

nits

)

Raman Shift (cm-1)

0.1

0.3

q (π

/dS

L)

Fig. 4.4 Bottom: Folded acoustic phonon modes measured by uv Raman scattering (E) in

comparison with a photoelastic model calculation of the Raman efficiency (T). Top:

Folded acoustic phonon dispersion obtained with a continuum Rytov model. The

horizontal dashed line indicates the wavevector q transferred in the Raman scattering

process.

95

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Chapter 5

Conclusions and future work

5.1 Conclusions.

Nanoscale BaTiO3/SrTiO3 superlattices were grown by shuttered sequential

deposition of constituent monolayers in reactive MBE on (001) SrTiO3, (101) DyScO3,

and (101) GdScO3 substrates. By carefully monitoring RHEED intensity oscillations, the

shutter opening times for sequential deposition of precise monolayer doses of BaO, SrO,

and TiO2 were calibrated. The behavior of the RHEED intensity oscillations at the

beginning and during the growth of BaTiO3/SrTiO3 superlattices on the aforementioned

substrates was described. Structural characterization made by XRD and HRTEM

revealed that these nanoscale epitaxial BaTiO3/SrTiO3 superlattices are of high quality

with nearly atomically abrupt interfaces. BaTiO3/SrTiO3 superlattices grown on DyScO3

and GdScO3 show the FWHM in ω as narrow as 9 and 7 arc sec, respectively, the

narrowest rocking curves ever reported for oxide superlattices. UV excitation enabled us

to overcome the problem of the overwhelming substrate contribution in the Raman

spectra and made possible measurements of TC in nanoscale BaTiO3/SrTiO3 superlattices

(the first ever reported use of UV Raman spectroscopy to study thin ferroelectric

superlattices). By using temperature-dependent UV Raman and XRD we have observed

ferroelectricity in BaTiO3/SrTiO3 superlattices having BaTiO3 layers as thin as 1 unit cell.

Depending on the thickness of the BaTiO3 layers and the mismatch strain applied by the

underlying substrate, the TC varies from ~150 K to ~640 K. Below the TC the

BaTiO3/SrTiO3 superlattices likely remain in the same (tetragonal) phase down to 7 K

99

indicating that the low-temperature phases (orthorhombic and rhombohedral)

characteristic for bulk BaTiO3 are suppressed by strain. Also the strained ferroelectric

BaTiO3 layers in the superlattices induce polarization in the much thicker unstrained

SrTiO3 layers. In addition, the strained SrTiO3 layers within the BaTiO3/SrTiO3

superlattices grown on DyScO3 and GdScO3 substrates exhibit strain-induced

polarization. Relaxation via the formation of misfit dislocation will occur if the critical

thickness of the superlattice is exceeded. The ~2000 Å in thick [(BaTiO3)8/(SrTiO3)4]40

superlattice grown on a SrTiO3 substrate showed partial relaxation of its strain by about

~1%, which resulted in a significant reduction of the TC by ~200 K as compared to the TC

of a superlattice with the same structure that was commensurate. Results obtained on

nanoscale BaTiO3/SrTiO3 superlattices demonstrate the importance of finite size and

strain effects on TC and are in good agreement with theoretical predictions.

The design and important material parameters of terahertz acoustic mirrors and

cavities made of BaTiO3/SrTiO3 and BaO/SrTiO3 heterostructures with superior acoustic

performance were discussed. The first step to phonon confinement structures is to grow a

λ/4 thick planar periodic stack of two different materials with different acoustic

impedance, which will work as a Bragg reflector with a stop band around λ and functions

as a phonon mirror. The second step is the construction of a phonon cavity by enclosing a

spacer of thickness dc = mλc/2 between two phonon mirrors, where λc is the acoustical

phonon wavelength at the center of the phonon minigap and m is an integer. The

advantages of using these ferroelectric superlattices are that they have an enormous stop

band compared to the GaAs/AlAs superlattices previously reported for this application

and that there can be greatly amplified light-sound interaction in these ferroelectric

100

materials. Fabrication and characterization of acoustic phonon Bragg mirrors made of

BaTiO3/SrTiO3 superlattices were demonstrated. The folded acoustic phonons were

observed and their positions agree well with the elastic continuum model calculations.

The obtained results may be considered as a first step towards a phonon “laser.”

5.2 Future work.

The value of spontaneous polarization (PS) in strain-engineered ferroelectric

BaTiO3/SrTiO3 superlattices is of great interest. The direct electrical measurements of PS

and dielectric permittivity in a parallel plate capacitor geometry using various bottom

electrodes such as epitaxial SrRuO3 and La0.67Ba0.33MnO3 films, as well as 0.075% La-

doped SrTiO3 and 0.5% Nb-doped SrTiO3 conducting substrates were not successful due

to the electrical leakage. This problem likely arises from the large number of oxygen

vacancies formed during superlattice growth in a low oxygen background pressure of

5×10-7 Torr. The subsequent increase of the growth pressure to 5×10-6 Torr in a ~10%

ozone/oxygen mixture followed by ex situ annealing in an oxygen atmosphere did not

help to fully oxidize the BaTiO3/SrTiO3 superlattices and solve the leakage problem.

Nevertheless, the solution to this problem might be found by increasing the percentage of

ozone in ozone/oxygen mixture. This can be done by using an ozone distiller that can

increase the ozone concentration in ozone/oxygen mixture to be as high as ~80%.

However, in this work distilled ozone was not used.

Specific heat and heat conductivity measurements could be used as an alternative

method to derive the information of the PS, excess entropy, and TC in BaTiO3/SrTiO3

superlattices. We are collaborating on this with Prof. B. Strukov’s group at Lomonosov

101

Moscow State University. They can measure the temperature dependence of the specific

heat of the BaTiO3/SrTiO3 superlattices by the 3ω-calorimetric method.1 The results of

these measurements will be compared with the Raman data and theoretical calculations,

which can shed additional light on the properties of BaTiO3/SrTiO3 superlattices. The

preliminary results obtained on several samples show TC similar to the ones obtained

from the UV Raman measurements and reveal the temperature dependence of PS. To the

best of our knowledge the specific heat measurements of BaTiO3/SrTiO3 superlattices are

the first time ever performed on ferroelectric superlattices. These studies show good

progress and results will be published elsewhere.

Information on the domain structures and their effects on physical properties of

BaTiO3/SrTiO3 superlattices are of great interest. Recently, Li at al. studied the single-

and multidomain states of BaTiO3/SrTiO3 superlattice, revealing the importance of

domain formation on the ferroelectric phase transitions and predicting that the size of the

domains is related to the superlattice structure.2 The experimental imaging of the domains

in BaTiO3/SrTiO3 superlattices can help us to reveal the domain structures and

investigate the possibility of changing the size of the domains by changing the

superlattice structure. Thus, we began collaboration with Prof. D. Bonnel’s group at the

University of Pennsylvania to conduct scanning probe microscopy (SPM) imaging of the

domains. The domain structure can be also obtained from high-resolution synchrotron x-

ray scattering. 3 These measurements were performed on thin (less than 100Å)

BaTiO /SrTiO superlattices in collaboration with D. Fong, P. Fuoss, J. Eastman, and S.

Streiffer at Argonne National Lab. By measuring a series of crystal truncation rods using

a synchrotron x-ray source it should be also possible to obtain the temperature

3 3

102

dependence of the degree of polarization, polarization distribution, and T in the

BaTiO /SrTiO superlattices. The results of these measurements will be published

elsewhere.

C

3 3

As I have shown the ReScO3 substrates (where Re is rear-earth material: La, Gd,

Dy, Ho, Sm, Nd...) are perfect candidates to study the mismatch strain effect in

BaTiO3/SrTiO3 superlattices. The results that I have obtained on BaTiO3/SrTiO3

superlattices grown on GdScO3 and DyScO3 substrates exhibit the narrowest rocking

curves ever reported for oxide superlattices. Further improvements of the superlattice

structure are expected if the methods to terminate ReScO3 substrates at specific atomic

layers (i.e., either the ReO of ScO2 layer) are developed or if in situ homoepitaxial

deposition of these ReScO3 materials is available in the same MBE system in which the

superlattices are grown. Recently, new SmScO3 and NdScO3 substrates having

pseudocubic lattice parameter ap = 3.99 Å and 4.02 Å, respectively, became

commercially available. These substrates are of particular interest since the mismatch

strain exerted on BaTiO3/SrTiO3 superlattices by the underlying substrate is such that

BaTiO3 layers are almost not strained while the SrTiO3 layers are highly strained (~2.2%).

Growth on such substrates would allow further investigation of strain and finite size

effects in nanoscale BaTiO3/SrTiO3 superlattices.

The next step towards the phonon “laser” is to check the efficiency of terahertz

acoustic phonon Bragg mirrors and cavities by measuring the transmittance and

reflectivity. Unfortunately, the maximum frequencies currently available in the “pump

and probe” technique lie in the sub THz range indicating that the individual BaTiO3 and

103

SrTiO3 layer thicknesses of the acoustic Bragg mirrors and cavities must be significantly

larger.

The growth of thick high quality superlattice structures can be challenging. High

densities of misfit dislocations will cause the thick superlattices to relax from their high-

strain state. Also the accurate control of the Sr, Ba, and Ti molecular beams is very

difficult, since they may drift during a very long deposition of the thick superlattices.

However, I have recently grown such BaTiO3/SrTiO3 superlattices ~0.5 µm in thickness

capped with a 1 µm thick SrTiO3 film. This thick superlattice stack is a part of ongoing

research and the results will be published elsewhere.

The calculations of our collaborator Dr. A. Fainstein have shown that another

combination of oxides, BaO/SrTiO3 superlattices, can be considered for acoustic phonon

Bragg mirrors and cavities. In fact BaO/SrTiO3 mirrors are expected to have significantly

better acoustic performance than BaTiO3/SrTiO3 mirrors. However, the growth of

BaO/SrTiO3 superlattices can be challenging. Although the in-plane lattice parameters of

BaO and SrTiO3 are close, the optimization of the growth parameters is difficult. More

details on the growth of BaO/SrTiO3 superlattices can be found in Appendix.

Other combinations of oxides such as superlattices of ReScO3/BaTiO3 and

ReScO3/SrTiO3 can be considered if information on the sound velocity of ReScO3

materials becomes available. The sound velocity is required to estimate acoustic

impedances and to calculate the structures of acoustic phonon Brag mirrors and cavities.

Recently, we have measured GdScO3 single crystals using resonant ultrasound

spectroscopy4 to determine their elastic constants and sound velocity. The results will be

published elsewhere.

104

REFERENCES:

1 S. N. Kravchun, S. T. Davitadze, N. S. Mizina, and B. A. Strukov, Fiz. Tverd. Tela (Leningrad) [Sov. Phys. Solid State] 39, 675 (1997). 2 Y. L. Li, S. Y. Hu, D. Tenne, A. Soukiassian, D. G. Schlom, X. X. Xi, K. J. Choi, C. B. Eom, A. Saxena, T. Lookman, Q. X. Jia, and L. Q. Chen, Appl. Phys. Lett. 91, 112914 (2007). 3 D. D. Fong, G. B. Stephenson, S. K. Streiffer, J.A. Eastman, O. Auciello, P. H. Fuoss, and C. Thompson, Science 304, 1650 (2004). 4 J. D. Maynard, Phys. Today 49, 26 (1996).

105

Appendix A

Practical aspects of the growth of BaTiO3/SrTiO3 superlattices by reactive MBE

A.1. Substrate preparation.

As described in Chapter 3, for the successful epitaxial growth of BaTiO3/SrTiO3

superlattices it is very important to have a highly perfect single crystal substrate with an

atomically smooth surface and complete termination at a known atomic leyer. I will

describe the substrate preparation for (001) SrTiO3, (101) DyScO3, and (101) GdScO3

used in this work.

Koster’s step-by-step recipe for TiO2-terminated (001) SrTiO3 substrates:1

1. Clean SrTiO3 substrates in Micro, Acetone, Isopropanol, and DI water for

~10 min in each solution in ultrasonic.

2. Etch in NH4F-buffered HF solution (NH4F:HF = 87.5:12.5 with pH = 5.5,

obtained from Merck) for 30 sec (this step will remove SrO and leave

single TiO2-terminated surface).

3. Rinse in DI water and spin-dry at 5000 rpm.

4. Anneal SrTiO3 substrates in dedicated tube furnace in flowing 99.994%

pure O2 atmosphere (UPH oxygen) at 950 ºC for 1 hr (set at least 2 hr for

heating up to the 950 ºC and let slowly cool down in O2 atmosphere after

annealing).

The (101) DyScO3 substrates were prepared by using method developed by Prof.

Blank’s group at University of Twente, Nederland:

106

1. Clean DyScO3 substrates in Acetone and Isopropanol for ~10 min in each

solution in ultrasonic.

2. Anneal DyScO3 substrates in dedicated tube furnace in flowing 99.994%

pure O2 atmosphere (UPH oxygen) at 1000 ºC for 13 hr (set at least 2.5 hr

for heating up to 1000 ºC and let slowly cool down in O2 atmosphere after

annealing).

Recently, new recipes were developed for (101) DyScO3 and (101) GdScO3

substrates by Prof. Eom’s group at University of Michigan. The termination method for

DyScO3 substrates is:

1. Clean DyScO3 substrates in Micro, Acetone, Isopropanol, and DI water

for ~10 min in each solution in ultrasonic.

2. Etch in NH4F-buffered HF solution (NH4F:HF = 87.5:12.5 with pH = 5.5,

obtained from Merck) for 90 sec.

3. Rinse in DI water and clean by spin-dry at 5000 rpm.

4. Anneal DyScO3 substrates in dedicated tube furnace in flowing 99.994%

pure O2 atmosphere (UPH oxygen) at 1100 ºC for 3 hr (set at least 2 hr for

heating up to the 1100 ºC and let slowly cool down in O2 atmosphere after

annealing).

The termination method for (101) GdScO3 substrate is:

1. Clean GdScO3 substrates in Micro, Acetone, Isopropanol, and DI water

for ~10 min in each solution in ultrasonic.

2. Anneal GdScO3 substrates in dedicated tube furnace in flowing 99.994%

pure O2 atmosphere (UPH oxygen) at 1100 ºC for 3 hr (set at least 2 hr for

107

heating up to the 1100 ºC and let slowly cool down in O2 atmosphere after

annealing).

However, in this work termination methods from Prof. Eom’s group were not

used.

A.2. Structural characterization of BaTiO3/SrTiO3 superlattices by four-circle x-ray

diffraction.

One of the most powerful methods to determine the structure, phase purity,

crystalline perfection, and lattice parameters of crystalline materials is x-ray diffraction

(XRD). This technique is based on Bragg’s law (Bragg condition): nλ = 2dsinθ, where n

is a positive integer, λ is the wavelength of the x-rays, d is the layer spacing, and θ is the

incident angle of the x-rays with respect to the diffracting plane. Figure A.2.1 (from

www.bmsc.washington.edu) shows the derivation of the diffraction condition. Intense

diffraction peaks will appear for certain specific incident angles θ and wavelengths λ that

satisfy the Bragg condition. In order to determine the epitaxial orientation relationship

between the BaTiO3/SrTiO3 superlattice and the underlying single crystal substrate, four-

circle Picker low-resolution and Philips X’Pert PRO high-resolution XRD systems were

used. It this part I will give an example of lattice constant calculations for BaTiO3/SrTiO3

superlattices grown on (001)-oriented cubic SrTiO3 and (101)-oriented orthorhombic

SmScO3 substrates. I will describe how I have determined the error bars for out-of-plane

and in-plane lattice parameters.

The first step in XRD analysis of superlattices is to run a θ – 2θ x-ray scan

aligned to diffract from crystallographic planes parallel to the substrate surface. An

108

example of such a scan is shown in Figure A.2.2(a). From this scan we can determine the

structure, phase purity, and out-of-plane orientation. The presence of all superlattice

peaks in the θ – 2θ x-ray scan is an indication of sharp interfaces between the superlattice

constituent monolayers. From this θ – 2θ scan we can also calculate the out-of-plane

superlattice parameter dS. Lattice parameters and d spacing are related in orthorhombic,

tetragonal, and cubic systems by Bragg formula: 2

2

2

2

2

2

2

1cl

bk

ah

d++= , here h, k, l are the

Miller indices, and d can be calculated from Bragg’s law d = nλ/2sinθ.

To minimize the errors in the measurement of d, a Nelson-Riley analysis was

used.2 This analysis includes a plotting the calculated out-of-plane lattice parameter for

each superlattice out-of-plane peak as a function of cos2θ/sinθ and extrapolating the

linear fit to zero, which yields the accurate out-of-plane lattice parameter of the

superlattice, dS. The error bar of the dS I have defined as the mean arithmetic spread of

this plot. The value of this error bar depends on the instrumental resolution and

superlattice quality in terms of interface roughness. The higher the resolution of the four-

circle XRD system and sharper the interface between the constituent monolayers in the

superlattice will result in the smaller error bar. As an example, Figure A.2.2(a) shows the

θ – 2θ scan of two [(BaTiO3)1/(SrTiO3)4]50 superlattices grown on (001) SrTiO3

substrates. Here the first superlattice (A132, red line) was deposited with correct

monolayer doses resulting in sharp interfaces (see Chapter 3, Fig. 3.16(b) for the Z-

contrast HRTEM image of this superlattice) and a second one (A128, blue line) with

incorrect monolayer doses. The combined Nelson-Riley plot for both of the samples is

shown in Figure A.2.2(b). Extrapolation of the linear fits to zero yield dS = 19.75 ± 0.1 Å

for sample A132 and dS = 19.69 ± 0.5 Å for sample A128. We can see that the mean

109

arithmetic spread and thus the error bar is smaller for the superlattice having sharp

interfaces (sample A132). For the θ − 2θ scans made on the Picker low-resolution XRD

system, Lorentzian fit were used to reduce the measurements error of 2θ that is due to the

large scan steps (Fig. A.2.3).

For the superlattice grown with incorrect monolayer doses there are additional

peaks in the θ − 2θ scan (Fig. A.2.2(a)). The position of these peaks and their shift

compared to the superlattice with the correct monolayer doses indicate that either both

BaTiO3 and SrTiO3 or one of them were deposited with less than one monolayer at a time.

This information can be used to better calibrate the monolayer dosage of BaTiO3 and

SrTiO3 for the growth of the subsequent superlattice samples that are grown soon after

this sample.

Information on the crystalline quality can be obtained from rocking curves (ω

scans). The full width at half maximum (FWHM) of the measured peak in the ω scan can

be used to determine the superlattice crystallinity. As an example, Figure A2.4 shows the

ω scan of the [(BaTiO3)8/(SrTiO3)4]40 superlattice grown on a (101)-oriented SmScO3

substrate. The lattice constants of the orthorhombic SmScO3 are a = 5.758(2) Å,

b = 7.975(2) Å, and c = 5.531(1) Å.3 The pseudocubic ap lattice parameters along the in-

plane [010] and [ 1 01] directions can be determined as ap = b/2 = 3.9876 Å and

ap = 2

22 ca + = 3.992 Å, reflecting the in-plane asymmetry due to the orthorhombicity

of the unit cell. Similar asymmetries along the in-plane [010] (φ = 90º) and [101] (φ = 0º)

directions were observed in the ω scans measured on the 1024 and 202 peaks of the

[(BaTiO3)8/(SrTiO3)4]40 superlattice and the SmScO3 substrate, respectively (Fig. A2.4).

110

Both superlattice and substrate peaks show the same FWHM values of ω = 0.0026º

measured along the [010] direction at φ = 90º and ω = 0.0031º measured along the [101]

direction at φ = 0º. Similar behavior was observed for rocking curve measurements of

BaTiO3/SrTiO3 superlattices grown on (101) DyScO3 and (101) GdScO3 substrates.

In order to completely determine the lattice parameters of the superlattice and the

epitaxial orientation relationship between the superlattice and its underlying substrate a φ

scan measurement of the off-axis peak must be carried out in addition to the θ – 2θ and ω

scans. In order to obtain the coordinates (θ, ψ, and φ) of the off-axis peak position where

the peaks are expected, a plot of the stereographic projection of both superlattice and

substrate peaks can be used. From this plot the values of ψ = 90º - χ can be determined

for every peak of the superlattice and substrate. In this work I have used the CaRine

Crystallography 3.1 program to plot the stereographic projections and calculate the 2θ

values. Thus, by knowing two coordinates we can run a φ scan to find the off-axis peak.

The steps for the φ scan measurements include an accurate alignment in ω and a careful

choice of an off-axis peak of the superlattice and substrate that must be intense and well

separated from each other. Figure A.2.5 shows an example of a θ – 2θ off-axis scan at

χ = 45º of the [(BaTiO3)8/(SrTiO3)4]40 superlattice grown on (101) SmScO3 substrate. The

2θ values obtained from this scan, together with the measured out-of-plane superlattice

parameter dS = 47.754 ± 0.05 Å, were used to calculate the in-plane lattice parameter of

the superlattice, a = 3.993 ± 0.005 Å, which indicate that the [(BaTiO3)8/(SrTiO3)4]40

superlattice is commensurate with the underlying SmScO3 substrate. To calculate the in-

plane lattice parameter error bar see the Mathematica4 code in Appendix A.3.

111

Fig. A.2.1. Schematic of Bragg condition. If the difference in the path length of each

wave is equal to an integer multiple n of the wavelength λ, the reflected waves remain in

phase and will interfere constructively. The path difference ABC is equal to 2dsinθ, thus

diffraction maxima will appear if nλ = 2dsinθ (from www.bmsc.washington.edu).

112

0 10 20 30 40 50

102

103

104

105

Inte

nsity

(arb

. un.

)

2θ (degrees)

A128

Fig. A.2.2. Calculation of the out-of-plane superlattice parameter dS and error bar from

the Nelson-Riley plot for the two [(BaTiO3)1/(SrTiO3)4]50 superlattices grown on (001)-

oriented SrTiO3 substrate (samples A128 and A132). (a) Combined θ – 2θ plot of

0 1 2 3 4 5 6 7 8 919.3

19.4

19.5

19.6

19.7

19.8

19.9

20.0

20.1

20.2

Latti

ce c

onst

ant c

(Å)

cos2θ/sinθ

A128 A132

linear fit to A132

A132**

001

003

0011

0010

009

008

007

006

005

004

002

(a)

(b)

113

samples A128 (blue line) and A132 (red line). (b) Combined Nelson-Riley plot of A128

(blue squares) and A132 (red circles) samples.

26.6 26.8 27.0 27.2 27.4 27.6

0

500

1000

1500

2000

Inte

nsity

(arb

. un.

)

2θ (degrees)

A132 Lorentz fit to A132

Fig. A.2.3. Lorenzian fit used for more accurate determination of the 2θ value of the 006

peak of sample A132, a [(BaTiO3)1/(SrTiO3)4]50 superlattice.

114

-0.10 -0.05 0.00 0.05 0.10100

101

102

103

104

105

106

107

φ = 0o

φ = 90o

SmScO3 φ = 90o

SmScO3 φ = 0o

Superlattice φ = 0o

Superlattice φ = 90o

Inte

nsity

(arb

. un.

)

ω (degrees)

Fig. A.2.4. Rocking curves of the [(BaTiO3)8/(SrTiO3)4]40 superlattice grown on a (101)-

oriented SmScO3 substrate revealing the asymmetry in the FWHM of the peaks in ω for

rocking curves taken along the in-plane [010] (φ = 90º) and [101] (φ = 0º) directions.

115

30 31 32 33100

101

102

103

104

105

106

Inte

nsity

(arb

. un.

)

2θ (degrees)

1013

1012

1011

*

Fig. A.2.5. Off-axis θ – 2θ scan at χ = 45º of the [(BaTiO3)8/(SrTiO3)4]40 superlattice

grown on a (101) SmScO3 substrate. The 121 SmScO3 substrate peak is marked with an

asterisk (*).

116

Appendix A.3. Mathematica code for the calculation of the lattice parameters and error

bars (from D. G. Schlom).

Derivation—for Orthorhombic a-Axis Films

SolveAd== &'''''''''''''''''''''''''''1

h2a2 + k2

b2 + l2c2

, cE

c=a bdl

è!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!a2 b2 − b2 d2 h2 − a2d2 k2;

∆c= SimplifyAè!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!∆a2 ∂ac 2 + ∆b2 ∂bc 2 + ∆d2 ∂dc 2H L H L H L E c-Axis Films Clear[c,∆c]

SolveAd== &'''''''''''''''''''''''''''1

h2a2 + k2

b2 + l2c2

, aE

a=bcdh

è!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!b2 c2 − c2d2 k2 − b2d2 l2;

∆a= SimplifyAè!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!∆b2 ∂ba 2 + ∆c2 ∂ca 2 + ∆d2 ∂da 2H L H L H L E

Use Clear[c,∆c,a,∆a] a-Axis Films

117

∆c= &'''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''l2 Ha6 d6 k4 ∆b2 + b6 Hd6h4 ∆a2 + a6 ∆d2LLH−b2 d2h2 +a2 Hb2 − d2k2LL3

;

λ = 1.541838;

d= &'''''''''''''''''''''''''''1

h2a2 + k2

b2 + l2c2

;

∆d= Abs@∆θ dCot@θDD;

θ = ArcSinA λ

2dE;

N@ @ ê 8 0.14451

Chop ∆c . a→ 3.85, b→ 3.85, c→ 11.70, h → 1, k → 0, l → 3, ∆a→ 0.01, ∆θ → 0.1 °<DD

c-Axis Films

∆a= &''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''h2 Hb6d6 l4 ∆c2 + c6 Hd6k4 ∆b2 + b6 ∆d2LLH−c2 d2k2 + b2 Hc2 − d2l2LL3

;

λ = 1.541838;

d= &'''''''''''''''''''''''''''1

h2a2 + k2

b2 + l2c2

;

∆d= Abs@∆θ dCot@θDD;

θ = ArcSinA λ

2dE;

N Chop ∆a . a→ 3.85, b→ 3.85, c→ 11.70, h → 1, k → 0, l → 3, ∆c→ 0.02, ∆θ → 0.1°@ @ ê 8 <DD Derivation—for Tetragonal c-Axis Films Clear[c,∆c]

SolveAd== &'''''''''''''''''''''''''''1

h2a2 + k2

a2 + l2c2

, aE

118

a=cdè!!!!!!!!!!!!!h2 + k2

è!!!!!!!!!!!!!!!!!c2 − d2 l2;

∆a= SimplifyAè!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!∆c2 ∂ca 2 + ∆d2 ∂da 2H L H L E Use Clear[c,∆c,a,∆a] c-Axis Films

∆a= &'''''''''''''''''''''''''''''''''''''''''''''''''''Hh2 + k2L Hd6 l4 ∆c2 + c6 ∆d2LHc2 −d2 l2L3

;

λ = 1.541838;

d= &'''''''''''''''''''''''''''1

h2a2 + k2

a2 + l2c2

;

∆d= Abs@∆θ dCot@θDD;

θ = ArcSinA λ

2dE;

N@

Chop@∆aê. 8a→ 3.925, c→ 3.935, h→ 3, k → 0, l → 1, ∆c → 0.01, ∆θ → 0.05°<DD

Determining Da and Dc from two Independent Peaks

Clear[a,∆a,c,∆c]

roots= SolveA9d1== &'''''''''''''''''''''''''''''''1

h12a2 + k12

a2 + l12c2

, d2 ==&'''''''''''''''''''''''''''''''1

h22a2 + k22

a2 + l22c2

=, 8a, c<E@@4DD;

a= aê. roots;c= c . roots;ê

a

d1d2è!!!! !! !! !! !! !! !! !! !! !! !! !! !! !! !! !! !! !! !! !! !! !! !! !! !! !! !! !! !!!h22 l12+ k22l12 −h12 l22− k12 l22

è!!!!!! !! !! !! !! !! !! !! !! !! !! !!!d12l12 −d22 l22 c

d1d2è!!!!!! !! !! !! !! !! !! !! !! !! !! !! !! !! !! !! !! !! !! !! !! !! !! !! !! !! !! !! !!!−h22l12 −k22 l12+ h12 l22+ k12l22

è!!!!!! !! !! !! !! !! !! !! !! !! !! !! !! !! !! !! !! !! !! !! !! !! !! !! !! !! !! !!!d12h12 − d22h22+ d12 k12− d22k22

∆a= SimplifyAè!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!∆d12H∂d1aL2 + ∆d22 H∂d2aL2 E

&''''' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '''

Hh22 l12+ k22l12 −Hh12 + k12L l22L Hd26l24 ∆d12+ d16l14 ∆d22LHd12 l12− d22l22L3

∆c= SimplifyAè!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!∆d12H∂d1cL2 + ∆d22 H∂d2cL2 E

&''''''' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' '' ''−

Hh22l12 +k22 l12− Hh12+ k12L l22L Hd26 Hh22+ k22L2 ∆d12+ d16Hh12 + k12L2 ∆d22LHd12 Hh12+ k12L − d22 Hh22+ k22LL3

119

Use Clear[a,∆a,c,∆c] General Tetragonal Film

a=d1d2è!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!h22 l12 + k22l12 −h12 l22 − k12 l22

è!!!!!!!!!!!!!!!!!!!!!!!!!!!!!d12 l12 −d22 l22;

∆a= &''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''Hh22 l12 + k22l12 −Hh12 + k12Ll22L Hd26 l24 ∆d12 + d16l14 ∆d22LHd12 l12 − d22 l22L3

;

c=d1d2è!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

−h22l12 −k22 l12 + h12 l22 + k12l22

è!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!d12 h12 − d22 h22 + d12 k12 − d22 k22;

∆c= ,I−IIh22l12 + k22 l12 − Ih12 + k12Ml22M Id26Ih22 + k22M2∆d12 + d16Ih12 +k12M2

∆d22MMëId12Ih12 + k12M− d22 Ih22 + k22MM3M;

λ = 1.541838;∆d1= Abs@∆θ1d1Cot@θ1DD;

θ1= ArcSinA λ

2d1E;

∆d2= Abs@∆θ2d2Cot@θ2DD;

θ2= ArcSinA λ

2d2E;

parameters= 8h1→ 1, k1→ 0, l1→ 3, d1 → 4.603, h2 → 0, k2 → 0, l2→ 2, d2→ 12.539, ∆θ1 → 0.05 °, ∆θ2 → 0.02Print@"a = ", Chop@aê. parametersD, " ± ", ∆a ê. parametersD;Print "c = ", Chop c . parameters , " ± ", ∆c . parameters ;@ @ ê D ê D

120

REFERENCES:

1 G. Koster, B. L. Kropman, G. J. H. M. Rijnders, and D. H. A. Blank, Appl. Phys. Lett. 73, 2920 (1998). 2 J. B. Nelson, and D. P. Riley, Proc. Phys. Soc. London 57, 160 (1945). 3 B. Velickov, V. Kahlenberg, R. Bertram, and M. Bernhagen, Z. Kristallogr. 222, 466 (2007). 4 Wolfram Research, Inc., Champaign, IL 61820.

121

Appendix B

Details on the growth attempts of BaO/SrTiO3 superlattices.

Acoustic phonon mirrors made of BaO/SrTiO3 superlattices were described in the

Chapter 4 and are expected to exhibit superior acoustic performance. However the

growth of such superlattices that include alternating perovskite SrTiO3 and rock-salt BaO

layers have not been reported yet. The main challenge is to preserve the phase separation

between the perovskite and rock-salt layers. I have attempted to growth BaO/SrTiO3

superlattices on the TiO2-terminated (001) SrTiO3 substrates by reactive MBE using the

shuttered growth method described in Chapter 3. The initial shuttered growth sequence

was ...SrO/TiO2/BaO/BaO/TiO2/SrO... and the growth parameters used were the same as

the optimized conditions described for the growth of BaTiO3/SrTiO3 superlattices (see

Chapter 3 for details). The θ – 2θ scan on this sample yielded an out-of-plane superlattice

parameter dS = 58.7 ± 1 Å, which is larger than the expected superlattice periodicity for

(BaO)2ML/(SrTiO3)13, dS = 56.3 Å, and close to the expected superlattice periodicity for

(BaTiO3)2/(SrTiO3)13, dS = 58.8 Å, calculated using bulk lattice constants (Figure B.1).

This indicates that the TiO2 layers reacted with the BaO forming two unit cells of BaTiO3.

A TEM study of this superlattice, sample A69, shows that the structure is

(BaTiO3)2/SrTiO3)13 (Fig. B.2(a)), consistent with the XRD results. The following

attempt to grow a BaO/SrTiO3 superlattice having three BaO monolayers followed by 13

unit cells of SrTiO3 was deposited with the same growth sequence conditions. The θ – 2θ

scan of this superlattice, sample A49, (Fig. B.3) reveals dS = 53.4 ± 0.1 Å instead of the

expected dS = 51.3 Å and TEM shows that both rack-salt BaO and perovskite BaTiO3 are

122

present in the superlattice (Fig. B.2(b)). Instead of the desired structure,

(BaO)3ML/(SrTiO3)13, the XRD and TEM results show that the grown superlattice consists

of two unit cells of BaTiO3 and one monolayer of BaO. Similarly, deposition of four or

more BaO monolayers resulted in a significant roughening of the growth surface that was

observed in RHEED during growth. Figure B.3 shows the RHEED patterns along the

[110] azimuth after the deposition of four monolayers of BaO (a) and that after an

additional monolayer of TiO2 (b).

The change of the growth sequence to ...TiO2/SrO/BaO/BaO/SrO/TiO2...

prevented the formation of BaTiO3. However, despite the various attempts at growth

pressures and substrate temperatures ranging from 2×10-7 Torr to 5×10-7 Torr of

molecular oxygen and from 550 ºC to 700 ºC, respectively, I was not able to obtain sharp

interfaces between the constituent monolayers of the BaO/SrTiO3 superlattice. Figure B.4

shows the combined plot of θ – 2θ scans on three BaO/SrTiO3 superlattices with desired

structures having 2, 3, and 4 monolayers of BaO and separated by 13 unit cells of SrTiO3

grown at a substrate temperature of ~610 ºC and an oxygen pressure of ~2×10-7 Torr. The

θ – 2θ x-ray measurements and calculated out-of-plane lattice parameters of these three

samples are consistent with the avoidance of BaTiO3 in the structure, i.e., the Ti atoms

did not diffuse into the BaO layers. Avoiding such interdiffusion is very important for

obtaining the correct BaO/SrTiO3 superlattice structure. However, more detailed research

needs to be done in order to obtain the proper growth parameters for the BaO/SrTiO3

superlattice. Unfortunately, the given time and number of attempts were not enough for

me to succeed with the growth of well-ordered BaO/SrTiO3 superlattices.

123

0 5 10 15 20 25 30 35 40 45 50 55

102

103

104

105

0034

0015

0014

Inte

nsity

(arb

. un.

)

2θ (degrees)

*

Fig. B.1. θ – 2θ scan of a [(BaTiO3)2/SrTiO3)13]20 superlattice grown on a (001) SrTiO3

substrate with the shuttered growth sequence shown on the right.

*

0033

0032

0031

0030

0029

0028

0027

0026

0025

0024

0023

0022

0021

0020

0019

0018

001700

16

0013

0012

0011

0010

009

00800

700

600

500

400

300

2

SSrrOO

SSrrOO

TTiiOO22

TTiiOO22

BBaaOO

BBaaOO

TTiiOO22

SSrrOO

TTiiOO22

SSrrOO

124

Fig. B. 2. (a) A cross-sectional HRTEM image of the sample A69 showing that

superlattice have alternating layers of 2 unit cells of BaTiO3 and 13 unit cells of SrTiO3.

(b) A cross-sectional HRTEM image of the sample A49 showing that superlattice have

layers consisting of a mixture of rack-salt BaO and perovskite BaTiO3 separated by 13

unit cells of SrTiO3.

125

0 10 20 30 40 50

102

103

104

105

In

tens

ity (a

rb. u

n.)

2θ (degrees)

0015

Fig.B.3 θ – 2θ scan of a [(BaTiO3)2+(BaO)1ML/SrTiO3)13]20 superlattice grown on a (001)

SrTiO3 substrate with the shuttered growth sequence shown on the right.

* *

0031

0030

0029

0027

0026

0025

0024

0023

0022

0021

0020

0019

001800

170016

0013

0012

0011

0010

009

008

007

006

005

004

003

002

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126

(a) (b)

Fig. B.4. RHEED patterns along the [110] azimuth after the deposition of four

monolayers of BaO (a) and that observed after adding one monolayer of TiO2 on top of

the BaO (b). The decrease in the RHEED intensity and the presence of the 3D spots

indicate the roughening of the surface.

127

Fig. B.5. combined plot of θ – 2θ scans of [(BaO)2ML/SrTiO3)13]20,

[(BaO)3ML/SrTiO3)13]20, and [(BaO)4ML/SrTiO3)13]20 superlattices grown on (001) SrTiO3

substrate with the shuttered growth sequence shown on the right.

0 10 20 30 40 5010 1

10 2

10 3

10 4

10 5

10 6

10 7

Inte

nsity

(arb

. un.

)

2 θ (deg rees)

[(B aO )2M L/(S rT iO 3)13]20

[(B aO )3M L/(S rT iO 3)13]20

[(B aO )4M L/(S rT iO 3)13]20

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128

Vita

Arsen Soukiassian

Education and Professional History:

1/2002- 12/2007: Ph. D. Student, Department of Materials Science and Engineering,

The Pennsylvania State University. Ph. D. thesis in Materials

Science and Engineering defended September 14, 2007.

10/2000-1/2002: Visiting Scholar, Department of Physics, The Pennsylvania State

University.

1/1997-10/2000: Graduate Student, P. N. Lebedev Physical Institute Russian

Academy of Sciences, Moscow, Russia.

2/1993-2/1996: M. S. in Physics, Moscow State Engineering Physics Institute,

Specialized Department of Physics, Moscow, Russia.

8/1990-2/1993: Undergraduate Student, Yerevan State University, Department of

Radio-Physics and Electronics, Yerevan, Armenia.

Publications:

Co-author of more than 25 technical papers in refereed journals.