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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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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
TTiiOO22
SSrrOO
BBaaOO
SSrrOO
TTiiOO22
TTiiOO22
BBaaOO
BBaaOO
TTiiOO22
SSrrOO
TTiiOO22
SSrrOO
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
SSrrOO
TTiiOO22
TTiiOO22
BBaaOO
BBaaOO
SSrrOO
TTiiOO22
SSrrOO
TTiiOO22
SSrrOO
SSrrOO
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.
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