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The effect of strain and defects on the dielectric properties of barium strontium titanate thin films for tunable microwave applications

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ABSTRACT
Title o f Dissertation:
THE EFFECT OF STRAIN AND DEFECTS ON THE
DIELECTRIC PROPERTIES OF BST THIN FILMS
FO R TUNABLE MICROWAVE APPLICATIONS
Hao Li, Doctor o f Philosophy, 2001
Dissertation directed by:
Professor L. Salamanca-Riba
Professor R. Ramesh
Department o f Materials and Nuclear Engineering
Ferroelectric materials enjoy a large nonlinearity in their dielectric response,
which gives rise to an electric field dependent permittivity. This feature makes them
particularly attractive for use as frequency-agile microwave electronic components,
including phase shifters, varactors, tunable filters and antennas. In this area,
(Ba,Sr)Ti0 3 (BST)-based ceramic thin films are considered by many as the forerunners
for room temperature (RT) applications. However, compared to bulk BST samples, the
dielectric constant and nonlinearity o f epitaxial thin films are markedly worse. Strain
and defects in the film are generally recognized as two major reasons for this
degradation o f dielectric properties. However, their exact role in this degradation is still
not clear.
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In this study, a series o f heteroepitaxial BST thin films o f thicknesses varying
from
8
nm to 500 nm were prepared on LSAT and MgO substrates to produce films
w ith systematically varying in-plane stresses. The in-plane dielectric constant ei i was
found to increase with increasing tensile stress and decrease with compressive stress.
The relationship between dielectric properties and stress agrees very well with our
theoretical calculations. We also derived the relationship between the dielectric constant
and electric field using an extended thermodynamic model. In addition, we define
tunabiiity as
'd e n
and the experimental data is analyzed using this new definition.
- dE ,
It is observed by many research groups that annealing leads to partial recovery in
the dielectric properties o f BST films. Therefore, in this study, carefully designed
annealing experiments were performed in different types o f gas ambient to study the
effect o f defects on the dielectric properties o f BST films. Extensive x-ray and
transmission electron microscopy studies were carried out to study the structural
evolution o f the BST films upon annealing. We report evidence showing that oxygen
vacancies (0-D defect) do not play an important role in the recovery o f the dielectric
properties o f BST thin films. In contrast, it is the decrease o f defects such as
dislocations (1-D defects) as well as antiphase domain boundaries and small angle grain
boundaries (2-D defects) and the relief o f local strain associated with these defects that
dominate the dielectric recovery process.
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THE EFFECT OF STRAIN AND D E FE C T S ON THE DIELECTRIC
PROPERTIES OF BST THIN FILMSS FOR TUNABLE MICROWAVE
APPLICATIONS
by
Hao ILi
Dissertation submitted to the Facuhty o f the graduate school o f the
University of Maryland, C ollege Park in partial fulfillment
of the requirements for the degree o f
Doctor o f Philosophy
20011
Advisory Committee
Professor L. Salamanca-Riba, Chairr/Advisor
Professor R. Ramesh, Co-advisor
Professor A. Roytburd
Assistant Professor I. Takeuchi
Associate Professor S. Anlage
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UMI Number: 3009031
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DEDICATION
To my wife, Tingfei
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ACKNOWLEDGEMENT
I am very grateful to m y thesis advisor Prof. Salamanca-Riba and co-advisor Prof.
Ramesh. Prof. Salamanca is always patient and listen to all the crazy ideals I have. And
she never discourages me on anything, even when sometimes she knew I was wrong.
The strongest word she ever said to me was: “ Maybe we could do this...” I thank her
not only for her intellectual guidance, which is tremendous by the way, but also for the
care she showed for me through these four years. I was lucky to have such a nice and
caring advisor.
I also cherish the freedom and encouragement Prof. Ramesh has given me. I argue
with him a lot and really enjoyed all the arguments except that he was right most o f the
time. I am thankful for all the lessons he has given me on knowing which direction my
research should go and how to get there. He has helped me in becoming a more
practical researcher.
I would like to thank Prof. A. Roytburd and Dr. P. Alpay for their kind assistance
on the theory calculations o f m y project.
I would like to thank the members of my committee Prof. I. Takeuchi and Prof. S.
Anlage for their constructive suggestions.
I would like to specially acknowledge the help of Chad who brought me into this
BST project. M y interaction with him has been very fruitful as a friend and as a
collaborator.
I would also like to thank Tri Tran for his help o f the photolithography work.
ii
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I would like to thank Dr. S. Chen in University o f Virginia for his kind assistance
on the TEM experiments I conducted there.
I want to thank my friend from my TEM research group, including Richard,
Shima, Yunxin, Wendy, Chris, Yinghai, Tim, Gaiying, and Randy. They offered a lot
helpful suggestions on my researches.
I want to thank my friends from my thin film growth research group, including
Sanjeev, Ryan, Nagarajan, Chandan, Monga, Ingrid, Brandah, Marcello, and John. It
has been a pleasure working with them.
I want thank my parents for their support and enthusiasm. Finally, I am very
grateful to my grand parents. I owe this achievement to their unfaltering belief and
support.
iii
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TABLE OF CONTENTS
Num ber
Page
A cknowledgem ent..................................................................................................ii
L ist o f Tables
.................................................................................................... vi
L ist of Figures
...................................................................................................vii
C h a p te r 1
In tro d u c tio n ..................................................................................1
1.1
Ferroelectric materials and their applications.................................... 1
1.1.1
Ferroelectricity and Perovskite structure.................................. 1
1.1.2
Lattice dynamic (soft phonon) theory of ferroelectricity
5
1.1.3
Thermodynamic (Landau-Ginzburg-Devonshire) theory
o f the spontaneous polarization o f ferroelectrics.................... 8
1.2
BST for tunable microwave applications........................................ 11
1.2.1
Dielectric properties o f BST.................................................... 11
1.2.2
Planar microwave Phase shifters based on BST thin films
and other competing technologies..........................................13
1.2.3
Review o f several key research interests on BST thin
films and motivation o f this thesis..........................................16
C h a p te r 2
E xperim ental T echniques........................................................18
2.1
Pulsed laser deposition.......................................................................18
2.1.1
Principles and applications...................................................... 18
2.2
Transmission electron microscopy................................................... 21
2.2.1
D iffraction................................................................................. 24
2.2.2
Imaging— diffraction contrast.................................................26
2.2.3
Imaging—phase contrast......................................................... 28
2.3
TEM Sample preparation.................................................................. 30
2.3.1
Cross section sample preparation.......................................... 31
2.3.2
Quadripod and the concept o f high angle wedge polishing31
2.4
Device fabrication and electrical measurement.............................. 46
C h a p te r 3
3.1
3.2
3.3
3.4
3.5
C h a p te r 4
4.1
Dependence of dielectric properties on in tern al stresses
in epitaxial BST thin film s...................................................... 48
Introduction......................................................................................... 48
Strain in BST thin films..................................................................... 49
Zero field dielectric constant of BST film s.....................................55
Tunability o f BST films..................................................................... 58
Summary...............................................................................................63
Role of defects on the dielectric properties of BST thin
films...............................................................................................65
Introduction......................................................................................... 65
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4.2
4.3
Role o f oxygen vacancies................................................................. 6 8
Role o f dislocations........................................................................... 71
4.3.1
TEM characterization o f dislocations in BST films on
LSAT substrate.........................................................................72
4.3.2
The effect o f dislocations on the dielectric properties o f
BST films...................................................................................95
4.4
The role o f antiphase domain boundariesand sm all angle grain
boundaries..........................................................................................1 0 1
4.4.1
Antiphase domain boundaries in BST film s........................101
4.4.2
Small angle sub grain boundaries.......................................... 112
4.5
Summary............................................................................................. 117
Summary and Future W ork........................................................................... 118
Appendix Ordering in LSAT Substrates....................................................122
A .l
Review o f structure characterization o f LSAT.............................. 123
A.2 X-ray Diffraction analysis................................................................123
A.3
TEM Two beam analysis.................................................................124
A.4
EDX analysis.................................................................................... 126
A.5 HREM and sim ulation...................................................................... 127
References
................................................................................................. 138
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LIST OF TABLES
Table 4.1 Methods used in the study o f role o f defects in BST film s............................. 6 8
Table 4.2 Reciprocal (g) and real (d) interplanar distances and extinction
distances (^g) for S T O ........................................................................................74
Table 4.3 Extinction distances o f BST for 300kV and lOOkV :...................................... 84
Table A .l Atomic positions for disordered L S A T ..........................................................133
Table A.2 Atomic positions for La-Sr ordered LSAT.....................................................133
Table A.2 Atomic positions for Al-Ta ordered L SA T ................................................... 133
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LIST OOF FIGURES
Figure 1.1 Perovskite structure................................................................................................. 2
Figure 1.2 Illustration o f the structure otf (a) CaTi0 3 , (b) SrTi0 3 , (c) BaTiCh................. 5
Figure 1.3 The square o f the frequency oof the soft mode o f the ferroelectric
branch is plotted versus tem perature in a solid line. The broken line
represents the temperature dependence o f the reciprocal dielectric
constant..................................................................................................................... 7
Figure 1.4 Schematic Ps versus temperatture curves for (a) second order phase
transition and (b) first order p h a se transition. There is a sudden jum p
o f Ps at Tc in the first order pHiase transition...................................................... 10
Figure 1.5 Free energies as functions o f- polarization in a first order phase
transition, in different temperrature ranges......................................................... 1 0
Figure 1.6 Ferroelectric transition tem perature as a function o f Ba to Sr ratio in
BST.......................................................................................................................... 11
Figure 1.7 Illustration o f the RF beam-s'teering concept using phase shifters at
each radiating element............................................................................................13
Figure 2.1 Schematic o f a pulsed laser deposition system .................................................18
Figure 2.2 Diagram o f an imaging systerm ..........................................................................23
Figure 2.3 The two basic operation m o d es o f the TEM imaging system: (a)
diffraction mode, and (b) im aging mode........................................................... 24
Figure 2.4 Ray diagrams showing how tlhe objective lens and objective aperture
are used in combination to produce (a) a BF image formed from the
direct beam, (b) a displace-aperture DF image formed with a specific
off axis scattered beam, and Cc) a CDF image where the incident beam
is tilted so that the scattered b e a m remains on the optic axis..........................27
Figure 2.5 Schematic o f high angle wedige polishing.........................................................35
Figure 2.6 Thickness measurement usin .g a simple geometric relationship....................36
Figure 2.7 Schematic o f the Quadripod jpolisher. The length o f the quadripod feet
determines the angle o f po lisliin g.......................................................................37
Figure 2.8 Sample and a piece of glass slid e glued together. A small area o f
interest on the sample is s h o w n ..........................................................................38
Figure 2.9 Sample position for first side= polishing............................................................ 38
Figure 2.10 First side polishing is termimated when the point o f interest is reach ed .... 39
Figure 2.11 Sample position for second side polishing......................................................40
Figure 2.12 Schematic o f second side hiigh angle polishing............................................. 41
Figure 2.13 Interference fringes appear "when the sample is electron transparent
43
Figure 2.14 Schematic o f second side lo«w angle polishing............................................... 43
Figure 2.15 Sample position for alternative parallel polishing.........................................45
Figure 2.16 Schematic o f parallel polishaing........................................................................45
Figure 2.17 Schematic o f the IDE structure used for dielectric measurement: (a)
top view (b) cross-section v ie w .......................................................................... 46
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Figure 3.1 (z)6-29 scan o f BST film on LSAT. (b) <j>scan showing four fold
symmetry................................................................................................................51
Figure 3.2 (a) TEM micrograph o f 14 nm BST film on MgO. (b) The SAD
pattern including both substrate and film, (c) H igh resolution image o f
the interface between the BST film and MgO substrate..................................52
Figure 3.3 6-26 X -ray diffraction spectra for two BST/MgO samples (140 nm
(solid curve) and 14 nm film (dotted curve)) Different scales were
used for the convenience of comparison............................................................53
Figure 3.4 Evolution o f ax as a function o f film thickness............................................... .54
Figure 3.5 Evolution o f Si i as a function o f film thickness. Both the solid line
(BST on MgO) and dashed line (BST on LSAT) are guide for the eyes..... .56
Figure 3.6 l/si i as a function o f strain. The straight lines are the fittings according
to Equation 3.7..................................................................................................... .58
Figure 3.7 (a) Theoretical and (b) experimental Su and
Figure 3.8
Figure 4.1
Figure 4.2
Figure 4.3
Figure 4.4
Figure 4.5
Figure 4.6
Figure 4.7
versus electric field
BE
curve...................................................................................................................... .61
(a) Conventional tunability as a function o f compressive and tensile
Be
misfit strain. The dashed lines are guides to the eyes, (b) ( — —)max as a
BE
function o f misfit strain....................................................................................... 62
The effect o f oxygen annealing on the dielectric constant o f a typical
BST thin film ....................................................................................................... 66
Si i as function o f voltage for two halves o f one BST film annealed in
different gas ambient. The dotted lines represent the as-deposited
samples. The sample on the left side was first annealed in O2 (dashed
line) for 14 hours at 950 °C and then annealed again in O 2 (solid line)
for another 14 hours at 950°C. The sample on the right side was first
annealed in N 2 (dashed line) and then annealed in O 2 (solid line). The
annealing conditions are the same as for the left side..................................... 69
Schematic o f dislocations in a perovskite epitaxial system........................... 71
Cross section dark field images o f the 26 nm sample viewed along (a)
[100] direction and (b) [110] direction. In both images the g vector
used was (002). Dislocation cores can be found at the interface in both
(a) and (b), however, the dislocation cores in (b) are not as clearly
defined as in (a), indicating that the dislocations are edge on in (a) and
inclined in (b)....................................................................................................... 77
Diffraction patterns taken in areas including both the film and
substrate o f the 26 nm sample. The zone axes are (a) [100], and (b)
[110]. The splitting o f the substrate and film spots indicates that the
film is relaxed....................................................................................................... 78
HREM image from the 26 nm sample viewed along [100]. The closure
failure indicates that the burgers vector is [010]BST..................................... 79
HREM image from the 26 nm sample viewed along [100] direction.
The dislocation at the interface is not edge-on, causing extended
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distortion along the interface. However, closure failure indicates a
Burgers vector o f [010] which is the same as in Figure 4.6............................79
Figure 4.8 HREM image from the interface o f the 26 nm sample viewed along
the [110] direction, indicating that the dislocation is inclined. The
closure failure gives a projected burgers vector o f /4[lT 0]B S T ................... 80
Figure 4.9 HREM image from the interface o f the 26 nm sample viewed along
[110]. Very clear core structure can be seen, indicating that this
particular dislocation (or this portion o f the dislocation) is along the
[110] direction. It also gives a projected Burgers vector o f 54[1 10]............. 80
Figure 4.10 (110) dark field plan view image o f the 26nm sample including the
interface. Only Moire fringes can be observed. The operating voltage
is 300kV.................................................................................................................81
Figure 4.11 (200) dark field plan view image o f the 26nm sample using an
operating voltage o f lOOkV. Still only Moire fringes can be observed.........83
Figure 4.12 (a) (200) and (b) (020) weak beam plan view images obtained using
100 kV....................................................................................................................87
Figure 4.13 Schematic o f the g-3g weak beam condition.................................................. 8 8
Figure 4.14 FFT from (a) Moire fringes in Figure 4.11 and (b) dislocations in
Figure 4.12(a). It can be seen that the distance between the two spots
in the FFT o f Moire fringes is twice as that o f the dislocations. This
indicates that the spacing between Moire fringes is half o f that o f the
dislocations............................................................................................................89
Figure 4.15 ( 1 1 0) weak beam image o f the 26 nm sample. The excitation error is
about 0.05nm_l ..................................................................................................... 90
Figure 4.16 (220) weak beam plan view image o f 26 nm sample obtained using
lOOkV. The s value is about 0.2nm_l. The inset is the FFT from the
dislocation network.............................................................................................. 91
Figure 4.17 Dark field image o f BST film on MgO substrate...........................................93
Figure 4.18 Plan view weak beam image o f threading dislocations in (a) asdeposited BST films, (b) annealed BST films.................................................. 96
Figure 4.19 Plan view HREM o f threading dislocations in BST films. The inset
shows the closure failure o f the Burgers V ector..............................................97
Figure 4.20 Weak beam plan view TEM images o f the (a) as-deposited and (b)
annealed BST films showing misfit dislocations. The m isfit
dislocations become longer and straighter upon annealing. Some o f the
misfit dislocations also change their directions upon annealing.................. 1 0 0
Figure 4.21 Antiphase domain boundary with a ^[OOl] shift.........................................102
Figure 4.22 Schematic o f the structure o f M gO ............................................................... 103
Figure 4.23 Schematic o f (a) (001) surface o f MgO, (b) AO layer o f BST, (c)
BO 2 layer o f BST, (d) a possible stacking sequence o f A O on MgO
where oxygen ions sit on top o f each other, (e) a possible stacking
sequence o f AO on MgO where cations sit on top o f each other, (£)
possible stacking sequence o f BO 2 on M g O .................................................. 105
Figure 4.24 Two possible in plane atomic arrangements (a) and (b) with a relative
lattice shift o f Vz[0 1 0 ] or ^[lOO]...................................................................... 106
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Figure 4.25 Plan view high resolution image o f a BST film showing an ADB
with an in plane lattice shift between two neighboring dom ains................ 107
Figure 4.26 Schematic o f (a) Sr/Ba rich and (b) Ti rich ADBs. The boundary is
the region between dashed lines....................................................................... 108
Figure 4.27 Plan view bright field images o f (a) as deposited BST film on MgO,
and (b) annealed BST film on MgO. Dashed lines show antiphase
boundaries........................................................................................................... 1 1 0
Figure 4.28 Schematic o f grain configuraion in BST films before and after
annealing..............................................................................................................I l l
Figure 4.29 Plan view HREM images o f (a) as deposited and (b) annealed BST
film on LSAT......................................................................................................113
Figure 4.30 (a) Schematic o f out o f plane dielectric measurement and (b) the
relationship between the ADBs/subgrain boundaries and the electric
field.......................................................................................................................115
Figure 4.31 Out o f plane dielectric measurement o f (a) as-deposited and (b)
annealed BST thin film s................................................................................... 116
Figure A.1 (a) {111} and (b) {222} Phi scans from L S A T ............................................125
Figure A.2 (a) Diffraction pattern o f LSAT in [1 10] zone axis, (b) (111) dark
field image, (c) (2 0 0 ) dark filed image............................................................ 126
Figure A.3 (a) The intensity (counts) o f each element versus position curve (b)
Relative ratio o f Al/Ta and Sr/La..................................................................... 128
Figure A.4 HREM image o f LSAT viewed along [010] zone axis................................129
Figure A.5 HREM image o f LSAT viewed along [110] direction.................................130
Figure A .6 Inverse FFT from {111} reflections o f the FFT o f the HREM image.
The ordered domains can be clearly seen........................................................ 131
Figure A.7 Schematic o f atomic structure o f disordered LSA T..................................... 132
Figure A .8 Schematic o f the unit cell for La-Sr ordering LSAT.................................... 134
Figure A.9 Schematic o f the unit cell for La-Sr ordering LSAT.................................... 134
Figure A. 10 Through focus HREM images and sim ulations......................................... 136
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Chapter 1 Introduction
1.1
1.1.1
Ferroelectric materials and their applications
Ferroelectricity and Perovskite structure
For the past few decades, ferroelectric materials have received a great amount o f
attention in m any fields o f materials research because o f their various potential uses in
many applications such as dynamic random access memories (DRAM)1,2, nonvolatile
ferroelectric random access memories (NVFRAM ) , 3’ 4 infrared sensors ,5’ 6 and
microactuators .7 Ferro electrics are polar materials that possess at least two equilibrium
orientations o f the spontaneous polarization vector in the absence o f an external electric
field, and in which the spontaneous polarization vector m ay be switched between those
orientations by an electric field. Most ferroelectrics undergo a structural phase transition
from a high-temperature non-ferroelectric (or paraelectric) phase into a low temperature
ferroelectric phase. The transition temperature o f the phase transition is called the Curie
point, Tc Above the Curie point the dielectric permittivity falls o ff with temperature
according to the Curie-Weiss law:
where C is the Curie constant, Tq (T c < T0) is the Curie-Weiss temperature and &o is the
optical dielectric constant. Most ferroelectric materials have perovskite structure, named
after the CaTiC>3 perovskite mineral, in fact ferroelectricity itself is closely related to the
intrinsic structure frustration associated with perovskite structures.
1
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A perfect perovskite structure has a general formula o f ABO 3, where A represents
a divalent or a trivalent cation, and B is typically a tetravalent or a trivalent cation. As
shown in Figure 1.1 below, A atoms occupy the comer o f the cube, while the B atoms
sit in the center inside the octahedral formed by oxygen atoms, which are at the face
centers. Barium titanate (BaTiCb) is one o f the ferroelectric materials that have been
extensively studied and can serve as an excellent example to illustrate intrinsic
structural frustration and thus ferroelectricity associated with perovskite structures.
The Ti ions o f BaTiC>3 (BTO) occupy the B site o f a perovskite structure and are
surrounded by six oxygen ions in an octahedral configuration. Since a regular TiC>6
octahedral configuration has center symmetry, the six T i-0 dipole moment cancel in
antiparallel pairs. A net permanent moment o f the octahedron can result only by a
unilateral displacement o f the positively charged Ti4+ ion against its negatively charged
O2' surroundings. Ferroelectricity requires the coupling o f such displacements and the
Figure 1.1 Perovskite structure
2
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dipole moments associated with the displacements. There are two reasons why
perovskite structure allows this coupling to happen.
Firstly, it allows the ionic dipoles to be aligned parallelly. In other types o f
structures containing TiC>6 octahedrals such as rutile, brookite and anatase (three
modifications o f TiC^), each oxygen ion has to be coupled to three Ti4+ ions if each Ti4+
is to be surrounded by six oxygen ions. So the T i-0 octahedrals are grouped in various
compensating arrays by sharing two, three, and four edges, respectively with their
neighbors. Consequently, all the Ti-O dipole moments cancel and none o f these TiCh
crystal forms are ferroelectric.
In the perovskite structure, however, each oxygen atom only has to be coupled to
two Ti ions. Consequently, the TiC>6 octahedral in the BTO can be placed in identical
orientations, joined at their comers, and fixed in position by Ba2+ ions. This gives the
opportunity for an effective additive coupling o f the net dipole moment o f each unit
cell.
The second reason comes from that the bond lengths o f Ba-O and Ti-O are
different, and all bonding lengths cannot be satisfied in a perovskite structure, resulting
in “incompatible” structure. In BTO the large Ba2+ ions and O2' ions form an/c.c.-like
lattice with Ti ions fitting into octahedral interstices. The lattice constant o f BTO is a =
0.401 nm (at just above the ferroelectric transition temperature 120°C), so the distance
between Ti4+ and O2' ions is 0.2005 nm. However, the sum o f the Ti4+ and O2' ion
radius is: r = r . + r 2- = 0.064«w + 0.132/im = 0.196«m. Obviously, the distance
between Ti4+ and O2' ions is larger than the sum o f Ti4+ and O2' ion radius, that is, the
space o f the octahedral interstices is larger than Ti4+ ion. Therefore, Ti4+ ion can move
3
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relatively freely inside the oxygen octahedral with very small restoring force. There are
consequently minimum energy positions for the Ti4+ ion that are off-center and
therefore can give rise to permanent electric dipoles.
A t a high temperature (T > Tc), the thermal energy is sufficient to allow the Ti4+
ions to m ove randomly from one position to another, so there is no fixed asymmetry.
The open octahedral structure allows the Ti4+ ion to develop a large dipole moment in
an applied field, but there is no spontaneous alignment o f the dipoles. In this symmetric
configuration the materials is paraelectric, (i.e., no net dipole moment when E = 0).
When the temperature is lowered to below Tc, the position o f Ti4+ ion and the octahedral
structure change from cubic to tetragonal symmetry with the T i4’1’ ion in an off-center
position corresponding to a permanent dipole.
Further insight can be obtained i f we compare three different perovskite structures
o f CaTiC >3 (CTO), SrTiOs (STO) and BTO. A t room temperature, the lattice constant o f
CTO a=0.380 nm, so the distance between Ti and O ions is 0.190 nm. This distance is a
little sm aller than the sum o f the Ti and O ion radius. Hence the movement o f Ti ions is
strongly limited. Figure 1.2 illustrates these three different structures. The differences in
these three perovskite structures suggest that BTO is the most likely one among them to
have ferroelectricity and CTO is the most unlikely one. This corresponds very well to
experimental results, which show that BTO has a paraelectric to ferroelectric phase
transition at 393K, and the Tc for STO is only 23 K, while CTO does not have any
ferroelectricity.
In the following two sections, more detailed lattice dynamic and thermodynamic
theory w ill be used to describe this phase transition.
4
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Ba2^ . — ..
( o2,2+
A
.2 +
° 2'
o
rl
O
ctl
I
Ba2^ — ^?Ba2+
O 2-
o2Yri4+Yo2-
o A (t? V o 2
v~“
a
b
c
Figure 1.2 Illustration o f the structure o f (a) CaTi0 3 , (b) SrTi 0 3 , (c) BaTiCb.
1.1.2
Lattice dynamic (soft phonon) theory of ferroelectricity
Some fifty years ago Cochran 8 ,9 and Anderson 10 suggested that the phase
transitions in certain ferroelectrics might result from instability o f one o f the normal
vibrational modes o f the lattice. According to this theory, for one particular normal
mode, it is possible for the short-range (ionic coulomb forces) and long-range
(interaction o f polarized dipoles) forces to almost cancel each other out at certain
temperature. The total restoring force is then very small and the crystal becomes
unstable for that particular mode. This mode is called the soft phonon or soft mode, for
it is much “softer” than o th er modes. The frequency o f the soft phonon decreases when
5
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approaching the critical temperature Tc and the restoring force for the mode
displacements tends to zero until the phonon has condensed out at the stability limit.
The theory predicts that the soft phonon frequency cos is temperature dependent and that
because o f the Lyddane-Sachs-Teller relation11:
1.2
the static dielectric constant es reaches a maximum when cos reaches minimum.
The relationship between the soft phonon frequency and the dielectric constant
can be derived using a simplified one-dimensional calculation. Assume .r is the
displacement of the Ti4+ ion along the polar axis; its vibrational equation can be
expressed as:
m x + ( k s —fc,+
where
ks and
= qE0e “*
1.3
Ki are the elastic constant o f the short range ionic interaction and long
range coulombic force, respectively, q is the charge for the ion and t^Tx is the
anharmonic force to the first order o f approximation. The polarization:
P = Nqx = ZE0e -ia*
1.4
where A is the number o f ions per unit volume, % is the dielectric susceptibility. This
equation has a solution as:
1.5
where a>s is the soft phonon frequency, and,
1.6
6
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Obviously, when T= Tc, cos = 0, where
Tc = K‘
c
C
.
1.7
So the static dielectric susceptibility
1.8
T
~
T c
where C ’=Nq2/m. This corresponds to the Curie-Weiss law:
C
T -T c
£ r = --------------F £ x .
So, if we plot both the reciprocal o f dielectric constant versus temperature and aF' versus
temperature, they should be two straight lines converging together at low temperaature.
The validity o f this theory was clearly shown by Cowley 12 for STO (Figure 1.3).
7/
x
100
Figure 1.3 The square o f the frequency o f the soft mode o f the
ferroelectric branch is plotted versus temperature in a solid
line for STO. The broken line represents the temperature
dependence o f the reciprocal dielectric constant 12
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1.1.3
Thermodynamic (Landau-Ginzburg-Devonshire) theory of the spontaneous
polarization o f ferroelectrics13,14
W hile the lattice dynamic theory gives the correlation between the microscopic
lattice vibration and the macroscopic properties such as dielectric constant, the
thermodynamic theory correlates different macroscopic values such as temperature,
polarization and energy. We can obtain a consistent thermodynamic theory of the
behavior o f a ferroelectric crystal by considering the form o f the expansion of the
energy as a function o f the polarization P. We assume that the free energy F in one
dimension m ay be expanded as:
F ( P ,T ,E ) = - E P + cc0 + j a tP 1 + ^ c c zP 4 +^-ar3P 6 + ...
1.9
where the coefficient a„ depend on the temperature.
This series does not contain terms in odd powers o f P if the unpolarized crystal
has a center o f inversion symmetry, which is usually the case for most ferroelectric
materials. The value o f P in thermal equilibrium is given by the minimum o f F a s a
function o fP ; differentiating eq. (1.9) with respect to P gives:
IT*
— = 0 = - E + a .P + a , P 3 +cc3P 5 + ...
3P
. 2
3
1.10
To obtain a ferroelectric state we must assume that the coefficient o f the term in
P2 in eq. (1.9) passes through zero at some temperature To'.
a i = r ( T - T 0),
1.11
where yxs taken as a positive constant and To m ay be equal to or lower than the
transition temperature. The validity o f this assumption is experimentally supported by
8
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the Curie-Weiss law. A small positive value o f a\ means that the lattice is “soft” and is
close to instability. A negative value means that the unpolarized (paraelectric) state is
unstable.
I f Oi is positive, nothing new is added by the term in <23 , and it can be neglected.
The polarization for zero field can be found from eq. (1.10):
y ( T —T0)PS + cc2P 3 = 0 ,
so that either P s= 0 or Ps2 = ( / /
cci)(Tq-T).
1.12
for T > To the only real root o f eq. (1.12) is
at Ps = 0 since /a n d or? are positive. Therefore, To is the Curie temperature. For T < To,
the minimum o f the free energy in zero field is at
\P,\ = yl<.y/a1HT0 - T ) ,
1.13
as plotted in Figure 1.4a.
The transition is first order if
<22 is
negative. We must now retain
<23
and take it
positive in order to restrain F from going to minus infinity. The equilibrium condition
for E = 0 is given by:
y ( T - T 0)Ps - \ a 2\P 3 + a 3P 5 = 0 ,
1.14
so that either Ps = 0 or
y ( T - T 0) - \ a 2\Ps2 +cc3P 4 = 0 .
1.15
At the transition temperature Tc the free energies o f the paraelectric and ferroelectric
phases will be equal. That is, the value o f F for Ps = 0 will be equal to the value o f F at
the minimum given by eq. 1.15. The plot o f the free energy versus polarization curves at
different temperatures according to the above equations is shown in Figure 1.5. The
existence o f meta-stable phases during the process o f the phase transition is
9
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characteristic to first order transition. Correspondingly, a sudden jum p o f polarization
occurs at Tc. Figure 1.4b shows the characteristic variation o f Ps versus temperature for
a first order phase transition.
u.
u.
a
b
Figure 1.4 Schematic Ps versus temperature curves for (a) second
order phase transition and (b) first order phase transition. There is a
sudden jum p o f Ps at Tc in the first order phase transition.
6 /C
Only fe rro e le c ­ F e rro e le c tric
tric p h a se can phase stcble.
Non -p o la r
e x is t
p hase m e ta ­
sta b le
C/D
F e rro e le c tric
p hase m e t a stab ie
N o n -p c la r
p h ase stab le
F e rro e le c tric
p h ase can
e x is t only if
in cu ce d by
appliea field
F e rro electric
p hase cannot
be induced by
applied field
T em perature
r
Figure 1.5 Gibbs free energies as functions o f polarization in a first order
phase transition, in different temperature ranges.
10
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1.2
1.2.1
BST for tunable microwave applications
Dielectric properties of BST
BaxSr(i-X) 0 3 (BST) is a solid solution o f BTO and STO. The ferroelectric transition
temperature is approximately a linear function o f the Ba to Sr ratio (see Figure 1.6).
Upon adding Sr into BTO, the paraelectric to ferroelectric transition temperature Tc
keep decreasing linearly and at about 30% o f STO, the ferroelectric transition takes
place near room temperature. So for use o f BST in its paraelectric state, usually
compositions o f Ba:Sr ratio from 50:50 to 60:40 are used (shaded area in Figure 1.6).
Near the phase transition Tc, the dielectric constant is very large since the BST
lattice is very “soft”, as we discussed in the proceeding sections. Because o f this large
dielectric constant (as large as 10000 in bulk state), BST is a promising candidate for
400
350
300
250
200
150
100
0.0
0.2
SrTi03
0.4
0.6
x
0.8
1.0
BaTi03
Figure 1.6 Ferroelectric transition temperature as a function o f Ba to
Sr ratio in BST.
11
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alternative dielectrics in dynamic random access memories (DRAM) to replace SiC^:
The size o f DRAM and logic devices has kept decreasing at a very fast pace over the
past few decades, currently the minimum feature size has decreased to around
0 .2
pm.
However, as the allowed capacitor area becomes smaller, the amount o f charge stored in
each capacitor has to remain constant (~ 30 fF) to keep the device functional. Therefore,
SiC>2 (dielectric constant 3.9) has to be replaced by some other dielectrics with lager
dielectric constant. With its exceptionally high dielectric constant, BST is one o f the
most promising candidates for this application, and much research work has been
conducted in this area . 1,2
Another very interesting property o f BST is that its dielectric constant can be
changed/tuned by an electric field. Actually the field dependence o f the dielectric
constant in ferroelectrics is one o f the most typical properties o f a ferroelectric and it
was discovered since the 50’s.15,16 Normally the tunability is the highest near the phase
transition temperature and vanishes quickly when going away from Tc. Since the phase
transition temperature o f BST can be controlled by varying the Ba to Sr ratio, we can
conveniently achieve high tunability at room temperature using BST. This property o f
BST has made it a potential candidate for tunable microwave devices. In the following
section, we are going to discuss the application o f BST in tunable microwave devices,
particularly phased array antennas and the materials issue o f BST for microwave
applications will be the focus o f this dissertation.
12
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1.2.2
Planar microwave Phase shifters based on BST thin films and other
competing technologies
Phased array antennas have many advantages over traditional rotating reflector
antennas because they are electronically steerable and thus are faster, more accurate,
more reliable, and able to track multiple targets at one time. Figure 1.7 17 shows a
schematic o f such an electronically steerable antenna. It is generally planar in shape and
made up o f thousands o f closely spaced, individual radiators whose composite beam
can be shaped and spacially directed in microseconds. This is accomplished
electronically by radio frequency (RF) phase shifters associated with each individual
radiating element: Each phase shifter produce a certain amount o f phase shift compare
to its neighboring radiators, thus the wave front o f each radiated RF bean changes
continuously through a series o f neighboring phase shifters. Therefore, the composite
Beam Direction
E quiphase Front
= - 2 S -d s in 0 (
Radiators
0° - 360°
[7x1 [5x1 |5 x | 14 x|
13 xj
Phase Shifters I AO| I ap I lAp| | Ap| | ap
Power
Distribution
Network
Antenna
Input
Figure 1.7 Illustration o f the RF beam-steering concept using phase
shifters at each radiating element.
13
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RF beam can be directed by controlling the phase shift o f each individual radiator. If the
separation between two neighboring radiator is d, to produce a RF beam having a angle
o f 6 fowith respect to the normal direction, a certain amount o f phase shift A<f>is needed
between neighboring phase shifters. This can be calculated by a simple geometry
relation:
=
2 tt
dshxdQ
A
1.16
Using this configuration, since no moving parts are required, phased array antennas are
more compact and more reliable than traditional rotating antennas. Also because
electronically steered beam can be directed to any direction in microseconds, they are
faster and can track multiple targets at one time. However, the cost o f such antenna is
very high. Even utilizing the latest technology and fabrication techniques, the required
phase shifters are not cheap, and with a typical array requiring thousands o f individual
antenna elements, each with its own phase shifter, the price o f the total system becomes
prohibitive. So, up to now, the use o f this type o f antennas is limited in the military
where the cost is outweighed by other more important factors. Therefore, lowing the
cost o f the phase shifters is the primary concern o f phased array antennas.
Currently two types o f phase shifters are used in the phased array antenna design:
ferrite phase shifters and PIN diodes phase shifters . 18,19 Ferrite phase shifters can
handle high power, typically hundreds o f kilowatts to megawatts region, and have very
low losses. However, They are usually large and heavy, also their operational speed is
relatively low, and most importantly they are complex and very costly. On the contrary,
14
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PIN diodes are much cheaper and faster, but with a high insertion loss and very low
power handling capacity, its use has also been limited. In order to make these devices
practical for many other military and commercial uses, such as airport traffic control
and automobile auto-drive systems, better materials for phase shifters has to be
developed. The recently proposed 17,19 ceramic phase shifters may provide a cost
breakthrough for the phased array antenna designer while maintaining low insertion
losses, low drive power and high power handling capacity. It utilizes the characteristic
property o f ferroelectrics: DC voltage tunable dielectric constant.
The propagation constant of a planar microwave is:
If the dielectric constant is a function o f a DC bias, i.e., s r = £r(ybiai) , then a phase
shift A<j> can be created and controlled through a DC bias since:
A#(V) = A/3(V)I,
1-18
where I is the media length. Therefore, a ferroelectric phase shifter can be built simply
by applying a DC voltage across a ferroelectric wave guide and the amount o f phase
shifting will be a function o f the applied voltage.
Among several possible candidate ferroelectric materials, for example, (Ba,
Sr)TiC>3 series, (Pb, Sr)TiC>3 series, and (Pb, Ca)TiC>3 series, BST has emerged as the
most promising one because it is easy to control and fabricate and do not have toxic
component. In the following section, we are going to discuss several key research
interests on BST thin films.
15
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1.2.3
Review of several key research interests on BST thin films and motivation
of this thesis
Two m ajor aspects are the focus o f research on the materials issue o f BST thin
film for microwave phase shifters: tunability and loss.
The intrinsic loss tangent serves to dissipate or absorb the incident microwave
energy and therefore is desired to be in the range o f 0.01 or less. A low loss tangent
decreases the phase shifter insertion loss and hence increases the phase shifting per
decibel o f loss. Also the operating frequency can be extended by reducing the loss
tangent. A lot o f effort has been exerted to decrease the intrinsic loss by fine tuning the
composition o f BST 20’ 21 and adding different dopants into the BST system .22' 25
However, usually the lowering o f loss also causes the lowering o f tunability o f the BST
system, so a compromise has to be made between tunability and loss depending on the
application.
The tunability o f a particular material means how much the dielectric constant
changes upon a certain applied field. It is conventionally defined as (Smax£min)/Smaxx 100% or (£ o v -S v -m a x )/£ o v > < 100%. (Obviously this definition can cause
ambiguity since different applied fields will result in different durabilities. This will be
discussed later in chapter 4.) The degree o f phase shift is directly related to the
tunability, therefore higher tunability is desired. Also, the insertion loss is inversely
related to the tunability so that the larger the tunability, the smaller the insertion loss. To
achieve optimum electronic properties, the tunability should range from at least
as high as 50%, depending upon the dielectric constant and the loss tangent.
16
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10%
to
The tunability o f BST is closely related to its dielectric constamt. It is generally
recognized that the higher the dielectric constant, the higher the tunalbility. However,
little work has been done regarding the exact relationship between thnem.
Both the dielectric constant and tunability o f BST are very higth in its bulk state
(e>5000 and tunability>60%). However, when BST is deposited as tfhin films, these
properties drop dramatically.21’ 26' 28 Though, a recent letter has reporrted values for a
BSTO/MgO thin film comparable to bulk specimens .29 This degradation in electric
properties o f BST thin films is generally attributed to misfit strain30' 3 3 (accrued via
lattice or thermal mismatch between film and substrate) and/or d e fe c ts such as
vacancies ,34"36 dislocations37’ 38 or grain boundaries39^ 1 as crystal imjperfections which
could lead to the observed behavior. However, there appears a lack »of consistent
interpretation in the literature as regards the disparity in the dielectrioc properties.
In this dissertation, the effect o f strain on the dielectric properties o f BST thin
films will be systematically studied. The Landau-Ginzburg-Devonshiire thermodynamic
theory is used to model the effect o f strain on both the dielectric consstant and tunability
o f the BST films. Also the role o f different types o f defects, i.e., vacsancies, dislocations,
and grain boundaries, is studied via annealing experiments. The re s o its w ill be
presented in following chapters
17
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Chapter 2 Experimental Techniques
2.1
2.1.1
Pulsed laser deposition
Principles and applications
All BST thin films studied in this dissertation were grown using pulsed Laser
deposition (PLD). PLD is an extremely versatile technique for preparing a wide range
o f thin films and multilayer structures. Figure 2.1 is a schematic diagram o f a basic laser
ablation system. In the process o f a PLD deposition, a pulsed laser beam (typically 30
ns pulses with energy in the range o f 0.01-1 J and at a frequency o f l-10Hz) is focused
by a lens external to the vacuum chamber onto the target. If the laser fluence (laser
pulse energy per unit area at the target) is above a threshold value, a luminous plume o f
Z48 nm, 30 ns
UVLaser Beam
Rotating
Multiple
Target Holder
Substrate Heater
30 - 900°C
Figure 2.1 Schematic of a pulsed laser deposition system
18
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the target material is ejected normal to the target surface and is collected on a suitably
positioned and heated substrate. Usually, a reactive gas such as oxygen (for oxides
growth) or nitrogen (for nitrides growth) is introduced into the chamber through a leak
valve during the deposition to assist the formation o f the needed phase. In this so-called
reactive laser ablation process, it is common to pump to a base pressure (usually <
lx lO ' 5 Torr) first to clean the chamber and to heat the substrate at base pressure to allow
outgassing to occur before the reactive gas is introduce to the chamber.
The lasers commonly used for laser ablation include ArF, KrF, XeF excimer lasers
and Nd:YAG laser. It is generally recognized that the shorter the wavelength, the more
effective the laser ablation is. So, excimer lasers have become the primary ones used in
PLD system. The laser used in this study was a KrF laser with a wavelength o f 248 nm
and 30 ns pulse width.
The biggest advantage o f PLD is its versatility. A wide range o f materials can be
grown by PLD, including metals, oxides, semiconductors and even polymers .42 Unlike
Molecular Beam Epitaxy (MBE) and Chemical Vapor Deposition (CVD), in which a
different source or precursors is required for each element o f the compound material to
be grown, all PLD needs is a piece o f target o f the interested composition. In addition,
multiple chambers can be set up around one laser source and the laser beam can be
directed to each chamber using mirrors and lenses. Thus, different compounds can be
grown in different chambers, avoiding cross contamination. Another advantage o f PLD
is that the energy associated with the high ionic content in laser ablation plumes
(typically o f the order o f 1 0 % and rising with increasing incident laser pow er density43)
and high particle velocities (of the order o f
106
cm-s’1) appears to aid crystal growth and
19
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to lower the substrate temperatures required for epitaxy. The ability o f congruent
deposition o f multi-component materials is also an advantage o f PLD. Because o f the
very short pulse width o f the laser, the evaporation o f the target is negligible and the
target material explodes toward the substrate, so different components have similar
deposition rates. Other advantages include that it is relatively clean, cheap and able to
produce multilayer hetero-structure simply by using several targets.
The plume o f ablated material is highly forward directed. This makes thickness
monitoring by conventional quartz monitors difficult. It also causes poor conformal step
coverage. In addition, this narrow distribution o f plume results in thickness non­
uniformity when depositing large wafers, which can be overcome, to some extent, by
rastering the laser beam on a large size target .44 The biggest disadvantage o f PLD,
however, is the intrinsic “splashing” associated with laser ablation itself, which results
in droplets and big chunks o f target material on the substrate surface. This is
particularly problematic for electronic devices where particulates can cause short circuit
and serve as scattering centers. Because o f these disadvantages, PLD is limited in the
use o f investigation o f new materials in research environments, where its flexibility,
versatility and affordability are very welcome.
All BST films studied in this dissertation were deposited using PLD at 800 °C
with a dynamic oxygen partial pressure o f 120 mTorr. The substrates were cleaned
using a sequence o f ultrasonic baths in trichloroethyene (TCE), acetone and methanol
prior to loading into the chamber for film deposition. A shutter was used to allow the
target to be cleaned by ablating the surface with the laser beam without contamination
o f the substrate. A laser fluence o f ~ 1.5 J/cm 2 was used, corresponding to a growth rate
20
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o f ~ 0.08 nm/sec. The samples were cooled down at a rate o f 5°C per minute in 700
Torr O 2 after deposition.
2.2
Transmission electron microscopy
Transmission electron microscopy (TEM) was the primary method used in the
microstructure characterization o f BST thin films in this dissertation. The high spatial
resolution o f atomic level (< 2A) and the ability to provide both structural and chemical
information in extremely small areas have made TEM a powerful tool in the
understanding o f the evolution o f both composition and microstructure and their
influence on the relevant properties o f the material under investigation.
The TEM studies in this dissertation were carried out on a JEOL 4000FX
microscope operated at lOOkV and 300kV and a JEOL 4000EX microscope operated at
400kV.
A TEM is similar to an optical microscope, except that optical microscopes use
fight sources and focus fight beams with glass lenses, while TEMs use electron sources
and focus electron beams with electromagnetic lenses. The electrons emitted from the
filament (cathode) are accelerated by a high voltage (100 kV-1000 kV) and focused
through a set o f condenser lens onto the specimen. The almost-parallel beam o f
electrons is scattered by the specimen. This scattering takes the form o f one or more
Bragg diffracted beams traveling at small angles (~ 1 or 2 degrees) with respect to the
incident (or transmitted) beam. The scattered beams are then brought to focus by the
objective lens on its back focal plane and form a diffraction pattern. Specific
21
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transmitted and/or diffracted beams are chosen by inserting an objective aperture on the
back focal plane o f the objective lens to produce a final TEM image on the fluorescent
viewing screen.
Similar to glass lenses in optical microscopes, an ideal electromagnetic lens can
also be described as a planar object having a transmission function o f T (x, y) =
exp {ik(x2+y2y 2 f} , where k = l/Z is the wavenumber, A is the wavelength o f the
electrons and f the focal length o f the lens, and the propagation o f a plane wave through
it can be described by a convolution o f the plane wave and the transmission function.45
Therefore, as shown in Figure 2.2, for one dimension, the amplitude given on a plane of
observation when a plane wave passes first through an object o f transmission function q
(x) and then an ideal lens is:
<P{x) =
?(x)*exp^
-ikx 2
2R
exp
I ikx2
U T
:exPi
—ikx2
2 R'
2.1
where the operations in the successive brackets represent transmission through the
object and propagation through a distance R, transmission through the lens, and
propagation through a distance R . By writing out the convolution integrals in detail it is
readily shown that if R ’ = f
<p{x) = FT.{qix)} = Q ( x / f l ) ,
2.2
a n d i f ( l / f l ) + ( l / R ’) = 1 If
<p(x) = F T .-' {FJ-.fe(x)}} = 9( - B x /R ’) .
2.3
where Q (x/fi) is the Fourier transform//7. T.) o f q (x). Therefore, the diffraction pattern
formed in the back focal plane (R ’ =_/) o f the objective lens is the Fourier transform of
22
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object
Plane o f
observation
lens
q(x)
<p(.x,y)
Figure 2.2 Diagram o f an imaging system
the transmission function o f the object. And the image formed in the image plane o f the
objective lens, (1 / i?)+(l / R ’) = 1 / / , is the Fourier transform o f the diffraction pattern
at the back focal plane, i.e., a double Fourier transform o f the transmission function o f
the object.
Since the focal length o f a magnetic lens can be easily changed by changing the
coil current, we can get both diffraction pattern and image at the same time in a TEM.
As schematically shown in Figure 2.3 ,46 by changing the focal length o f the
intermediate lens, we can either make its objective plane coincide with the back focal
plane o f the objective lens or with the image plane o f the objective lens. Thus both the
diffraction pattern and the image o f the sample can be observed at the viewing screen.
These are the, so-called, diffraction mode and imaging mode.
23
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Specimen
Objective lens
Remove
aperture
Objective aperture
(back focal plane)
Fixed
SAD aperture
Intermediate
image I
— Change —
strength
Remove
aperture
Intermediate
lens
Second
intermediate _
'image' —
.
Fixed —►
strength
Diffraction pattern
Projector lens
Final image
— Screen
Figure 2.3 The two basic operation modes o f the TEM imaging system:
(a) diffraction mode, and (b) imaging mode.
2.2.1
Diffraction
Just like x-ray diffraction but for a much smaller area, electron diffraction gives us
information about a crystal structure through its reciprocal lattice. For a crystal with unit
cell dimensions o f a, b and c in the x, y, and z directions, the transmission function g
(x,y,z) o f the sample can be expressed as:
S ( x —nxa ,y —n2b, z —n3c)
g (x ,y ,z)= f(x ,y ,z)*
2.4
nl 'n 2 -n3
where f (x, y, z) stands for the contents o f the unit cell. The diffraction pattern G (h, k, I)
is the Fourier Transform o i g (pc, y, z ):
24
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G ( h , k , 0 = FT.[g(x ,y,z)]
S { x - n la , y - n 2b , z - n 3c)
= F T A f ( x , y, z ) *
n l ,n 2.n 1
= F T .j f (x, y, z)]- F T .
^ ^ ( x - « , a , y - n 26 , z - n 3c)
2.5
while:
FT.
y S ( x - n la , y - n 2b , z - n 3c)
n, ,/i2 ,n3
2.6
= -^7 '^S Q h —nxa * ,k —n2b* ,/ —« 3c*)
/t| ./ I j ./I
3
where a*, b* and c* are the unit cell dimension o f the reciprocal lattice, which are
defined as:
a =
bxc
a- ( f i x e )
b'
cxa
a ■{bxc')
axb
c —■
a-{b xc)
2.7
So the
G (h ,k,l) =
F{x, y, z)
5(h —nyd’ , k —nzb*, I —n3c*)
2.8
where F (x, y. z) =F.T.[f (x, y, z)], which is called the structure factor.
Therefore, the diffraction pattern obtained in the TEM is just a two dimensional
interception o f the reciprocal lattice (x-y plane, z is usually used for the incident beam
25
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direction). And the intensity of each lattice point is determined by the structure factor.
Multiplied by the factor in square brackets in eq. (1.8 ).
2.2.2
Imaging—diffraction contrast
Normally, in a diffraction contrast image, only one electron beam, either the
transmitted beam or one o f the diffracted beams, is allowed to pass through the
objective aperture. When only the transmitted beam is allowed to pass through the
objective aperture, as shown in Figure 2.4(a ) , 46 a bright field image (BF) is formed. On
the other hand, if a diffracted beam is allowed through the objective aperture, as shown
in Figure 2.4(b), a dark field image (DF) is formed. To avoid the aberrations and
astigmatism associated with off-axis imaging, usually the incident beam is tilted to keep
the diffracted beam on the optic axis when DF is needed. This is called the centered
dark-field (CDF) imaging, as shown in Figure 2.4(c). For the simplicity o f image
interpretation, it is a common procedure to tilt the specimen to a so-called two-beam
condition, where only one diffracted beam is excited (at Bragg reflection), so that the
total intensity can be regarded approximately as the sum o f the diffracted beam and the
transmitted (direct) beam.
Assuming the contribution to the diffracted beam comes only from a narrow
column
(~ 2
nm in diameter) of crystal in its path (the column approximation), we can
calculate the total amplitude <
f>
g at the point where the diffracted beam g exits the sample
by integrating the scattered wave through the film thickness: 4 7
^ exp(—2mg ■R) exp(—2m s z)d z ,
s
26
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2.9
O p t ic axis
Incident
beam
Reflecting
plane
y
Direction o f
Optic axis
till o f incident
beam
*"
26 = angle o f lilt of
incident beam
Incident
Reflecting
plane
specimen
29
^
specimen
29
i^bjccuve^.
bj’ective
lens
Diffracted
beam
Diffracted
Direct
beam
Objective
aperture
Direct
Obj'ective
aperture
~ -
.D v-'! 'Qfg
Diffracted
beam
:i
- -v
'
O • -; O
~
Objective v
-Direct beam‘d
jy .
• '■
- V : : » .y V tg j- z -
Figure 2.4 Ray diagrams showimg how the objective lens and objective
aperture are used in combination t o produce (a) a BF image formed from the
direct beam, (b) a displace-aperture DF image formed with a specific off axis
scattered beam, and (c) a CDF imasge where the incident beam is tilted so that
the scattered beam remains on the optic axis.
where & is called the extinction distances which depends on the g vector, the material
o f the sample, and the acceleration voltmge, R is the displacement o f the unit cell from
its proper position in a perfect crystal, s i s the excitation error (i.e., the deviation o f the
Ewald sphere from the reciprocal lattice point g ) and t is the sample thickness. For a
perfect crystal (R — 0), eq. 2.9 reduces ton:
<f>g = — jexjp(—2msz)dz
^z
i7t sm arts
exp(—mst)
7ZSS
27
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2.10
The intensity therefore varies as ^
^ t).
(*s)2
T h is
gives rise to thickness fringes in a
wedge crystal.
For an imperfect crystal, the imperfection introduces an additional phase factor e
ta, where a = 2ng ■R . Thus, if the displacement R is normal to g , no contrast in
comparison to the perfect crystal is produced, while the contrast due to the imperfection
is expected to be a maximum i f R is parallel to g . This is the basis o f defect analysis in
diffraction contrast.
2.2.3
Imaging— phase contrast
A phase contrast image is obtained when two or more diffracted beams are
included in the objective aperture for the image formation. Normally, it is obtained at a
region where the sample is very thin, in which situation the absorption can be neglected
and the scattering o f electrons b y the sample only causes a phase change o f the wave
function. This approximation is called the phase object approximation. With this
approximation the interpretation o f the image is more direct. Thus the transmission
function o f the object can be expressed as:
q(x, y ) = exp[/a^?(x, y) Az]
2.11
where cris the interaction constant, (p (x, y) is the projected potential o f the object along
the z axis, and Az is the sample thickness. As mentioned in section 2.2, the amplitude at
the back focal plane o f the objective lens is the Fourier transform o f the transmission
function o f the object while the image is a double Fourier transform (inverse F.T.) of
28
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the transmission function. However, now the effect o f the objective lens and aperture
has to be considered. Thus, the amplitude at the back focal plane can be expressed as :48
Y (u, v) = F.T.[q(x, j/)]exp[yf(«,v)]
~ 8 (u, v) + iF.r.[cr^(x, y ) Az]exp|/^(«, v)]
2
^
where exp[/;{f(w, v)] is the contrast transfer function o f the lens. It stands for the phase
change caused by the objective lens. %(u, v) can be expressed as:
= 7t^fz{ii2 4-v2)—0.5CSA3(u2 + v 2)"j
2.13
where A /is the defocus value, Cs is the spherical aberration o f the objective lens, and u,
v are the coordinates in the back focal plane o f the lens.
B y taking account o f the objective aperture, the amplitude at the image plane is:
<p(x, y) = FT.[C(u, v)T(m, v)]
2.14
where C (u, v) is the aperture function o f radius r given by:
C (u,v) = 1 when y u 2 + v 2 < r
C(u,v) =0 when -Ju1 + v 2 > r
2.15
Therefore, the intensity at the image plane is:
I ( x , y ) = <p\x,y)(p(x,y)
= |1 + iF T .fc (u , v)F T^a(p(x, y ) Az]exp(i^(z<, v)) f
W1+ /(<x, A/, Cs, Z, r, Az) • cr<p(—x,—y)Az
2.16
It can be seen from the above equation that a phase contrast image is a direct reflection
o f the projected crystal potential <p(x, y) and this is the basis o f high resolution TEM
(HREM) imaging. However, as also can be seen from the equation, the intensity is not
29
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exactly the crystal potential (p (pc, y); it depends on many parameters, such as, the
defocus value Af the sample thickness Az, and the spherical aberration o f the objective
lens Cs. So, the interpretation o f an HREM image is not trivial. While it is easy to obtain
a so-called lattice image, where the symmetry o f the crystal and the unit cell
arrangement is reflected, it is not as simple to obtain the atomic arrangement inside a
unit cell. A computer simulation has to be performed before one can determine the
exact atomic position in a HREM image. In such a HREM simulation, all the
parameters needed for the calculation are inputted to a pre-compiled computer program,
for example, MacTempas,49 and a series o f calculated images is compared with the
HREM images obtained under different value o f Af etc. to reconstruct the true atomic
structure o f the crystal. Usually a through focus series o f HREM images are needed to
get a reliable result.
2.3
TEM Sample preparation
Sample preparation is a practical bottleneck in TEM analysis. Since electrons are
very easy to scatter, extremely thin samples (< 1 pm) has to be obtained to let the
electrons pass through. Cross-section and plan-view specimen preparation for TEM
observation are frequently used in the characterization o f thin films. For a cross section
sample, the transmitted electrons are parallel to the film-substrate interface, while for a
plan-view sample, they are perpendicular to the interface. Sample preparation for planview specimen is much simpler than cross-section, so usually the focus o f sample
preparation method is on the preparation o f cross-sectional samples.
30
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2.3.1
Cross section sample preparation
Conventional cross-sectional TEM specimen preparation involves several steps.
The first step is to cut o ff two pieces o f ~ 1mm x 5mm from the large sample by using a
diamond saw or cleave by using a diamond scriber. These pieces are then glued
together with the film sides facing each other using M-bond 610 adhesive. The
backsides o f the pieces are usually reinforced by two dummy pieces o f the same
material as the substrate. Then the glued stack is mounted on a tripod polisher holder
with acetone dissolvable wax. Using the tripod polisher 30 the glued stack is
mechanically thinned down to about 20-40 pm using diamond lapping paper. The
specimens are then removed from the tripod holder and glued on a slotted copper grid.
Finally, the specimens are ion-milled until a hole appears at the interface. The area near
the edge o f the hole is usually thin enough for TEM observation. For the
characterization o f BST films studied in this work, conventional TEM sample
preparation causes damage to the sample and makes very thin area bend due to the high
stresses in the film. To prevent this problem a new technique was developed for sample
preparation. This technique allows thickness monitoring during sample thinning and is
described in more detail below.
2.3.2
Quadripod and the concept of high angle wedge polishing
As mentioned above, to get a thin enough sample for electrons to go through, the
m ethod most commonly used is mechanical polishing followed by ion milling.
However, ion milling can cause serious damage to the sample being prepared. Emerged
in the early 90’s, Tripod polisher50 takes advantage o f the improved polishing media,
31
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making it possible to prepare TEM samples with little or no ion milling. The Tripod
polisher greatly enhances the quality o f TEM samples and shortens the time needed in
sample preparation. However, some difficulties still exist in Tripod polishing:
1.
It is difficult to determine the exact thickness o f the sample during the sample
preparation. In practice one has to change polishing material using finer and finer
particle size as the sample gets thinner and thinner. If the polishing paper is not
changed in time, for example, 15 pm polishing paper is still used when the sample is
already thinner than 20 pm, the sample will most likely be damaged. I f ion milling is to
be followed, it is very important to know when to stop polishing. This also requires the
awareness o f the sample thickness. So, a thickness monitor is crucial to TEM sample
preparation.
There are usually two ways to determine the sample thickness in traditional
Tripod polishing. The first one is to visually compare the sample with some standard
thin sheet o f known thickness, such as a TEM copper grid or a piece o f paper .51 The
second method to determine the thickness is to use an optical stereo microscope. Both
methods give only approximate values o f sample thickness and require a certain amount
o f experience.
Neither method mentioned above can accurately determine sample thicknesses
less than 10 pm. This is not a problem for Si-based samples, because the thickness o f Si
can be determined by the color it displays. Namely, when the thickness is less than 10
pm, Si changes color from dark red (—10 pm) to light yellow (—1 pm). However, most
other materials do not show any color change during thinning. So in traditional tripod
polishing, the sample has to be thinned together with a Si sample to determine the
32
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thickness using Si as a reference.
However, even with Si as a reference, under most
circumstances, the most crucial stage in the sample preparation process is when the
sample is between ~50 pm to 10 pm, in which range none o f the techniques mentioned
above is effective. This lack o f thickness control has made TEM sample preparation
dependent very m uch on personal experience. It usually takes considerable practice
before one really feels confident in estimating the sample thickness.
2.
Frequently, locating a specific two-dimensional area, such as a particular
capacitor on a chip or a specially treated area o f a few tens o f micrometers per side on
the sample, is required. Traditional Tripod polishing has the ability to locate areas in
one direction, such as a thin stripe, but lacks control for the other direction. The reason
is that the sample is already very thin before the area o f interest can be located along the
second direction. So, one has to be very careful to avoid breaking the sample.
The Quadripod 33 is a simple but major improvement over the widely used Tripod
polishing. We propose for the first time the concept o f high angle wedge polishing in
TEM sample preparation and the concept of converting lateral measurement into
vertical (thickness) measurement. Utilizing these ideas, we designed the Quadripod.
The Quadripod overcomes the difficulties mentioned above in traditional Tripod
polishing, making TEM sample preparation almost experience independent and
providing the ability to locate a specific 2-D area o f the sample. Using the Quadripod,
one can determine the thickness o f the sample down to
10
pm by eye, even though the
"official resolution" for human eyes is above 50 pm, and down to 1 pm with an optical
microscope. The ability o f easy and accurate thickness determination makes Quadripod
very friendly to novices in TEM sample preparation. In addition, as locating a specific
33
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area o f the sample is becoming more and more a requirement, especially in failure
analysis, Quadripod provides a much cheaper and damage free alternative to Focused
Ion Beam preparation. 54
2.3.2.1 The concept of high angle wedge polishing in TEM sample preparation.
In traditional TEM sample preparation, the sample is polished flat (such as with a
GATAN disk grinder) or almost flat (Tripod polishing). However, parallel polishing is
the ultim ate reason for the two most important causes o f failure in TEM sample
preparation.
The first cause o f failure results from the lack o f control o f the thickness o f the
sample as mentioned above. The second cause is that when the sample is very thin
<50 pm , every little scratch can be fatal to the sample. Because in a very thin sample,
one scratch not only damages its path, but can also cause the whole sample to crack. In
practice, due to a variety of reasons, such as defective polishing paper, sample debris
and hum an error, a few scratches on the sample are almost inevitable. This has made
TEM sample preparation very difficult when one tries to make the sample scratch free.
However, if the sample is polished using a high angle wedge (15° to 45°
depending on the sample material), the thickness monitor and the prompt change o f
p o lis h in g
material are not required anymore because the material is removed in the
lateral instead o f vertical direction (see Figure 2.5). Furthermore, most o f the sample
will rem ain thick enough to support itself while the tip o f the wedge is already thin
enough to allow electrons to go through. This makes the sample much less sensitive to
scratches, because one scratch will only damage its path, not the whole sample.
34
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>- Sample recedes laterally
M ost o f the sample
remains thick enough to
support itself
Surface being polished
at an angle a
The tip is electron
transparent
I
Figure 2.5 Schematic o f high angle wedge polishing
2.3.2.2 The concept of converting lateral distance measurement into vertical
thickness measurement
Thickness control is crucial to TEM sample preparation, but it is not easy to
measure a thickness vertically since most optical microscopes only have high lateral
resolution but not vertical resolution. However, by converting lateral w idth into vertical
thickness, the measurement becomes much easier. This is done by first polishing the
sample at a certain high wedge angle a as shown in Figure 2.6. The w idth w can then be
measured very easily using an optical microscope. And the sample thickness t can be
determined by a simple geometric relation:
2.17
t=vvtana
Since w can be very precisely measured and a is known, the sample thickness can
be determined very precisely (within ± 0.5 pm) and quickly.
2.3.2.3 The construction of the Quadripod
The Quadripod is a modified Tripod polisher. It has two removable feet that attach
to the base o f a Tripod polisher, as shown in Figure 2.7. It is named Quadripod because
35
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Sample recedes vertically
I«" J -
V1
Figure 2.6 Thickness measurement using a simple geometric
relationship
essentially only four (out o f five) feet are used during the polishing process and the
other foot is used only when examining the sample under a microscope.
The length o f the removable feet determines the angle for wedge polishing. The
length can be varied either by changing to a set with different length or by the use o f a
micrometer. If a set o f feet with different lengths is used, only specific angles for
polishing can be obtained. However, a pair o f micrometers will allow a range o f angles
for polishing. With a traditional Tripod polisher, one can only polish at an angle less
than 10 degree. By adding two more feet, the Quadripod offers the ability to adjust a
wedge angle greater than 45 degrees if desired and thus the ability to utilize the concept
o f high angle wedge polishing and thickness measurement as presented above.
2.3.2.4 The procedure of TEM sample preparation using the Quadripod
The sample preparation procedure using the Quadripod is divided into 3 steps: 1.
First side polishing, 2. Second side high angle polishing and, if necessary, 3. Second
side low angle polishing. Each step will be discussed in detail in the following sections.
Also, an example o f polishing a cross section sample with the requirement o f locating a
36
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Figure 2.7 Schematic o f the Quadripod polisher. The length o f the
quadripod fe e t determines the angle o f polishing
specific capacitor is illustrated, ffo r any other sample preparation such as plan view and
general cross section without locating a specific area o f the sample, essentially the same
procedure can be followed, but several steps can be skipped as mentioned below.
1. First side polishing
I.
Glue a thin glass slide a n top of the film. I f no specific area is required, glue
two pieces o f sample with film sid e face to face (see Figure 2.8).
EL Mount the sample on tthe side o f the L-bracket o f the Tripod polisher using
wax (see Figure 2.9)
37
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Area o f interest
Glass slide
Film
Substrate-
Figure 2.8 Sample and a piece o f glass slide glued together. A
small area o f interest on the sample is shown
L bracket
Point o f interest
Sample
Figure 2.9 Sample position for first side polishing
38
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m . Polish the first side at zero degrees and with the Quadripod feet removed
until the point o f interest in this direction is reached, using a sequence o f polishing
media with finer and finer particle size, starting from 30 pm and ending with colloidal
silicon or colloidal diamond (see Figure 2.10). If no specific area is required, polish to
get a flat and smooth surface.
IV.
Mark the point o f interest on the glass slide for the second direction o f
polishing to follow.
2. Second side high angle polishing
I.
Planarize the sample holder (without the sample) with the two rear feet o f the
Tripod polisher.
n . Use either wax or super glue to mount the sample perpendicular to the edge o f
the sample holder (Figure 2.11).
m . Polish the sample down to 100-200 pm using 30 pm diamond lapping paper.
Polish to the point of interest
Figure 2.10 First side polishing is terminated when the
point o f interest is reached
39
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IV. Mount the two removable feet onto the Quadripod. Choose one set o f feet o f
certain length corresponding to the desired wedge angle a (such as 15°, 30°or 45°),
depending on the sample material. Generally, the more brittle the material is, the higher
the angle.
V. Polish the sample down to the point o f interest, using a sequence o f diamond
paper with particle size from 30 jam down to I pm, colloidal silicon being used for the
final polishing, just like in the first side polishing (Figure 2.12). The advantage o f high
angle wedge polishing is that one does not need to worry about the sample getting too
thin and cracking. This makes the second side polishing as easy as the first side.
Bottom view of the L-bracket
Sample
Marker in the glass slide indicating
where to stop second side polishing
Figure 2.11 Sample position for second side polishing
40
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Sample holder
Sample
Polishing paper
Thin Area
Figure 2.12 Schematic o f second side high angle polishing
I f a large thin area is not required, for example, the TEM sample is prepared just
to identify the thickness o f a certain layer, the polishing process can end at this point
and the sample be mounted onto a copper grid and ready for TEM examination without
ion milling. Simple calculations show that a 30° wedge produces a thin area (thickness
< 500 nm) along the film interface for about a micrometer into the sample.
3. Second side low angle polishing
If a relatively large thin area, >1 pm in width into the sample, is required for TEM
analysis, low angle polishing o f the second side is necessary. In this case, thickness
checking becomes very important for the reasons discussed above, namely, flat or
41
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almost flat polishing requires prompt changing o f the polishing paper at specific
thicknesses o f the sample. As mentioned in the discussion o f converting lateral
measurement to vertical thickness, the high angle polishing makes it very easy to check
the thickness. The procedure is described below:
W hen low angle polishing o f the second side is to be performed, the high angle
polishing can stop at 1 pm polishing paper in step V o f section 2: “Second side high
angle polishing”.
I. Remove the removable feet o f the Quadripod. Raise the two rear feet o f the
Tripod by 0.2~2mm, depending on the material o f the sample to be polished. Generally,
the more brittle the sample, the higher the angle.
II. Polish the sample down to electron transparency. Change the polishing media
promptly. Namely, use 30 pm diamond paper to polish down to a thickness o f about
150 pm, 9 pm diamond paper to 50 pm, 3 pm to 20 pm, 1 pm to 5 pm and finally
colloidal silica to electron transparency when light interference fringes can be seen
across the sample, Figure 2.13.
The thickness o f the sample can be easily determined by measuring the width o f
the material remaining after the high angle polishing, as shown in Figure 2.6 and Figure
2.14. And very conveniently, since the high angle polishing has given the sample a
slope w ith a very shiny surface, the width o f the slope can be roughly determined by
how m uch light the sloped face reflects, which can be easily seen by the naked eye. In
this fashion, a sample thickness as small as
10
pm can be judged by looking at the
reflected light from the high angle polished slope even though the official resolution o f
the hum an eye is above 50 pm.
42
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Interference
fringes
Interface
Figure 2.13 Interference fringes appear when the sample is
electron transparent
■
n
Polishing wheel
Sample thickness can be determined
by measuring the width o f the
sloped region under a microscope,
or roughly estimated by judging the
light reflected by the slope
Sample holder
Smnple
Polishing wheel
Figure 2.14 Schematic o f second side low angle polishing
43
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This sim ple estimate o f thickness saves a lot o f tim e by eliminating the necessity
o f checking the sam ple thickness frequently under an optical microscope. Usually, the
author uses an optical microscope only to check the interference fringes during the final
polishing stage, w hile the determination o f a thickness > 5 pm to decide when to change
the polishing paper is done by eye.
m . Soak the sample in acetone until it falls o ff the sample holder and then rinse
it with methanol.
IV. M ount the sample onto a copper grid with M -bond 610. Under m ost
circumstances, the sample is ready for TEM analysis. However, in some situations
where, for example, the sample has a metal layer that deforms easily, or the sample is
sensitive to contamination by wax or super glue, 5-20 minutes ion milling is necessary.
A final note
If an extrem ely large thin area, >10 pm into the sample from the edge, is required
for a particular sam ple, it is also possible to mount the sample with the interface
between the sam ple and the glass slide parallel to the edge o f the sample holder (Figure
2.15). The same procedure as described in sections 1, 2 and 3 can be followed to obtain
very large thin area. However, in this case, attention has to be paid during the second
side high angle w edge polishing, i.e., the polishing has to stop just before it reaches the
film (Figure 2.16). Since the distance “d” between the sample tip and the glue line
serves as a thickness indicator, it is not difficult to determine when to stop the high
angle polishing. W ith this parallel mounting, however, the sample often has to be coated
44
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with about
1
p thick Si0 2 before gluing it to the glass slide to prevent the film from
being rounded away by the polishing process.
.Glass slide
Sample
Figure 2.15 Sample position for alternative parallel polishing
Glue line Film
Glass Slide
Sample
Stop high angle polishing just
before it reaches the film
Figure 2.16 Schematic o f parallel polishing
45
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2.4
Device fabrication and electrical measurement
The dielectric measurements were performed by using the conventional
interdigital electrode (IDE) method. The schematic o f the IDE structure is shown in
Figure 2.17. It consists o f 50 fingers separated by a 15 pm gap. Each finger has a width
o f 25 pm and length o f 0.70 cm. Under this configuration, the electrical field lines are
primarily in plane, i.e., parallel to the film surface. Standard photolithography
"■mm
Figure 2.17 Schematic o f the IDE structure used for dielectric
measurement: (a) top view (b) cross-section view.
46
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techniques were used to define the pattern and metallizatrion was performed via
deposition o f a 100 nm Au layer using PLD. The dielectnic properties were then
measured using an HP 4192 Impedance/Gain analyzer. T'ypical measuring frequencies
were 1 MHz and 10 kHz. The DC bias was applied from -4 0 V to +40 V and the AC
measuring voltage was 200 mV. The permittivity o f the E3ST films was extracted from
the capacitance data using a model outlined by Gevorgiam. et al .55
47
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Chapter 3
Dependence of dielectric properties on internal stresses
in epitaxial BST thin films
3.1
Introduction
It is has been observed by many research groups that, compared to bulk, the
dielectric constant and nonlinearity o f epitaxial thin films are markedly worse .21,26,56
Possible causes for this degradation in dielectric properties include: residual stress
created by the lattice m isfit and thermal expansion coefficient (TEC) mismatch between
the substrate and the film, defects, such as vacancies, dislocations, grain boundaries and
second phases, and interfacial capacitance. In this chapter we will discuss the effect o f
stress on the dielectric properties o f BST thin films; the effect o f defects will be
discussed in the following Chapter.
The effect o f stress on the dielectric properties o f BST thin films has been
extensively studied by m any groups .30,33,57,38 However, all works are not in total
agreement. Chang 33 considered strain as a limiting factor in obtaining high tunability to
loss ratio, and no obvious correlations between the dielectric properties and strain was
established. Shaw 30 performed an experiment in which external stress was applied by
bending the BST film. Compressive stress was found to decrease the dielectric constant
and no in plane polarization was found in the BST films. In contrast, Pertsev 57 proposed
that a modified Curie-Weiss type law defines the behavior o f the dielectric constant for
BST films and that in-plane polarization states exist in BST films on Si substrate,
opposite to what Shaw suggested. In other experiments by Hyun, small tensile stress
was found to enhance the tunability o f BST films.38
48
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In this dissertation, in order to systematically study the effect o f strain, we
introduced different amount o f strain by varying the film thicknesses. In addition, the
sign o f strain was controlled by depositing on substrates with negative or positive
misfit. The strain was then measured by XRD and the dielectric properties were
measured using IDEs. We show experimentally and theoretically the dependence o f in
plane relative dielectric constant £n o f epitaxial BST films on the internal stresses. The
relationship between the dielectric constant and electric field is also described by
extending the Ginzburg-Landau thermodynamic model and taking into account the
effect o f electric field. In addition, a new definition o f tunability is adopted to study the
effect o f strain on tunability.
3.2
Strain in BST thin films
As will be described in Chapter 4, during a deposition, the film initially grows
coherently on the substrate. After the film reaches a critical thickness hc, misfit
dislocations start to form to relax the elastic strain. At h > hc, the film relaxes more as
its thickness increases. Assuming that no additional dislocations form during cooling
down from the growth temperature To, 59 this relaxation can be taken into account using
an “effective” substrate lattice parameter as given by 60,61:
3.1
where
3.2
49
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is the equilibrium linear dislocation density at the deposition temperature, x°M(Tc ) is
the misfit strain at To, a° (Tc ) is the substrate lattice constant at growth temperature,
and hc is the critical thickness for dislocation generation below which dislocation
formation is not feasible. Since the density o f the dislocations depends on the ratio hjh,
it is obvious that as the film thickness increases, the degree o f relief provided by misfit
dislocations also increases.
Based on the room temperature lattice parameters o f bulk BST, we have chosen
LSAT substrates (average perovskite structure, <35=0.3868 nm) to create negative strain
and MgO substrates (NaCl structure, lattice parameter <35=0.4212 nm) to create positive
strain in the BST thin films. The magnitude of the strain is controlled by varying the
film thickness. However, the film quality usually degrades as the film gets thinner,
especially on MgO substrates whose structure is not perovskite. Nevertheless, by
carefully controling the deposition parameters, we have successfully grown a series of
high quality BST thin films on both LSAT and MgO substrates with film thicknesses
ranging from
8
nm to 500 nm.
First, the crystallinity o f the BST thin films was assessed using four circle x-ray
and TEM. A typical set o f <9-2<9XRD and
<j)
scans are shown in Figure 3.3(a) and (b)
respectively. Only (OOl)-type reflections can be observed in the 0-20 scans, indicating
no second phase formation in the film; four-fold symmetry is found on all films through
(j) scans and the four {011} peaks occur at the same p angle as those o f the substrate. For
BST films on LSAT, the typical full width at half maximum (FWHM) o f rocking curve
50
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co-scans for (002) reflections is less than 0.15°, which is the resolution o f the x-ray
diffractometer. A similar investigation o f (O il) reflection reveals a larger value of 0.65°,
indicating larger in-plane mosaic spread. For BST films on MgO substrate, the FWHM
for (002) reflections are about 0.45°, while the rocking curves o f the (011) reflections
have a surprisingly small value o f FWHM o f 0.68°. These values compare favorably
100000
10000
(0
c
o
i
1000
100 -
i. .minini
F
;i
4000
3500
(A
■£ 3000
3
O 2500
O
>.
(7)
c
Qi
2000
1500
1000
500
50
100
150
200
250
300
350
Phi [degrees]
Figure 3.1
scan o f BST film on LSAT. (b) <j) scan showing four
fold symmetry.
51
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
with others reported in the literature for heteroepitaxial BST thin film s .29,62-64
Figure 3.2(a) shows a cross section TEM micrograph o f the thinnest (14 nm)
sample on MgO. Figure 3.2(b) is a selected area electron diffraction pattern (SAD)
pattern from the area in Figure 3.2(a) including both film and substrate. Together with
<{)-scans this verifies heteroepitaxy o f the films with the crystallographic relationship
given by (OOlXlOOjBsr^OOlXlOOjMgo- As expected, the crystallographic relationship
Figure 3.2 (a) TEM micrograph o f 14 nm BST film on MgO. (b) The SAD pattern
including both substrate and film, (c) High resolution image o f the interface between the
BST film and MgO substrate.
52
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
/
between LSAT and BST is also
(O O I^ IO O J b s t ^ C O O I^ IO O J l s a t -
It can be seen from
Figure 3.2(a) that even this extremely thin BST film exhibits very uniform contrast. No
obvious columnar structure can be found in the film. In addition, the high-resolution
micrograph (Figure 3.2(c)) shows a very clean interface with no indication o f a second
phase and a well-oriented epitaxial growth. These XRD and TEM results demonstrate
high crystallinity o f our BST films.
Figure 3.3 demonstrates typical strain relaxation o f the BST thin films through xray 6-26 scans o f the out o f plane lattice constant a1. We have chosen the 140 nm (solid
curve) and 14 nm (dotted curve) films on MgO as examples. A clear peak shift o f the
(002) reflection o f the film can be observed by overlapping the reference MgO peaks.
Different scales were used to counter the fact that the film (002) peaks have different
intensity due to the difference in thickness.
The out-of-plane lattice constants ctL for all films were extracted and are shown as
20000
15000
</>
c
3
O
o
J
<
5000
0
y
41
-----------------------
800
- - 14 nm
600
;
i1
1
1
/
10000
1000
1i
■
1!
1
1
1
----------11---------/
•
1
I
#
•/
•
^ K
\
\
400
<(0
*->
c
3
O
o
200
j
0
43
D e g re e
45
47
Figure 3.3 6-26X-ray diffraction spectra for two BST/MgO samples (140 nm (solid curve)
and 14 nm film (dotted curve)) Different scales were used for the convenience of
comparison.
53
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a function o f film thickness in Figure 3.4. The maximum error associated with this
measurement is 2x10“*nm. The lattice parameter o f the target (a = 0.39505 nm) is
shown as the dotted line in Figure 3.4 and is used as the unconstrained reference state. It
can be seen that the out-of-plane lattice constant aL for BST films on MgO substrate is
the smallest for the thinne st film and it gradually relaxes towards the reference state as
the film thickness increases and saturates at a value slightly above it (squares). For BST
film s
on LSAT substrate (diamonds), the trend is just the opposite: the thinnest film has
the largest a^ and it decreases as the film thicknesses increases. The theoretical values
o f the out-of-plane lattice parameter was calculated 61,65 and also plotted in Figure 3.4
(solid line for BST on MgO and dashed line for BST on LSAT). They are in excellent
agreement with the experimentally observed values. Although thicker films (/z>100 nm)
are almost completely free o f epitaxial stresses at the growth temperature To, there will
be some compressive thermal stresses that develop upon cooling due to the difference in
0.3965
_________________ ■ MgO
i
I♦ LSAT
0.396
|
0.3955
5
0.395
X 0.3945
0.394
0.3935
0
200
400
Thickness
Figure 3.4 Evolution o f ax as a function o f film thickness.
54
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600
the thermal expansion coefficients (TEC) o f the film and the substrate (10x1 O' 6 °C ~1 for
BST, 11x1c 6 °C~l for LSAT and 13.8xlO-6/°C for MgO). This is reflected in both the
experimental and the theoretical values o f the out-of-plane lattice parameter o f the film.
The strain produced by difference in TECs and lattice mismatch are opposite in signs in
the case o f BST films on MgO. For the thinner films, tensile epitaxial stresses at Tq are
only partially relaxed by the compressive thermal stresses, resulting in films under
tension at room temperature.
3.3
Zero field dielectric constant of BST films
To investigate the effect o f strain on the dielectric response in these films, the
capacitance o f BST films was measured at 1 MHz using IDEs with a dc bias from 040V. The permittivity was extracted from the capacitance data using the model outlined
b y Gevorgian .55 We extracted from the relative dielectric constant vs. applied voltage
curves the zero field value and plotted it as a function o f film thickness (Figure 3.5). For
BST films on tensile substrate MgO, as the solid line suggests, the dielectric constant
decreases rapidly with increasing thicknesses up to
100
nm. s\ i saturates for the thicker
films at a value o f about 1700. In contrast, the trend for BST films on compressive
LSAT substrates (dashed line) is just the opposite.
These opposite trends can be explained as a consequence o f the in-plane strain in
BST films using the Ginzburg-Landau thermodynamical model. The dependence o f the
dielectric constant on internal stresses can be determined from the Helmholtz free
energy o f a constrained film :61,65
55
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F ( P ) = ^ a lP 2- P E + F el(P)
3.3
where a\ = (T-Tc)/2£qC is the dielectric stiffness, Tc and C are the Curie temperature
and Curie constant, respectively, Sq is the permittivity o f free space, P is the polarization
induced by the electric field E along the [100] direction, and Fe[ is the elastic energy.
The latter is given in terms of the components o f the stress and strain tensors a; and x,
(in the Voight notation65), respectively, as:
Fe /= y (c r 1X i+cr 2x2)
3.4
since the mechanical boundary conditions require that
plane) and
01=02
04 = 05 = 0 6 = 0 (no
03=0
shear stresses). If there is no applied field, Fd = oxM since
and xi=X2=x,^ where xM = (as - a ° ) / a s is the in plane residual misfit strain.
■ MgO
♦ LSAT
2200
=
(no normal stressout-of­
1700
H
0
-
r
-
4
200
-------------------------------
400
600
Thickness
Figure 3.5 Evolution o f su as a fimction of BST film thickness. Both the solid line (BST on
MgO) and dashed line (BST on LSAT) are guide for the eyes.
56
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
However, if there is an applied field E // [LOO], x, (P) = x M + Q UP 2 and
x 2(P) = x M + Ql2P 2, where 0,y are electrostrictive coefficients. In this case, for cubic
anisotropy the elastic energy is:
Fel(P) = Cx;{ - C x „ (Qu + Qn ')P2 + A P 4
3.5
where:
2C 2
cH
—
1
C = C l l + C a - - ^ , A = - Cu(Qc, + Q n ) - ^ Q u + Q n f + 2 C l2QuQl! . 3.6
z
^11
The relative dielectric constant is thus gilven by:
's
£
=
^ ii
—
=
fo2s0—
d 2Fdp­
P=oJ
2s 0\ccl
1
C xM(Qy, + Qy2 )]
3.7
The residual in-plane strain xm in tlie film can be measured through the out of
plane lattice constant <2 X obtained from the &-20XRD pattern as follows:
xx =
ar —a0
a
2 C'12
x
C "M
— -a c
2 C,12 r as
C
3.8
Thus, both the in plane dielectric constants and in-plane strain can be obtained
through direct measurement and they shaould follow a relationship described by
Equation (3.7). We plot the 1/^n versus th e in-plane strain in Figure 3.6 for samples in
both substrates. Two straight fitting lines indicate that Equation (3.7) correctly predicts
the trend observed experimentally (for topical perovskite oxides such as PbTiC>3 and
BaTiC>3, C , Qn+Qn, and a\ above Tc atre positive). They have different slopes and
intersections with the y-axis because o f tthe different compositions: BST 50/50 is
deposited on MgO substrates while B S T 60/40 for LSAT substrates. However, both
57
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curves have shifted towards lower dielectric constant from bulk values, indicating a
systematic decrease in the dielectric constant. W e attribute the difference to the defects
in the BST films, as will be discussed in Chapter 4.
3.4
T u n ab ility o f BST films
For applications in frequency-agile microwave electronic components the
tunability o f BST films is a very important issue. Equation (3.7) only calculates the
dielectric constant at zero field and does not show how the dielectric constant changes
with electric field and ultimately, the relationship between strain and tunability.
Generally, tunability is defined as ^n(max)- £\ i (m in)]/^ i(max) or Ai(OV)£\ i(m in)]/a i( 0 V ) . 2 1’29,6i £n(max)/£n(min) is also frequently used by some authors .58
0 .9
■
♦
0.8
0 .7
BST on MgO
BST on LSAT
Linear fit on MgO
Linear fit on LSAT
CO
O
0.6
CO
0 .5 0 .4 -0 .4 -0 .2 0 .0
0 .2
0 .4
0 .6
0 .8
1.0
xMMisfit Strain (%)
Figure 3.6 l /s u as a function o f strain. The straight lines are the fittings according to
Equation 3.7
58
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Obviously the results calculated by these definitions largely depend on the amount o f
applied field and the exact configuration o f the electrodes used. Thus, a universally
comparable definition o f tunability may be desirable to carry out meaningful
comparisons.
Equation (3.3) only considers the zero field dielectric constant and does not take
into account the nonlinearity o f the BST films by dropping the fourth power term and
above. By taking into account the fourth order term, we can describe the relation
between the dielectric constant and the electric field. In this case the equation (3.3)
becomes
F (P ) =
+ i a 2P 4 - PE + C x % - C xu (Qu + Ql2)P 2 + A P 4
3.9
rearranging, we get:
F ( P ) = j o P 2 + j /? P 4 - P £ + C x ; , ,
3.10
where a = or, —2C xM(Qx, + Ql2), p = a 2 + 4/1.
From dF/dP=0, we get: aPQ(E) + PP03(E) —E = 0 . If P is small, P0(E) » E l a ,
so,
S r£ 0 = £ u
dP
1
1
-------= ------------------- 1--------- ~ --------------- -----------
dE
cc + 3PP2(E)
a + 2J _ E *
a2
3.11
and the electric-field derivative o f the dielectric constant can be described by:
deu d 2P
dE dE 1
~6PP0(E)
[ a + i/3 P ; ( E ) f ~ (q, + 3
312
a2
59
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ds
We plot the S\ \ and — — versus the electric field from Equations (3.11) and (3.12)
dE
in Figure 3.7(a), and a set o f typical experimental data from one o f the BST films in
Figure 3.7(b). It can be seen from Figure 3.7(a) and (b) that except for the small
hysteresis in the experimental data, the curves predicted by theory and the experimental
curves are extremely alike, indicating the validity o f our calculations. From Equation
ds
(3.12) and Figure 3.7, we notice that the nonlinearity — — is also a function of the
dE
electric field. So, in order to compare the tunability from different samples, we define
ds
d “s
the tunability as ( — —)max- By se ttin g
7 - = 0, we arrive at the equation:
dE
dE~
,
' dS“ 'I
y dE max
3.13
a^ 5/1
The in plane residual strain xm is included in a as a = or, —2C x M(Qx, + QX1). We
have determined the value o f a through fittings in Figure 3.6. We also determined an
approximate value of ft = a 2 -f-4A « 5.65xl09 J-m^CT* for BST (60/40) and 3.35xl0 9
J-nr^C "4 for BST (50/50). (The value o f ax is not available for BST, neither is it for
SrTiOa, so we used the value for BaTiC>3 (<22=- 5 .5 x l 0 8J-m 5-C^) in our estimation. The
value o f A for composition (60:40) is 1.55xl0 9 J-m5 -C’4 and that for (50:50) is 0.97xl0 9
J-m^CT4 approximately.66 Therefore, /?60:40 is ~ 5.65xl09 J-m ^C 4 and >650:50 is ~
3.35xl0 9 J-m5-C^) We plot the conventional tunability [su(max)~ sn(m in)] /su (max)]
versus the strain in Figure 3.8(a) and both theory and experimental
r Ubu
de '
k 9E
60
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curves
max
/
/
^
2000
Y
7
60
40
--------- d s / d E
\
\
x
~\
/
20
\
\
a. 1500
\
LLi
0
\
\
\
\
y
A
x- '
-20
-40
-60
-
1000^
WVIcm)
80
a
de/dE
3000
•
500
-60.0 -40.0 -20.0
0.0
20.0
-80
60.0
40.0
E Field (kV/cm)
60
^
\
o" ^ y / I/
/
/ / v '
/ /
'
/ /
v \
/ /
' t
/ /
' '
^ v
8
----------- d s / d E .
\
45
30
15
\ \
\ \
\A
Y\
0
y
-1 5
-
-
1100
1000
n r*
-
^
N^X,
-
-
-26.7
-13.3
0.0
13.3
1/(kV/cm)
b
26.7
-30
-45
de/dE
1800
1700
1600
1500o 140013
Q. 1300LU
1200
-60
E Field (kV/cm)
ds
Figure 3.7 (a) Theoretical and (b) experimental Sn and —r f versus
dE
electric field curve
61
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
BST 50/50 on MgO
BST 60/40 on LSAT
O
tension
com pression
-0.6
-0.4
-0.2
0.0
0.2
0.4
Misfit Strain, x
(% )
■
•
-0.6 -0.4 -0.2 0.0
0.2
0.6
0.8
BST 50/50 on MgO
BST 60/40 on LSAT
Theory fit for LSAT
Theory fit for MgO
0.4
0.6
0.8
1.0
Misfit Strain, xM(% )
Figure 3.8 (a) Conventional tunability as a function o f compressive and
ds
tensile misfit strain. The dashed lines are guides to the eyes, (b) ( — —)maxas a
dE
function o f misfit strain.
62
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versus strata in Figure 3.8(b). Several points o f BST film on MgO substrate enter the
compressive strain region because o f the difference in thermal expansion coefficient as
we mentioned above. It can be seen that Figure 3.8(b) is very different from Figure
3.8(a), especially in the tensile strain side. The conventional tunability decreases with
increasing strain regardless o f the sign o f the strain, as the dashed lines in Figure 3.8a
suggest. In contrast,
r Ubu
ds N
K 3E
more or less follows the trend described by equation
(3.13). However, obvious deviation from the theory curves given by equation (3.13) can
be observed. This is because in this treatment we are only considering the variation o f
strain in the film by the change o f film thickness. However, the defects present in the
films and possibly a clamping effect from the substrate could cause this deviation. Also,
some modification to the model is needed to take into account the non-uniform electric
field o f the IDEs, which is in progress and will be reported in a later publication.
There is no obvious trend in the dielectric loss value with the residual strain,
fluctuating around 0.02. It appears that the losses are relatively insensitive to strain/film
thickness and it is probably determined by other mechanisms.
3.5
Sum m ary
In summary, a series o f heteroepitaxial BST thin films o f thicknesses varying from
8
nm to 500 nm were prepared on LSAT and MgO substrates to produce films with
systematically varying in-plane stresses. Four-circle XRD and TEM analysis showed
high-quality and high epitaxial relationship of the films. The dielectric constant Sj i
increases with increasing in plane tensile stress and is in good agreement with the
63
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theoretically predicted behavior. We also derived the relationship between the dielectric
constant and electric field using thermodynamic theory. In addition, we define the
f ds ^ and the experimental data was analyzed is in good agreement
tunability as — —
v\ dE s max
with this new definition.
64
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Chapter 4 Role o f defects on the dielectric properties o f BST thin films
4.1
Introduction
Strain and defects are the two primary causes for the degradation o f the dielectric
properties o f BST thin films. We have presented a systematical study o f the effect of
strain in Chapter 3. In this chapter, we will discuss the effect o f defects on the dielectric
properties o f BST thin films.
There are several types o f defects in BST films. Zero dimensional (0-D) defects
include vacancies and interstitials, among which oxygen vacancies are the most likely
ones to be present in BST films. One dimension defects are primarily dislocations,
which include threading dislocations and misfit dislocations. Since misfit dislocations
are at the interface, they usually do not contribute to the dielectric properties o f BST
films. However, they are closely related to the morphology and density o f threading
dislocations, which do affect the dielectric properties. We w ill discuss the effect o f
threading dislocations on the dielectric properties of BST films and their formation and
observation in this chapter. In thin films epitaxially grown on closely matched
substrates, it is unlikely to have large angle grain boundaries in the film. However, other
types o f two dimensional (2-D) defects such as stacking faults and small angle subgrain
boundaries are very often seen in epitaxial oxide films. Antiphase domain boundaries
(ADB) are a special type o f stacking fault. They form when two domains with a relative
lattice shift, which is not an integer times o f the unit cell, meet with each other. They
are o f particular importance for the dielectric properties o f BST films and will be
discussed in detail in this chapter. Three dimensional (3-D) volume defects such as
65
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second phases and voids are rarely found in films deposited in optimized conditions. In
fact we did not find any o f them in our BST films and therefore they are not discussed.
We have chosen annealing as the primary method for our study o f the effect o f
defects in BST thin films. It is observed by many research groups that annealing leads
77
67
to partial recovery in the dielectric properties o f BST films. ’ ’
AC
One o f the examples
is shown in Figure 4.1. As can be seen from Figure 4.1, upon annealing in O2 at 950°C
for 14 hours, both the dielectric constant and tunability increased by about 30%,
recovering towards the values o f bulk BST. Although there is a few reports that
attribute this enhancement o f dielectric properties to the relief o f micro stress in the
BST thin films,69 XRD analysis o f our BST films did not show an appreciable change o f
the lattice constants upon annealing, indicating that annealing did not change the macro
BST-193 (120 nm BSTO / LSAT)
2000
-
- - As-deposited
— Annealed
,
18001600-
q
q
.
O
14001200
-
1000
-
800
-40
0
-20
20
40
Voltage [Volts]
Figure 4.1 The effect of oxygen annealing on the dielectric
constant of a typical BST thin film
66
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stress state o f the BST thin films. Thus, the increase o f dielectric properties upon
annealing should due to a change (reduction) o f defects present in the BST films.
Therefore, annealing has provided an effective means for us to study the effect o f
defects on the dielectric properties o f BST films. By comparing the microstructure o f
the as deposited and annealed film, we should be able to obtain some insight on the role
o f defects on the dielectric properties o f BST thin films. In the literature, the recovery o f
dielectric properties o f BST thin films is generally attributed to a reduction o f defects in
BST thin films, including the filling o f oxygen vacancies.2 4 ,70 and the reduction o f
grain/subgrain boundaries.39,41 However, the role or contribution o f specific defects in
the recovery o f the dielectric properties is not clear. In this chapter, w e will discuss the
role o f defects of all dimensionality, including oxygen vacancies (0-D), dislocations (1D) and antiphase domain boundaries (ADB) and subgrain boundaries (2-D).
Table 4.1 summarizes the methods used in this dissertation to study these defects.
For oxygen vacancies, since they are difficult to observe directly, we compare samples
annealed in different gas ambient; for dislocations, TEM observations were used to
compare their density and morphology before and after annealing; for ADBs and
subgrain boundaries, we notice that these 2-D defects are primarily perpendicular to the
interface in thin films and thus compare the effect of annealing on the in plane and out
o f plane dielectric properties. We show some evidences that oxygen vacancies do not
play a major role in the recovery o f dielectric properties o f BST thin films. In contrast,
the decrease o f defects such as dislocations and ADBs and the relief o f local strain
associated with them are dominant in the recovery process.
67
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Table 4.1 Methods used in the study o f role o f defects in BST films
4.2
Defect
Type
Studied
work
0-D
Oxygen vacancies
Annealing
ambient
1-D
Threading
and
misfit dislocations
TEM comparison o f before and
after annealing
2-D
Grain boundaries
Comparison o f out o f plane and
in-plane dielectric properties
3-D
Not found
TEM
in
this
Study method
in
different
gas
Role o f oxygen vacancies
To determine the effect o f oxygen vacancies in the process o f annealing recovery,
we compare the dielectric properties o f two identical samples annealed under different
annealing ambient o f N 2 and O 2 . The two samples were prepared by depositing a 140
nm BST film on LSAT substrate and then cutting it into two halves. One h a lf was
annealed in O 2 , and the other in N 2 , at 950 °C for 14 hours. The
611
as a function o f
voltage at 1 MHz for both halves before and after annealing is shown in Figure 4.2. The
left side o f Figure 4.2 represents the results from O2 annealing, the dotted line for the as
deposited sample and the dashed line is for the annealed sample. The same notation was
used in the right side for the N 2 annealed sample. As expected, the oxygen annealed
sample shows improved dielectric constant and tunability upon annealing. However, the
sample annealed in N 2 showed the same improvement and their loops are strikingly
identical. N 2 is generally considered inert under our annealing conditions. Therefore, if
68
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the filling o f oxygen vacancies were the primary reason for the recovery o f the
dielectric constant, annealing in N 2 should not enhance the dielectric properties or at
least would enhance them much less than annealing in O 2 does. This suggests that, for
the growth conditions used in this experiment (800 °C, 120 mTorr), oxygen vacancies
may not give rise to a measurable improvement in the recovery process o f the dielectric
properties upon annealing. To exclude the possibility that N 2 may have reacted with the
BST film at the annealing temperature, we performed another annealing experiment in
Ar (instead o f N 2) and O 2 . These samples show similar results to those shown in Fig. 1.
Therefore, some other factor besides the filling o f oxygen vacancies may have played a
major role in the recovery o f dielectric properties upon annealing.
Upon annealing in N 2, it is possible that oxygen was actually “pulled out” o f the
film because o f the elevated temperature and essentially zero O 2 partial pressure. To
2800
2600
2400
As dep.-» N2 Ann-> O2 Ann
As dep.-> O2 Ann-» O2 Ann
- - - As-dep
— — Ann in 0 2
— — Ann in 0 2 again
lrA A
/ nY^X
- - - As-dep
— — Ann in N,
Ann in 0 2 again
-2800
-2600
-2400
-2200
2200
j - 2000
-2000 c
M
-1800 |
-1600 [g-
1800-
0 -1 6 0 0 1400-
-1400
1200 -
-1200
-1000
1000 -
-800
800-40
-20
0
20
40
-40
Voltage (V)
-20
0
20
40
Voltage (V)
Figure 4.2 811 as function o f voltage for two halves o f one BST film annealed in different
gas ambient. The dotted lines represent the as-deposited samples. The sample on the left
side was first annealed in O 2 (dashed line) for 14 hours at 950 °C and then annealed again
in O 2 (solid line) for another 14 hours at 950°C. The sample on the right side was first
annealed in N 2 (dashed line) and then annealed in O 2 (solid line). The annealing conditions
are the same as for the left side.
69
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examine this possibility, we re-annealed the N 2 annealed sample at 950 °C but this time
under O 2 for another 14 hours to investigate if the oxygen vacancies would get refilled.
As the solid line in the right part o f Figure 4.2shows, the dielectric constant as well as
the tunability both increased by a small but noticeable amount. However, we do not
think this increase is caused by refilling o f oxygen vacancies because re-annealing the
O 2 annealed sample under the same condition in O 2 gives rise to similar improvement of
the dielectric constant, as can be seen from the solid line in the left part o f Figure 4.2.
We believe that once a sample has been annealed in O 2 at 950 °C for 14 hours, all the
oxygen vacancies that can be filled upon the annealing conditions have been filled.
Since the films were only 140 nm thick, any further annealing will not appreciably
decrease the density o f oxygen vacancies anymore. The improvement o f the dielectric
properties therefore should result primarily from other factors. (The BST films with N 2
followed by O2 annealing appear to have a slightly higher dielectric constant than the
one with O 2 followed by O 2 annealing. Further investigation is needed to understand
this small difference) Therefore, we can safely draw this conclusion: under our growth
conditions, oxygen vacancies do not play a very important role in the recovery o f the
dielectric properties o f BST films. It should also be mentioned that we have observed
that the loss, tan8, is relatively insensitive to annealing, fluctuating around a value o f
0.025.
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4.3
Role o f dislocations
Having excluded the filling o f oxygen vacancies (O-dimensional defects) as the
primary reason for the improvement o f the dielectric properties upon annealing, we
proceed to study the change o f 1-dimesional defects, mainly dislocations, upon
annealing.
Usually in an epitaxial perovskite film on a perovskite substrate, the dislocation
morphology can be described by the schematic shown in Figure 4.3. M isfit dislocations
form at the surface o f the film during the deposition and then glide to the interface
form ing two threading segments and one misfit segment. The misfit segment then
extends along <100> directions. If the dislocation is stopped before m eeting with other
misfit dislocations so that the threading segments cannot be annihilated through a
dislocation reaction, the threading segments will remain in the film, forming threading
dislocations. We will start this chapter with TEM characterizations o f the misfit and
threading dislocations and then discuss the effect o f these dislocation on the dielectric
properties o f BST thin films.
Threading segment
M isfit segment
4 m Interface
Substrate
Figure 4.3 Schematic o f dislocations in a perovskite epitaxial system.
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4.3.1
TEM characterization o f dislocations in BST films on LSAT substrate
4.3.1.1 Introduction
Generation o f misfit dislocations at the interface between film and substrate is the
primary strain relaxation mechanism in thin film heteroepitaxial growth. It is generally
recognized that during growth, the film initially grows coherently on the substrate.
After the film reaches a critical thickness, misfit dislocations form to relax the elastic
strain.71,72 Misfit dislocations play a very important role on the properties o f
semiconductor heteroepitaxial structures and have been extensively studied in these
systems.73'76
M any transmission electron microscopy (TEM) studies 41*56,77'83 concerning
misfit dislocations in epitaxial ferroelectric films have been performed. However, in
most o f those studies,41,56,79'83 only cross sectional TEM microscopy was used to
characterize the misfit dislocations. In these studies, the spacing between dislocations is
estimated by calculating the distance between dislocations cores in cross sectional
images; the line direction determined by judging the size o f the dislocation cores along
different zone axis and the burgers vector b determined by the closure failure o f a
Burgers circuit drawn around the dislocation cores in high resolution lattice images.
However, conventional plan view TEM has many advantages over cross sectional high
resolution transmission electron microscopy (HRTEM) in the analysis o f misfit
dislocations by providing a 2-D projection o f the dislocation network and exact
determination o f b using the g.b criterion 47
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The difficulties o f using conventional TEM to analyze misfit dislocations in
ferroelectric oxides arise from two reasons:
1. Practically, ceramic TEM samples are usually made by ion milling at the final
stage o f sample preparation, which causes serious bending in the thin area of the
sample. The bending o f the sample results in difficulties in plan view TEM observation
that require precise tilting o f the sample to acquire different two beam conditions. This
bending effect, even though seldom mentioned,78 is a very important concern in plan
view TEM since the dislocation contrast strongly depends on the excitation error, s.
2. Theoretically, as misfit dislocations get closer together (due to larger lattice
mismatch, overlapping strain fields cause difficulties in distinguishing individual
dislocations. The misfit between film and substrate in the heteroepitaxy of perovskite
structures is usually large (>1 %). This results in small spacing between individual
dislocations in the misfit dislocations network o f fully relaxed films. The spacing
between dislocations along one direction in a fully relaxed film can be expressed as:
K
f
K
a film
a sub
a sub
where be is the edge component o f the Burgers vector o f the misfit dislocation in the
plane o f the interface,/ is the misfit between substrate and film and af,im and aSUb are the
film and substrate lattice constants, respectively.
It is obvious that when the misfit gets larger, the spacing D becomes smaller
because be is usually fixed. As dislocations get closer together, their strain fields
overlap, creating difficulties in distinguishing individual dislocations. Tholen84 proved
73
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that for two beam dark field imaging conditions where the excitation error, 5 = 0, screw
dislocation networks at a small angle rotation grain boundary w ith a mesh size
(dislocation separation) < 0.3
can not be distinguished from Moire patterns. Here £g
is the extinction distance for the g reflection used to obtain the dark field image.
It should be m entioned that this criterion is not exactly valid for perovskite
heteroepitaxy. First o f all, the dislocation type in these systems is usually edge instead
o f screw. Secondly, the incident electron goes through two different layers, which
usually have different values o f gg. However, one can still obtain an idea o f the
minimum m esh size that can be distinguished according to the 0 .3 ^ criterion. To
simplify the situation o f two different layers, the values o f ^ o f a typical perovskite
structure, namely, STO is used.85 The data is shown in Table 4.2 for several most often
used g vectors.
Table 4.2 Reciprocal (g) and real (d) interplanar distances
and extinction distances (^g) for STO
Space-group : P m 3 m; Accelerating voltage [kV] : 300; W avelength [pm] : 1.9688
(hkl)
00 1
10 1
111
002
102
1 12
202
g [nm-1]
2.5641
3.6262
4.4412
5.1282
5.7335
6.2807
7.2524
d [nm]
0.3900
0.2758
0.2252
0.1950
0.1744
0.1592
0.1379
^e [nm]
5350.3975
78.5912
113.9706
59.0343
8938.4238
142.5206
86.8332
multiplicity
6
12
8
6
24
24
12
It can be seen from Table 4.2 that for an accelerating voltage o f 300kV, the three
most often used reflections 101, 002 and 202 have extinction distances around 70 nm.
74
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So, according to the 0.3^g criterion, mesh sizes less than 20 nm cannot be distinguished
from Moire fringes using conventional two beam dark field method. This means that the
largest misfit allowed for two beam dark field observation is around 2%, assuming full
relaxation o f the film and a Burgers vector o f —0.4 nm, which are reasonable for most o f
the perovskite films.
Stemmer78 showed a very clear misfit dislocation network at the interface between
PbTiC>3 (PTO) and STO using plan view TEM images. The misfit between film and
substrate in that system at the growth temperature is 0.6 % and the observed dislocation
spacing is around 200 nm. For PTO and STO films on MgO, which have 8.1 % and 8 %
misfit, respectively, the author did not show misfit dislocations in plan view TEM,
stating that it is ‘difficult to achieve’ and ‘did not provide useful information.’ Suzuki77
showed the misfit dislocation network between BaTi0 3 and STO, which have a 2.17 %
misfit. The contrast of the dislocations, however, is very diffuse and sim ilar to Moire
fringes. Also, bright field was used instead o f dark field. (We found that when
dislocations get closer, it is easier to distinguish them using bright field instead o f dark
field. This phenomenon was also mentioned by Tholen , though not proved.)
Therefore, our estimate o f / « 2 % as the maximum misfit for visibility o f dislocations
using dark field is in good agreement with experimental observations in perovskite
heteroepitaxial systems.
In this dissertation, we present TEM studies o f misfit dislocation networks in
epitaxial BST films on LSAT substrates
misfit in this system
(<z b s t
= 0.3965nm,
<2l s a t =
0.3965nm). The
2.4 % and assuming full strain relaxation gives rise to misfit
dislocations separated by —17 nm. Both conventional plan view TEM and HRTEM o f
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cross section samples were used to show the morphology o f the misfit dislocations.
Also we show that in order to resolve dislocation networks w hen the misfit is larger
than 2 %, weak beam technique and a reduced accelerating voltage are preferred.
4.3.1.2 Cross section imaging of misfit dislocations
Figure 4.4(a) and (b) are cross section dark field images o f the 26 nm sample
viewed (a) along [100] direction and (b) [110] direction. For both images the g vector
used was (002). Dislocation cores can be found at the film/substrate interfaces in both
(a) and (b), indicating that the film has relaxed by forming dislocations. The average
spacing o f the dislocation cores is about 17 nm, corresponding to almost full relaxation.
It can be seen that when viewed along the [110] direction (Figure 4.4(b)), the
dislocation cores are not as clearly defined as when they are viewed along the [100]
direction (Figure 4.4(a)). Since the most favorable directions for misfit dislocations in
perovskite system are < 1 10> and <100>, Figure 4.4(a) and (b) suggest that the misfit
dislocations are primarily along <100> directions.
Diffraction patterns taken along both zones (Figure 4.5) show the splitting o f the
substrate and film spots, confirming that the film is relaxed. Detailed measurement o f
the splitting shows that the film is very close to full relaxation. To determine the
Burgers vector o f the misfit dislocations, we began with the popular HREM method.
Figure 4.6 and Figure 4.7 are two HREM images taken from the interface and along the
[100] direction o f the 26 nm film. Both of the closure failures indicate that the Burgers
vectors are
[0 1 0 ]b st-
However, it is clear that not all misfit dislocations are along the
[100] direction (while Figure 4.6 shows an ‘edge on’ dislocation, the dislocation in
76
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Figure 4.7 is clearly not parallel to the [100] beam, direction). Whem the dislocation is
inclined with respect to the beam direction, it appears to split w hen. viewed from the
bottom o f the picture (i.e., along [001] direction in the picture). Thiis splitting was
mentioned by Gao83 as dissociation o f misfit dislocations. Howeveir, we believe that this
apparent splitting in Figure 4.7 is simply caused by the fact that the= dislocations are
inclined. This was confirmed by plan view TEM as shown below.
HREM images taken along the [110] direction (Figure 4.8 a n d Figure 4.9) also
show both inclined (Figure 4.8) and edge on (Figure 4.9) misfit dislocations. The
closure failures give Burgers vectors o f Vs[l 1 0]ssTfor both dislocations, which is the
projection o f [100] b s t along the [110] direction. Most o f the cores th a t we observed are
edge on when viewed along [100] direction and inclined when view ed along [110]
5»0rim
Figure 4.4 Cross section dark field images o f the 26 nm samgjle viewed along
(a) [100] direction and (b) [110] direction. In both images tb»e g vector used
was (002). Dislocation cores can be found at the interface in Fboth (a) and (b),
however, the dislocation cores in (b) are not as clearly defnned as in (a),
indicating that the dislocations are edge on in (a) and inclined in (b).
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direction. Therefore, we may draw the conclusion that most o f them, are along [100].
However, HREM can only examine a relatively small area o f the sample, so it is hard to
determine the actual ratio between dislocations along [110] and those along [100]. And
yet several other very important questions remain:
•
Do the two different dislocation directions correspond to dislocations that nucleate
independently or to dislocations that change direction?
•
Do all misfit dislocations have the same Burgers vector? It is obvious that if only
Figure 4.9 is presented, one may draw the conclusion that the m isfit dislocations
H■
HH
■H
DHH
■ ■
HH
■
■■
Figure 4.5 Diffraction patterns taken in areas including both the
film and substrate o f the 26 nm sample. The zone axes are (a) [100],
and (b) [110], The splitting o f the substrate and film spots indicates
that the film is relaxed.
78
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Figure 4.6 HREM image from the 26 nm sample viewed along [100]. The
closure failure indicates that the burgers vector is [010]gST-
Figure 4.7 HREM image from the 26 nm sample viewed along [100] direction.
The dislocation at the interface is not edge-on, causing extended distortion along
the interface. However, closure failure indicates a Burgers vector o f [010] which is
the same as in Figure 4.6.
79
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Figure 4.8 HREM image from the interface o f the 26 nm sample viewed along
the [110] direction, indicating that the dislocation is inclined. The closure
failure gives a projected burgers vector o f lA [l I0 ]b S T
*«
f 4'J
* * * a * # * a # f #. $ f s
S*
* f t ? -U j
", 4 j * 4 i $ * * % ■
<i
i •" 5 g '
* * 5 **»••#**§*##**$***$•> ■* | f
Figure 4.9 HREM image from the interface o f the 26 nm sample viewed along
[110]. Very clear core structure can be seen, indicating that this particular
dislocation (or this portion of the dislocation) is along the [110] direction. It
also gives a projected Burgers vector o f 14[1 1 0].
80
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are along [110] with Burgers vector o f 'A[ 110]. However, Figure 4.6 shows that
some o f the dislocations are along [100] with b=[010].
•
How long are the m isfit segments?
4.3.1.3 Plan view imaging o f misfit dislocations
To answer these questions, plan view TEM has to be performed. Figure 4.10 is a
dark field plan view image o f the 26 nm sample including the interface. The g vector is
(110). Since the film is relaxed, we would expect to see a square network o f
dislocations. The lattice parameter for bulk BST is 0.3965 nm and that o f LSAT is
0.3868 nm resulting in a lattice mismatch o f about 2.44 % and —17 nm spacing between
m isfit dislocations if we assume that the film is very close to full relaxation. However,
only Moire fringes can be observed in the region containing both film and substrate.
5 0 n m
Figure 4.10 (110) dark field plan view image o f the 26nm sample including
the interface. Only Moire fringes can be observed. The operating voltage is
300kV.
81
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The region at the edge (below the dashed line) does not show Moire fringes because it
only contains film since the substrate was removed during the sample preparation
process. Some threading dislocations can be found in the area where only the film is
present but no misfit dislocations can be found in the area where both film and substrate
are viewed. Different two beam conditions were used and all o f them failed to show
dislocations. The appearance o f M oire fringes indicates that the film has relaxed and
therefore misfit dislocation must have formed at the interface. However, they do not
show up in regular dark field imaging because their strain fields overlap when they are
close to each other and because their contrast is masked by that o f the Moire fringes.
Thus, they become indistinguishable from Moire fringes. Notice that Moire fringes will
appear regardless o f the interface structure, i.e., with or without misfit dislocations, as
long as the film and substrate have different lattice parameters. In this case the film and
substrate are in contact, consequently misfit dislocations have to form. From the Moire
fringes and the cross section results we can draw the conclusion that the dislocations are
present, however, strong beam dark field imaging is not the best way to image them.
The Tholen (1970) 0.3
criterion tells us that if the mesh size (dislocation
separation) is > 0.3^g, then the dislocations can be distinguished. However, since the
mesh size is fixed for a given value o f lattice mismatch, the only parameter that can be
changed is the extinction distance <|g- We know that
depends on the lattice parameters
o f the material, the atomic numbers o f the elements in the unit cell, and the acceleration
voltage used. Namely,
C
_
tzVc
cos 0bl
82
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A o
where Vc is the volume o f the unit cell, 0b the Bragg angle for the reflection g, /L the
wavelength o f the electrons and Fs the structure factor for reflection g.
Since gg is inversely proportional to the wavelength o f the electrons which is in
turn inversely proportional to the acceleration voltage, lowering the voltage used to
image the sample decreases £g. However, the electrons must have enough energy to go
through a relatively thick sample (we have to include both film and substrate to see the
misfit dislocations). Therefore, the voltage can not be too low. With this requirement in
mind, a voltage o f 100 kV was chosen as the optimum voltage. Figure 4.11 is a strong
beam dark field image of the 26 nm sample with accelerating voltage o f lOOkV.
Unfortunately, again only Moire fringes and no misfit dislocations can be seen.
Table 4.3 shows the extinction distances for several (hkl) reflections in BST for
both 100 and 300 kV electrons. It can be seen from Table 4.2 that a lower voltage o f
Figure 4.11 (200) dark field plan view image o f the 26nm sample using an
operating voltage of lOOkV. Still only Moire fringes can be observed.
83
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100 kV reduces the
for each reflection. The smallest one is for {002} reflections
(about 40 nm). This value is already lower than the required 50 nm (D/0.3 = 17 nm/0.3
« 50 nm). However, the (200) dark field image in Figure 4.11 also shows only Moire
fringes even though it was taken at 100 kV. It seems that the visibility criterion becomes
stricter in the case o f misfit dislocations. The reason for this m ay be that misfit
dislocations in these materials are edge dislocations and they have different and usually
larger strain fields than screw dislocations.
T able 4.3 Extinction distances of BST for 300kV a n d lOOkV :
(h,k,l)
001
110
111
002
102
112
220
221
003
103
113
222
g
[nm '1]
2.5221
3.5667
4.3684
5.0441
5.6395
6.1778
7.1335
7.5662
7.5662
7.9755
8.3648
8.7367
d
[nm]
0.3965
0.2804
0.2289
0.1983
0.1773
0.1619
0.1402
0.1322
0.1322
0.1254
0.1195
0.1145
[nm]
300 kV
363.8080
69.9264
100.8349
56.9231
889.6525
126.7104
85.5176
1319.8497
1319.8497
178.2327
208.1140
113.7045
[nm]
lOOkV
256.8775
49.3733
71.1964
40.1913
628.1459
89.4642
60.3789
931.8611
931.8611
125.8377
146.9337
80.2776
Multip­
licity
6
12
8
6
24
24
12
24
6
24
24
8
It is well known that w eak beam imaging technique can greatly enhance the
resolution o f diffraction contrast images. This technique has been w idely used since the
70’s to study dense dislocations and dissociation o f dislocations (Jenkins 1972,
Cockayne et al. 1971). However this technique is not used very often to study misfit
dislocations in heteroepitaxial oxide films because the overall intensity o f the image is
84
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low. This is particularly important in oxide materials containing La, Pb or other heavy
elements where absorption o f electrons could be very high. Under weak beam
condition, the effective extinction distance is given by,
1
s~ +
f
"\2
I 1
4.3
where w = s%g, and s is the excitation error.
So, if s is sufficiently large, ^ c a n be small enough to resolve the dense m isfit
dislocations.
In principle, a weak beam image does not depend on the operating voltage.
However, a practical concern is that at 300 kV the Ewald sphere is much flatter than at
100 kV. This has several consequences:
1.
Under the sam eg-3g condition needed in w eak beam imaging, using 100 kV gives
a much larger value o f s than using 300 kV.
2.
Frequently, if the (hkt) reflection is strong the systematic row o f (2h2k2l) and
(3h3k3[) reflections are also reasonably strongly excited. This situation is
accentuated at accelerating voltages > 200 kV.
3.
For the same sample thickness, it is harder to determine where the Kikuchi line
lies when using higher voltage.
These reasons make voltages >200 kV not ideal operating voltages for weak beam
observations.
Figure 4.12 shows two plan view weak beam images o f the 26 nm sample
obtained using 100 kV electrons. The reflections used are (a) (200) and (b) (020).
85
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Typical g-3g conditions were used to obtain these images. Figure 4.13 shows a
schematic o f the g-3g condition and the deviation parameter, s, which is given by:
s = l/2(n -l)|g| 2X,
4.4
where g is the reflection used and ng is where the Kikuchi line crosses this systematic
row o f reflections. For our case ^.=3.7015 pm, g=5.13 nm '1 and n=3. This gives a value
o f s o f about 0.1 nm '1. It can be seen (Figure 4.12) that under this condition dislocations
can be clearly distinguished. The dislocations, however, do not show sharp contrast as
we would expect. This is caused by the overlap o f the strain fields from misfit
dislocation in the network and the superposition o f contrast associated with dislocations
with that from Moire fringes. The intensity o f the Moire fringes is directly proportional
to the intensity o f the reflections used in forming the weak beam image. Thus, as the
value o f s increases the intensity o f Moire fringes decreases.
Because o f the diffuse contrast o f the dislocations, the images in Figure 4.12 look
similar to Moire fringes. However, if we compare Figure 4.11 and Figure 4.12, we will
notice that the contrast for dislocations (Figure 4.12) is still much sharper than that o f
the M oire fringes (Figure 4.11), and most importantly, they have different average
spacing. The spacing o f Moire fringes dCmis given by:
1
(S'cm |
1
|Si
Si |
1
1
Si
Si
1
1
Si
Si
^2^1
d \-d x
86
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Figure 4.12 (a) (200) and (b) (020) weak beam plan view images obtained
using 100 kV.
87
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Figure 4.13 Schematic o f the g-3g weak beam condition.
where g i, g i and d\, di are the magnitude o f the reciprocal lattice vectors o f film and
substrate and their corresponding interplanar distance i.e., g, = 1j d x, g 2 = l/d 2 , and
Stm
Si
Si
However, the spacing for misfit dislocations in a fully relaxed film is:
b
b
f
a film
a sub
^
b • a sub
film
^ sub
a sub
It can be seen from the above equations that the spacing o f Moire fringes depends
on the reflections used while that o f misfit dislocation does not. Also, the direction o f
the Moire fringes is along g , —g, while the direction o f the dislocations is independent
o f the g vectors used to obtain the image. If a reflection o f {200} type is used to obtain
the image and full relaxation o f the film and Burgers vector o f the type o f <100> are
assumed, the spacing o f the Moire fringes should be half o f that o f the misfit
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dislocations. This is exactly the case in Figure 4.11 and Figure 4.12 where the spacing
o f the observed contrast are about 8 nm and 17 nm, respectively.
Because the dislocations and Moire fringes are not regularly spaced, it is relatively
difficult to determine their average spacing. Therefore, Fast Fourier Transformation
(FFT) was obtained from the images shown in Figure 4.11 and Figure 4.12(a) to get the
average spacing. Figure 4.14 shows the results. Even though only diffuse spots were
obtained due to the irregularity of Moire fringe and dislocations, it can still be seen that
the distance between the two spots in the FFT image from Moire fringes is twice that of
the dislocations. Therefore, the spacing between Moire fringes is about h alf o f that of
the dislocations. To get a more accurate average spacing a standard grid was used to
give the camera length and an intensity profile was used to give the average position of
the spots in the FFT image. The results show that the average spacing o f the Moire
fringes (Figure 4.11) is about 8.2 nm and that o f the dislocations (Figure 4.12) is about
a
b
Figure 4.14 FFT from (a) Moire fringes in Figure 4.11 and (b) dislocations in
Figure 4.12(a). It can be seen that the distance between the two spots in the
FFT o f Moire fringes is twice as that o f the dislocations. This indicates that the
spacing between Moire fringes is half o f that o f the dislocations.
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16.8 nm . Therefore, the use o f the weak beam imaging technique with g-3g condition
makes it possible to clearly distinguish the misfit dislocations from the Moire fringes.
Figure 4.15 is a (1 1 0) weak beam image with a g-3g condition. The excitation
error is about 0.05 nm '1. It can be seen that because o f the smaller value o f s (compared
to (200) weak beam), strong Moire fringe contrast is present and the dislocation
netw ork can hardly be distinguished. Another reason why it is hard to see the
dislocation in this image is that the (1
10)
reflection will pick up strain fields from both
sets o f dislocations (along [ 1 0 0 ] and [0 1 0 ]), so the strain overlapping does not only
come from parallel neighboring dislocations, but also from a perpendicular set o f
dislocations. If the reflection (220), which gives an s value o f about 0.2 nm '1, is used
instead o f (1
1 0 ),
then the entire network can be clearly seen with little superposition o f
Figure 4.15 ( 1 1 0) weak beam image o f the 26 nm sample. The excitation
error is about 0.05nm_l.
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Moire fringe contrast (see Figure 4.16). The inset to Figure 4.16 is the FFT from, the
dislocation network which gives a dislocation spacing along both directions o f about
16.9 nm.
With the results from the weak beam plan view images, the questions we asked
above can now be answered.
Most o f the misfit dislocations are along <100> directions, however, they are not
perfectly straight and the direction o f an individual dislocation can vary greatly (see
Figure 4.16). This gives rise to inclined dislocations when viewed along the [100]
direction and edge on ones when viewed along the [ 1 1 0 ] direction in cross section
images (see Figure 4.7 and Figure 4.9).
Figure 4.16 (220) w eak beam plan view image o f 26 nm sample obtained using
lOOkV. The s value is about 0.2nm "l. The inset is the FFT from the dislocation
network.
91
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It can be seen from Figure 4.12, Figure 4.15 and Figure 4.16 that as we change the
g vector, different sets o f dislocations appear. According to the g.b criterion all misfit
dislocations observed are edge dislocations with the same family o f Burgers vector o f
< 1 0 0 >BST. Therefore, the observed A
l [l 10] Burgers vector in cross section HREM
images (see Figure 4.8 and Figure 4.9) is only the projection o f the <100> Burgers
vector along the [ 1 1 0 ] direction.
The average spacing o f the dislocations in both [100] and [010] directions is about
17 nm, corresponding to almost full relaxation.
The individual dislocation segments are very short (~150 nm). And they are even
shorter in as deposited films (~50nm). It is generally recognized that in an epitaxial
system larger misfit causes shorter m isfit dislocation segment. The very short misfit
dislocations in this BST/LSAT system, however, cannot be explained by the misfit o f
this system. We deposited two BST films with the same conditions for comparison, one
on LAO with a larger misfit o f -4.5% and the other on MgO with an even larger misfit
o f +5.88%. Both o f these as-deposited systems have longer and straighter misfit
dislocation segments than even the annealed BST/LSAT system. Figure 4.17 shows a
dark field image o f BST thin film on MgO substrate. It can be clearly seen that the
Moire fringes are much longer and straighter than the Moire fringes shown in Figure
4.11 for BST on LSAT, indicating longer and straighter misfit dislocations. Therefore, it
seems that misfit is not the primary reason for such short misfit dislocation segments. In
addition, even after very high temperature (950 °C for 14 hours) annealing, the misfit
dislocations did not extend very long. Together with the fact that misfit dislocations are
92
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much longer in other systems deposited using the same conditions, it suggests that non­
equilibrium conditions during deposition is not the primary reason either.
We suspect that the primary reason for this configuration o f very short misfit
dislocations is because o f the ordering domains that exist in the LS AT substrate (see
Appendix). As shown in Figure 4.3, Misfit dislocations form at the surface o f the film
during the deposition and then glide to the interface forming two threading segments
and one misfit segment. The misfit segment then extends along <100> directions. At the
BST/LSAT interface, because o f the ordering in LS AT, the Burgers vector o f a perfect
misfit dislocation in a disordered region becomes a partial dislocation in the ordered
region. Therefore, the propagation o f misfit dislocations into the ordered region has to
be accompanied with a stacking fault/anti-phase boundary at the interface.
o/r
Figure 4.17 Dark field image of BST film on MgO substrate.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
This
increases the energy associated with the misfit dislocations and limits the extension o f
misfit dislocations along the interface. Because o f the small regions o f inter-twined
disordered and ordered domains o f LSAT, many dislocations are stopped before
meeting with other m isfit dislocations, thus only very short segments o f misfit
dislocations exist at the interface.
One o f the m ost important consequences o f short misfit segments is that the
density o f their threading dislocation segments will be very high because they cannot be
annihilated through dislocation reactions and remain in the film, hi fact, we have
observed a very high density o f threading dislocations (~ 1 0 llcm"2) in the as deposited
films. This is two to three orders o f magnitude higher than dislocation densities in
systems with sim ilar structure and misfit. In addition, even after annealing, the density
o f the threading dislocations only decreases by about 35% and remains in the same
order o f magnitude. This observation further supports our speculations: because the
ordered domains do not change upon annealing, they cause difficulties for dislocation
propagation even at elevated temperature and hence the high density o f threading
dislocations can not decrease dramatically upon annealing.
Next we w ill discuss the influence o f these threading dislocations on the dielectric
properties o f BST films.
94
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4.3.2
The effect o f dislocations on the dielectric properties o f BST films
As discussed in the last section, we have observed a very high density o f threading
dislocations in the BST films on LSAT substrates. Figure 4.18(a) is a plan view weak
beam image o f the as deposited film and Figure 4.18(b) is an image o f the same film
after annealing. We have measured in the as-deposited film a dislocation density o f
2.2X10 1’em'2, representing 1 threading dislocation within every 12.6 nm radius. This
density o f dislocations is 3-4 orders o f magnitude higher than typically observed in
these ceramic films. All BST/LSAT films imaged for this work show similar threading
dislocation densities.
In Figure 4.19 we show a high-resolution image o f the threading dislocation cores,
which are marked by the white arrows. These dislocations are edge dislocations and
have the same Burgers vector as their misfit counterparts: b = [100] b s t (see inset Figure
4.19). Associated with each dislocation is a local strain field which, in the vicinity o f
the core, is much greater than the macroscopic residual misfit strain. Due to the
extremely high-densities measured for these films, it is quite likely that neighboring
dislocations still have overlapping strain fields. Skulski et al
^7
have shown a
broadening of the phase transition along with an overall decrease in dielectric constant
as the density o f dislocations increases. The density we measure represents a 5 order
increase over the values used in that work. These arguments suggest that local strains
associated with threading dislocations are another mechanism for dielectric degradation
in these heteroepitaxial BST thin films. We focus the following discussion on the
difference in dislocation density before and after annealing.
95
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$ lOOnm
Figure 4.18 Plan view weak beam image of threading dislocations in (a) asdeposited BST films, (b) annealed BST films.
96
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Figure 4.19 Plan view HREM off threading dislocations in BST films. The inset
shows the closurre failure o f the Burgers Vector
97
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By counting the number o f these dislocations within a lOjjm 2 area we have
estimated a dislocation density o f —2 .2 x l 0 ! 1 cm ' 2 for the as-deposited film and
—1.4x10li cm ' 2 for the annealed film. In semiconductor films annealing improves the
electron transport properties only if the threading dislocation density decreases one or
more orders o f magnitude because electron transport is limited by the scattering o f
electrons by dislocations and other extended defects. In the case o f BST films it is the
strain associated with each dislocation that alters the dielectric stiffness. Thus, even
small changes in the density o f dislocations effectively change the overlapping o f strain
fields from neighboring dislocations. Such considerations are especially important
when the separation o f threading dislocations is very small (—15 nm in our BST films).
Hence, a 35% reduction in the dislocation density should have some impact on the
dielectric properties. However, calculations from first principles are needed to quantify
the effect o f dislocations on the dielectric properties o f BST films. In addition to the
reduction o f dislocation density, the threading dislocations appear straighter and cleaner
after annealing. Also, the large number o f threading dislocations might have served as
paths for oxygen diffusion during the film deposition and the cooling down under
oxygen, and thus effectively reduced the amount o f oxygen vacancies for the asdeposited films.
Associated with the reduction o f threading dislocation densities, there should be a
corresponding increase in the length o f the misfit segments. Figure 4.20 shows the
misfit dislocations before (Figure 4.20(a)) and after (Figure 4.20(b)) annealing. It can be
seen that the misfit dislocations change drastically upon annealing. The misfit
dislocations in the as-deposited BST films are very short (most o f them less than 50 nm)
98
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and their directions vary even within an individual segment. The misfit dislocations in
the annealed film, however, appear much straighter. They are also longer (—150 nm)
than in the as-deposited films, corresponding to a lower density o f threading
dislocations in the plan view image. Another very important difference between the asdeposited and the annealed films is that the overall dislocation direction has changed
upon annealing. A closer observation o f the misfit dislocations in the as-deposited films
reveals that a large portion o f the dislocations lie along < 1 1 0 > directions (see, e.g. the
upper half o f Figure 4.20(a)). However, most o f the misfit dislocations in the annealed
film lie along <100> directions. Nonetheless, the Burgers vectors o f the misfit
dislocations remain <100> b s t after annealing. This is confirmed by both high resolution
TEM o f the interface and conventional two-beam analysis. Since the Burgers vector is
< 1 0 0 >
b s t
,
the dislocations along < 1 1 0 > direction have a screw component, which does
not relax the misfit strain. The screw component can only compensate for small
rotations between the film and the substrate. The fact that the misfit dislocations have a
screw component is direct evidence of small angle columnar rotations between the film
and the substrate. In addition, the change o f the misfit dislocation direction from <110>
to <100> means that the screw component o f the Burgers vector vanishes upon
annealing. This is because the grains in the film align themselves to the substrate during
the annealing process. This result is confirmed by XRD analysis, which will be shown
later in this chapter.
The reduction o f threading dislocation density by itself, however, may not be
enough to explain the dramatic change o f dielectric properties upon annealing since
threading dislocations remained at a very high density after annealing. In addition, the
99
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Figure 4.20 Weak beam plan view TEM images o f the (a) as-deposited and (b)
annealed BST films showing misfit dislocations. The misfit dislocations become
longer and straighter upon annealing. Some of the misfit dislocations also change
their directions upon annealing.
100
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misfit dislocations themselves are not expected to contribute much to the dielectric
properties measured b y IDEs when the electrical field is in plane, provided that the film
is not too thin (>50nm). Therefore, we proceed to discuss the effects o f twodimensional defects such as ADBs and subgrain boundaries on the dielectric properties
o f BST films.
4.4
4.4.1
The role o f antiphase domain boundaries and small angle grain boundaries
Antiphase domain boundaries in BST films
There are two possibilities for antiphase domain boundaries (ADB) to form is epitaxial
BST films. In the first configuration the phase shift is perpendicular to the interface. In
this case the two antiphase domains have a shift o f 54[0 0 1 ] along the c axis o f the film
with respect to each other, as shown in Figure 4.21. These types o f ADBs are not
observed very often in BST films on either LSAT or MgO substrates. For BST grown
on LSAT, since both o f them have a perovskite structure o f ABO 3 type, it is
energetically favorable for them to form a pseudomorphic structure. That is, if the
surface o f the substrate ends at the AO layer, then the first layer o f BST w ill be the BO 2
layer, and vise versa, regardless o f whether there is a step on the surface o f the substrate
or not. However, if an antiphase boundary with a shift o f */2[0 0 1 ] is to be formed, a
wrong stacking sequence where either AO layer grown on AO surface or BO 2 layer
grown on BO 2 surface is required, therefore, it is not very likely for this type o f
antiphase boundary to form. In fact, our TEM results show that they usually do not start
101
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- - <‘- ,■>
■*•*?Jss&ll £ ± ■.-:■■.a M .Vt i ■«!
; >.
- v , •■; i ,... j -.
•'
■-.i
; •
V
■■
-
•
-
1
.
;
■j & .> -It- » *. --.
B a/S r
o
o
Figure 4.21 Antiphase domain boundary with a i4[001] shift.
102
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at the interface but from a partial dislocation with a Burgers vector o f ^[001] inside the
film, as shown in Figure 4.21.
To discuss the possibility o f this type ADBs on MgO substrate, we begin with a
discussion on possible configurations for the stacking sequence o f BST on MgO. MgO
has a rock salt structure (Figure 4.22) and the (001) surface o f MgO is shown in Figure
4.23(a). Since the structure o f MgO is different than perovskite, we need to investigate
which layer AO or BO 2 is most likely to be the first layer deposited on MgO.
Schematics o f both layers are shown in Figure 4.23(b) and (c), respectively. An
interface between ionic crystals has the lowest energy if the nearest neighbors have
charges o f opposite sign. If AO is the first layer nucleating on MgO, however, this
condition can not be satisfied. It can be seen from Figure 4.23 that either the anions
Mg
O
O
Figure 4.22 Schematic o f the structure o f MgO
103
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(oxygen ions) have to stack next to each other (Figure 4.23(d)) or the cations (Mg and
Sr/Ba) have to become nearest neighbors (Figure 4.23(e)). However, if BO 2 is the first
layer nucleating on M gO the bonding for both anions and cations can be satisfied
without any conflict (Figure 4.23(f)). Thus, it is more energetically favorable for the
BO 2 layer to be the first layer o f BST film on MgO substrate. In fact, it is theoretically
proven and experimentally verified that for materials with similar perovskite structure
epitaxially grown on MgO substrate the BO 2 layer is always the first layer on the MgO
surface.87,88 Therefore, since the stacking sequence is determined, ADBs with a !4[001]
shift are not likely to form in BST films on either LSAT or MgO substrates. In fact we
did not observe any ADBs o f this type in BST films on MgO substrates and very few on
LSAT.
The second possibility for antiphase boundary has a phase shift o f '/-[010] or
Vz[100], i.e., the phase shift is in plane and parallel to the interface. This type o f
antiphase boundary is also not likely to form in the BST/LSAT system because BST
and LSAT tend to from pseudomorphic structure (both are perovskite) and thus the in
plane atomic sequence is also predetermined by the atomic sequence o f the substrate.
For BST on MgO, however, there are two possibilities o f in plane atomic arrangements
that are equally favorable, as shown in Figure 4.24(a) and (b). Both types o f stacking
have exactly the same neighbors for each ion across the interface but they have a shift
o f lA [010] or !^[100] in plane with respect to each other. This is because MgO has an
f c .c . structure with two equivalent lattice positions in the (001) plane, while the simple
cubic BST does not. Therefore, when two domains with different in plane atomic
arrangements meet during the film growth, an ADB with a phase shift o f *A[010] or
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l/4[100] will form at the plane where they meet. Since both domains are equally possible
to form during nucleation, it is very likely for BST to form this type o f ADBs. In fact
we have observed many o f these ADBs in plan view BST/MgO samples. One of them is
shown in Figure 4.25. The boundary appears thicker than one unit cell probably because
it is not perfectly parallel to the [001] direction.
o
o
o
O
O
a
#
O
o
C)
-e -
Mg
Sr/Ba
O
Ti
Figure 4.23 Schematic o f (a) (001) surface o f MgO, (b) AO layer o f BST, (c) BO2
layer o f BST, (d) a possible stacking sequence of AO on MgO where oxygen ions sit
on top o f each other, (e) a possible stacking sequence o f AO on MgO where cations
sit on top o f each other, (f) possible stacking sequence o f BO 2 on MgO
105
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We notice that ADBs in BST films are intrinsically low dielectric constant defects.
As shown in Figure 4.26(a), the boundary between the dotted lines assumes a
composition o f (Sr/Ba)0, which has a dielectric constant around 20. I f the ADB moves
a half unit cell towards either domain, as shown in Figure 4.26(b), it will be Ti4+ rich at
the boundary and have a composition o f TiC>23which has a dielectric constant o f 110.
Even though the ADB is either (Sr/Ba)2+ or Ti4+ rich, it remains neutral because the
charges are compensated by oxygen ions. To keep the overall stoichiometry, the ADBs
usually assume a curved or zigzag configuration so that the overall (Sr/Ba) to Ti ratio
remains 1:1.
a
Mg
O Ti
O O
Figure 4.24 Two possible in plane atomic arrangements (a) and (b) with a
relative lattice shift o f V2[0 1 0 ] or J4[100].
106
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Ba/Sr
Q
O
0
/T
p -tL
O-
v i/ 2[q iq ]
Figure 4.25 Plan view high resolution image o f a BST film showing an ADB with
an in plane lattice shift between two neighboring domains
107
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B a/S r
a
b
Figure 4.26 Schematic o f (a) Sr/Ba rich and (b) Ti rich ADBs. The
boundary is the region between dashed lines.
108
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We have observed that after annealing, corresponding to an increase o f dielectric
constant, there is a large decrease in the number o f antiphase boundaries. Figure 4.27(a)
and (b) are two plan view bright field images o f the as-deposited and annealed BST
films on MgO substrates, respectively. It can be seen that the size o f the antiphase
domains, as shown by the white dotted lines, increased from about 50 nm to about 150
nm upon annealing. We suspect that the decrease o f these ADBs is one o f the primary
causes for the recovery o f dielectric properties upon annealing. It is reasonable to
assume that the ADBs have a dielectric constant around 65, which is the average o f
Sr/BaO and Ti02- Therefore even though ADBs occupy a very small portion o f the total
volume o f the film, they form continuous low dielectric constant walls, such as A-B and
C-D in Figure 4.28. In an IDE configuration, the applied electric field is perpendicular
to one set o f these walls. Thus, a large portion o f electric field drops across these thin
low dielectric walls, lowering the measured “effective” dielectric constant for the film.
Thus the measured (effective) capacitance Q^-can be expressed as:
1
ce f f
1
1
c
4.7
c
'-'b u lk
u g i.
where Cgb is the capacitance from ADBs and Cbuik is the capacitance from inside the
domain. So that:
f
1
1
A
'eff
D g .b. +
D bulk
(
\
A
Csb D S-b.
V
\
1
+
4.8
A
^ b u lk
V
p.
bulk
y
109
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where Seff is the measured or the effective dielectric constant and
and Sbuik are the
dielectric constants for the ADBs and the domain itself, respectively. (We assume a
bulk dielectric constant, SbuiK- within an antiphase domain) Dg b. is the width o f the ADB
Figure 4.27 Plan view bright field images o f (a) as deposited BST film
on MgO, and (b) annealed BST film on MgO. Dashed lines show
antiphase boundaries.
110
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and Dbulk is the doamin size, Sefis then given by:
— ^
£ af r
'eff
—
sJ>- ' ^ b u l k ) ' ( D g J ) - +
_
n
• Pbulk
U g .b .
^ b u lk )
_
4^
D bulk ■£
b gJ>.
. r.
T - -7
As mentioned above, the width o f an ADB is one unit cell, 0.4 nm, and the
average grain size o f the annealed sample is about 150 nm while that o f the as-deposited
D
A s-deposited
Anneale
Figure 4.28 Schematic of grain configuraion in BST films before and after annealing.
Ill
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sample is about 50 nm. I f we assume Sbuik =5000 and %6. =65, equation (4.9) gives a
value o f seff= 3120 for the as-deposited film and 4160 for the annealed film. This huge
difference o f the calculated dielectric constant (>1000) for the BST films before and
after annealing agrees reasonably well with our measured values o f e, suggesting that
ADBs play a very important role in the recovery o f the dielectric properties o f BST
films grown on MgO. In addition, the fact that even with ADBs considered, our thin
films still have lower dielectric constant than expected suggests that the dislocations
also played an important role in the degradation o f dielectric properties o f BST thin
films.
4.4.2
Small angle subgrain boundaries
Grain boundaries have been shown to lower the effective dielectric constant of
bulk BST materials by forming walls o f low dielectric constant.89 However, large angle
grain boundaries normally do not exist in epitaxial BST thin films. Instead only low
angle subgrain boundaries can be found in our BST films. The density o f these subgrain
boundaries decreases upon annealing through rotation and coalescence. Figure 4.29(a)
shows a high resolution plan view o f an as deposited BST film on LSAT substrate. A
small subgrain with a very small rotation (<1°) with respect to its neighboring grains is
marked by dotted white lines. This rotation is compensated by 4 threading dislocations,
whose cores appear as white dots in the image. Upon annealing, these subgrains align
themselves to the substrate, resulting in a decrease o f subgrain boundaries, which also
corresponds to a decrease in the threading dislocation density, as shown in Figure
4.29(b).
112
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Figure 4.29 Plan view HREM images of (a) as deposited and (b)
annealed BST film on LSAT.
113
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The rotation and coalescence o f subgrains is also reflected in our XRD results.
The full width at half maximum (FWHM) o f the (002) co-scan from the as deposited
BST films was typically less than 0.15°, which is the resolution limit o f our x-ray
diffractometer. However, the FW HM o f the (101) peaks were much higher ~ 0.65°.
This large difference in the FWHM o f the two peaks indicates that the films are very
well (001) oriented but with larger in-plane mosaic spread and thus the existence o f
sub grains in the film. Also, another reason for the widening o f the (101) co peaks comes
from the fact that this reflection is more sensitive to in-plane distortions. Since the
Burgers vectors o f the threading dislocations are along [100] or [010] directions, the
distortions o f the lattice are in-plane. After annealing the FWHM o f the (002) peaks
remained below the resolution o f o u r x-ray diffractometer while the FW HM o f the
(101) peaks decreased to about 0.60°, indicating grain rotation and coalescence during
the annealing process.
We suspect that the distortions associated with these subgrain boundaries will
lower the dielectric constant o f the films just like the ADBs. However, it is difficult to
determine to what extent the subgrain boundaries affect the dielectric constant o f BST
thin films. Nevertheless, we may be able to determine whether or not they play an
important role in the recovery o f the dielectric properties o f BST films. We notice that
these 2-D defects are primarily perpendicular to the film/substrate interface. Thus, when
measured using IDEs, the electric field lines are perpendicular to the grain boundaries,
resulting in a series connection o f the low dielectric boundaries. So if the measurement
is done out o f plane or vertically, then the electric field lines will be parallel to the grain
boundaries, as shown in Figure 4.30, and the measured capacitance C ^ w ill be:
114
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where t is the film thickness, £q the permittivity o f vacuum and A gb. and A bulk are the
area o f the grain boundary and the area o f the grains, respectively.
Obviously the apparent capacitance should not change significantly upon
annealing if these 2-D defects are the primary reason for the lowering o f the dielectric
constant.
Au pad
a
f ie ld
Figure 4.30 (a) Schematic o f out o f plane dielectric measurement and (b) the
relationship between the ADBs/subgrain boundaries and the electric field.
115
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0.07
45-
0.06
0.05
0.04
C
w/)
0.03 o
o 30m
CL
0.02
O 2 5-
0.01
20
-6
-4
-2
0
2
-4
4
Voltage (V)
•2
0
0.00
2
4
6
Voltage (V)
Figure 4.31 Out o f plane dielectric measurement o f (a) as-deposited and (b) annealed
BST thin films
The result o f out o f plane/vertical dielectric measurement is shown in Figure 4.31.
It can be seen from Figure 4.31 that there is no appreciable difference between the
measured capacitance for the as deposited sample and the annealed sample as expected
from equation (4.10). this results suggest that these 2-D low angle subgrain boundaries
play a very important role in the degradation o f in plane dielectric properties o f BST
films. In addition, the loss o f the annealed sample in Figure 4.31 is much lower than
that of the as deposited sample, suggesting that these boundaries are a major factor for
dielectric loss. This result also supports the argument that O vacancies do not play a
very important role in the recovery process since if they did, the increase of dielectric
constant would not have any directionality.
116
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4.5
Summary
We have shown a correlation between the microstructure and the dielectric
properties o f BST films on LSAT substrates. Our results show that oxygen vacancies do
not play an appreciable role in the recovery o f the dielectric properties o f BST films
upon annealing. We attribute the increase in dielectric constant upon annealing to the
decrease o f ADBs and subgrain boundaries in the film.
We also conducted an extensive TEM analysis on the dislocation morphology in
BST films. It was found that if the spacing o f the dislocation network is less than 0-3 &
the dislocations can not be imaged using regular bright/dark field technique. Instead
weak beam technique is required. Lower voltage and large excitation error are preferred
when obtaining the weak beam images.
Most o f the misfit dislocations are along <100> directions, however, they are not
perfectly straight and the direction within an individual dislocation can vary greatly.
Individual segments o f the misfit dislocation network are very short, and consequently,
the threading dislocation density is very high. We believe that this particular dislocation
morphology is caused by the partial ordering o f the LSAT substrate.
The recovery o f the dielectric properties is accompanied by a decrease in the
threading dislocation density and hence a decrease in the local strain inside the BST
films. However, further investigation is necessary to study the actual role o f
dislocations.
We believe that the reduction o f these 2-D (grain boundaries) and 1-D
(dislocations) defects is the primary reason for the improvement in the dielectric
properties o f BST films upon annealing.
117
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Summary and Future Work
Realization o f BST thin films for tunable microwave applications requires the
understanding o f issues closely related to thin film deposition: strain developed via
lattice mismatch and thermal mismatch, and defects present in the films due to lattice
mismatch and non-equilibrium conditions. In this dissertation, we have performed
careful analysis on the effect o f strain and defects on the dielectric properties o f BST
thin films.
In order to study the effect o f strain, a series o f heteroepitaxial BST thin films o f
thicknesses varying from 8 nm to 500 nm were prepared on LSAT and MgO substrates
to produce films with systematically varying in plane stresses. The in plane dielectric
constant en was found to increase w ith increasing tensile stress and decrease with
compressive stress. The relationship between dielectric properties and stresses agrees
very well with our theoretical calculations, namely, the reciprocal o f sn is inversely
proportional to the in plane strain. W e also derived a relationship between the dielectric
constant and the electric field by including the fourth order o f Landau expansion of
polarization in the expression o f the Helmholtz free energy. The calculated dielectric
constant versus electric filed curve agrees well with our experimental curves. In order to
study the effect o f strain on the tunability o f BST thin films, we propose for the first
time that tunability should be defined as
r d sn
\
\
J max
S E
. This new definition enables us to
universally compare tunability from different samples without knowing the details of
the configuration used for the electrical measurement. Our experimental data is
118
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analyzed using this new definition and it shows good agreement with theoretical
calculations.
However, there are still some discrepancies between our calculations and the
experimental data. The discrepancies come from three reasons:
1.
We vary the in plane stress by changing the film thicknesses. Thus film quality
m ay vary, especially for very thin films. Therefore, it is desirable to have a
systematically varying stress without affecting the film quality. Changing the
stress by using different substrates with different lattice parameters while
maintaining a certain film thickness or applying external stress are viable
alternatives for future studies.
2.
We have assumed uniform electric field distribution in our IDE configurations.
This is, however, a very rough approximation. Therefore, a detailed electric field
mapping is needed for more accurate calculations o f the relationship between
dielectric constant and electric field.
3.
We have made small field (first order) approximations in our calculations o f the
relationship between dielectric constant and electric field. It is desirable to
consider higher order approximations, however, numerical approaches maybe
needed since it involves transcendental equations.
It is observed by many research groups that annealing leads to partial recovery in
the dielectric properties o f BST films. Therefore, in this study, carefully designed
annealing processes were performed in different types o f gas ambient to study the effect
o f defects on the dielectric properties o f BST films. Extensive x-ray and transmission
119
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electron microscopy studies were carried out to study the structural evolution o f the
BST films upon annealing. We have shown that oxygen vacancies (0-D defect) may not
play an important role in the recovery o f dielectric properties o f BST thin films since N2
annealing produced essentially the same effects as O2 annealing. In contrast, it is the
decrease o f defects such as dislocations (1-D defects) as well as antiphase boundaries
and small angle grain boundaries (2-D defects) and the relief o f local strain associated
with these defects that dominate the dielectric recovery process. We have found a very
high density o f threading dislocations in our BST films on LSAT substrate. This is
correlated with the very short misfit dislocation segments at the interface o f BST and
LSAT. Since other systems with even larger misfit did not show such a short misfit
dislocation configuration, we attribute this to thef.c.c. ordering in LSAT substrate,
which was carefully studied using HREM technique and determined as La-Sr ordering.
We also found a large density o f antiphase domain boundaries in BST films on MgO
substrates. This is attributed to the rock salt structure o f MgO, which produces two
equally favorable lattice positions for BST film to nucleate, and thus creating antiphase
boundaries when two island with different “phase” meet. The densities o f threading
dislocations and antiphase boundaries both decrease when annealed at an elevated
temperature and this is considered as the reason for the improvement o f dielectric
properties o f BST films upon annealing
However, since the origin o f the large dielectric constant o f BST comes from the
existence o f soft phonons in its crystal, it is desirable to perform calculations from first
principles for the effect o f defects, such as threading dislocations and antiphase
boundaries, on the behavior and propagation o f soft phonons and hence the dielectric
120
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properties o f BST thin films. Such calculations will give more insight and better
correlations on the effect o f defects on the dielectric properties o f BST films.
Finally, since ultimately the BST are considered for microwave applications, it is
necessary to perform microwave measurements o f the dielectric properties o f BST films
and correlate them with low frequency measurements. This includes local dielectric
measurement (microwave microscopy) and device performance measurement (coupled
microstrip phase shifters).
121
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Appendix Ordering in LSAT Substrates
The quality o f thin films is closely related to the properties o f the substrate on
which they are deposited. For the epitaxial growth o f films with perovskite structure,
single crystal substrates with the following specifications are required: The lattice
constants o f the substrate should be closely matched to those o f the films; the substrate
should not have phase transitions which create micro twins; and only a minimal
chemical reaction can be tolerated in the interfacial region between substrate and film.
In addition, a similar thermal expansion coefficients of substrate and film from room
temperature to growth temperature as well as low dielectric constants and dielectric
losses are required. And finally, the cost should be relatively low. M any single crystals
such as STO, LaA 1 0 3 (LAO) and MgO are used for growth o f perovskite films.
However, these single crystals satisfy only some o f the required substrate specifications
mentioned above. Therefore, approaches using mixed perovskite substrates have been
used to meet these requirements.90 In the search o f new substrates for superconductor
films, (La, Sr)(Al, Ta ) 0 3 (LSAT), a 30/70 mole % solid solution between LaAlCh
(LAO) and Sr2AlTa 0 3 (SAT), was fabricated at AT&T Bell laboratories.91 This new
material LSAT eliminates the difficulties o f twinning strain and non-isotropic properties
found in pure LAO and the cost is much lower than that o f STO. In addition, it is also
found to have low dielectric loss and m edium dielectric constant (—22.5) which makes it
suitable for microwave applications. Therefore, it has received a lot o f attention since its
introduction and is used as substrate for various thin film depositions.92'94
122
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A.1 Review o f structure characterization of LSAT
Despite its increasing popularity, the exact atomic structure o f LSAT is not yet
well know and has received little attention up to now. For example, LSAT is considered
as f.c.c. structure with a lattice constant of 0.737 nm in some references,91’94 while
treated as a simple cubic perovskite structure with a lattice constant o f 0.386 nm in
some other references,92 It is generally recognized though that the structure o f LSAT
either follows the structure o f cubic LAO phase (at 800 K) (disordered s.c. LSAT) with
a lattice constant o f 0.386 nm, or the structure o f SAT, which is an ordered perovskite
structure with a “double unit cell”, with a lattice constant o f 0.386x2 = 0.737 nm
(ordered f.c.c. LSAT). In this dissertation, a series o f experiments using x-ray
diffraction (XRD), TEM and energy dispersive spectrometry (EDS) were conducted to
determine the atomic structure o f LSAT. It is found that the cause o f this discrepancy,
as w e’ll show in the following sections, is because LSAT consists o f domains
corresponding to both structures.
A.2
X-ray Diffraction analysis
The most commonly used method for structure determination is x-ray diffraction.
However, the XRD spectra o f LSAT are sometimes misleading, because the
{ h , k , 1}
peaks for the ordered f.c.c. LSAT coincide with the (1/2 h , 1/2 k , 1/2/} peaks o f the
disordered s.c. LSAT. Therefore, the extra peaks caused by ordering need to be o f
(2/z+l,
k , l}/.c.c.
type, whose indices include at least one odd number. Their
corresponding simple cubic reflections do not have integral indices and therefore do not
exist. For these type o f indices, those most often used peaks are o f (2/H-l, 0, 0} type,
123
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such as {100}, {300}, etc. However, due to the structure factors o ff.c.c. structures,
these reflections are not allowed, eliminating the possibility o f distinguishing the
ordering using these m ost often-used reflections. Thus, the only extra peaks caused by
ordering are {2/H-l, 2k+\, 2/+l}y;c.c. types o f reflections, such as {111}, and {311}.
Accordingly, we conducted XRD ^ scans o f the f.c.c. LSAT {111} and {222} peaks.
The results are shown in Figure A .l.
The very existence o f the {111} peaks in Figure A .l(a) suggests that LSAT has an
f.c.c. structure. However, compare to its {222} peaks, the full width half maximum
(FWHM) o f the {111} reflections are much larger than that o f the {222} reflections
while the intensities are much lower, suggesting that the f.c.c. ordering does not prevail
through out the material but may consists o f small domains. The size o f these domains
can be estimated from the FWHM o f the {111} peaks by taking account o f the size
effect o f x-ray diffraction. However, the measurement is more accurate in TEM
analysis, in which the size o f those domains can be directly measured from dark field
images.
A.3
TEM Two beam analysis
Since only {2/HT, 2k+\, 21+1} types o f reflections are characteristic to the ordered
f.c.c. LSAT, <00h> zone axis cannot be used in the electron diffraction analysis.
Therefore, [110] zone axis was chosen since it is the lowest index other than <00h>
type.
Figure A.2(a) shows the diffraction pattern along the [1 1 0] zone axis. In
agreement with the XRD spectra in Figure A. 1, the intensities o f the {111} peaks are
124
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much lower than those o f the {002} peaks. A dark field image using the (111) reflection
(Figure A.2(b)) clearly shows the existence o f ordered domains, which have a white
contrast due to their contribution to the (111) reflection. These domains have very
irregular shapes and range from 5 nm to 30 nm in sizes. They appear to be larger in
60 - {111} LSAT
cn
c
oo
40
30
co
c
o
c
50
20
-
Q ifoAAlvM
0
50
100
150
20 0
250
300
350
Phi [degrees]
a
2000 - {222}LSAT
co
c
1500
=3
O
0
1000
co
1
500
50
100
150
20 0
250
300
350
Phi (Degree)
Figure A.1 (a) {111} and (b) {222} Phi scans from LSAT
125
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thicker areas because o f the vertical (along the beam direction) overlapping o f different
domains. In contrast, the dark field image using the (200) reflection, Figure A.2(c), does
not produce any contrast since (200) is a common reflection for both the disordered and
ordered regions.
A.4 EDX analysis
In order to determine if the ordered f.c.c. domains have different composition
b
c
Figure A.2 (a) Diffraction pattern o f LSAT in [1 1 0] zone axis, (b) (111)
dark field image, (c) (200) dark filed image.
126
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than the disordered regions, EDS analysis was performed. However, under the
conditions for EDS analysis where the objective aperture has to be removed, it is
difficult to distinguish these domains. So we had to perform “blind” line scans across
adjacent domains to determine if a difference in composition exist in different domains.
EDS data were collected using a 1 nm spot along a 35 nm line length with one
nanometer spacing between each spot. In this manner, enough counts were recorded in a
limited time along a line longer than most domain diameters. The intensity/counts
versus position curve for each element is shown in Figure A.3(a) and the normalized
intensity ratio o f different elements is shown in Figure A.3(b). It can be seen that the
relative ratio o f these element fluctuates around unity, indicating that there is no
apparent composition change associated with the ordering o f LSAT. Several similar
scans in different areas were performed and none o f them showed an obvious
composition difference. This result indicates that this ordering is due to structural
ordering without any change in the composition o f the domains from the average
composition o f LSAT.
A.5
H REM and sim ulation
Figure A.4 shows a HREM image of LSAT viewed along [010] direction. Similar
to the two-beam analysis, there is no obvious contrast difference between the ordered
region and disordered region since only common reflections are used in the image
formation.
127
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EDS line scan
1400
1200
1000
-L a i
-T a j
800
c
3
i
Al i
O
600
r !
400
200
0
0
5
10
15
20
25
30
35
P o sitio n (nm )
a
1.2
0.8
-Al/Ta |
:£? 0.6
“
-L a /S r ,
0 .4
0.2
0
5
10
20
15
25
30
35
P o sitio n (nm )
Figure A.3 (a) The intensity (counts) o f each element versus
position curve (b) Relative ratio o f Al/Ta and Sr/La.
128
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For HREM images viewed along [110] direction, however, clear differences can
be found between the disordered regions and ordered regions under most defocus
conditions. Figure A.5 shows one o f them. The ordered regions can be seen more
clearly by performing a Fast Fourier Transform (FFT) o f the HREM image and the
result is shown in Figure A.6. The image was reconstructed by an inverse FFT for
which only the {111} reflections were selected, as marked by the white circles in the
FFT pattern. It can be seen from Figure A .6 that the ordered regions are about 5 to 20
nm in size, in agreement with the diffraction contrast observations (Figure A.2(b)).
Figure A.4 HREM image o f LSAT viewed along [010] zone axis
129
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Ordered
domains
Figure A.5 HREM image of LSAT viewed along [110]
direction
It is straight forward to construct the structure model for disordered LSAT unit
cell. As mentioned above, the disordered s.c. LSAT should follow the structure o f high
temperature LAO phase. That is, on the basis o f the perovskite structure, the La and Sr
atoms are randomly mixed at the A sites and the A1 and Ta atoms are mixed at B sites,
as shown in Figure A.7. The space group is Pm 3 m, same as high temperature LAO.
The atomic basis o f the disordered structure is shown in Table A.I.
130
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Figure A.6 Inverse FFT from {111} reflections o f the FFT o f
the HREM image. The ordered domains can be clearly seen.
For ordered LSAT, however, there are several possibilities to construct a unit cell
with f.c.c. symmetry. The possibility o f oxygen vacancy ordering can be ruled out
because it is very unlikely that it w ill form small domains as we have seen from
diffraction contrast and high resolution images. It is also unlikely for LSAT to have
131
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both A site and B site ordering at the same time because that would lead to a
“quadruple” unit cell instead o f a double unit cell. Therefore there left two possibilities
that are equally likely: La-Sr ordering and Al-Ta ordering. Both o f these two structures
would have a space group o f Fm 3 m. For La-Sr ordering, La and Sr atoms occupy
alternating A sites in the f.c.c. lattice with a = 0.737 nm, as shown in Figure A.8. In this
structure the A1 and Ta atoms take random position in the B-site superlattice with an
occupancy o f 0.65 and 0.35 for Al and Ta, respectively. Since the ratio o f La/Sr is
0.3/0.7 instead o f 0.5/0.5, the order parameter for this structure is not 1 because the
(000) sites are occupied by 0.6 La and 0.4 Sr as shown in Table A.2. The order
parameter for this structure is S = 0.71. Similarly, for Al-Ta ordering, the Al and Ta
atoms occupy alternating B sites, as shown in Figure A.9. The atomic basis is given in
Table A.3. In this case the La and Sr atoms take random position in the A site with an
occupancy o f 0.3 and 0.7 for La and Sr, respectively. The order parameter for this
structure is S = 0.77.
•
•
•
•
La
Sr
Al
Ta
O
Figure A.7 Schematic o f atomic structure o f disordered LSAT
132
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Table A .l Atomic positions for disordered LSAT
Element
La
Sr
Al
Ta
0
X
0
0
0.5
0.5
0.5
Y
0
0
0.5
0.5
0.5
Z
0
0
0.5
0.5
0
Occupancy
0.3
0.7
0.65
0.35
1
Table A.2 Atomic positions for La-Sr ordered LSAT
Element
La
Sr
Sr
Al
Ta
O
X
0
0
0.5
0.25
0.25
0.25
Y
0
0
0
0.25
0.25
0.25
Z
0
0
0
0.25
0.25
0
Occupancy
0.6
0.4
1
0.65
0.35
1
Table A.3 Atomic positions for Al-Ta ordered LSAT
Element
La
Sr
Al
Al
Ta
O
X
0.25
0.25
0.5
0
0
0.25
Y
0.25
0.25
0
0
0
0.25
Z
0.25
0.25
0
0
0
0
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Occupancy
0.3
0.7
1
0.3
0.7
1
•
•
•
•
La
Sr
Al
Ta
O
Figure A.8 Schematic o f the unit cell for La-Sr ordering LSAT
•
•
•
•
La
Sr
Al
Ta
0
Figure A.9 Schematic o f the unit cell for La-Sr ordering LSAT
134
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In order to determine the exact atomic structure o f both the disordered and ordered
LSAT, a through focal series o f HREM images viewed along the [110] direction was
obtained and compared to simulated images obtained for the proposed structure models
using the MacTempas simulation software. It was found that the La-Sr ordering did not
match the experimental HREM images at all while the Al-Ta ordering showed very
good agreement. The images and the simulation using Al-Ta ordering m odel are shown
in Figure A. 10. The defocus values are from 5 nm to 75 nm. All images were taken at a
sample thickness o f about 25 nm. Next to each HREM image are two simulated images,
the upper one is for the disordered structure and the lower one is for the ordered
structure with the same defocus conditions as the experimental images. Due to practical
experimental limitations (for example, sample holder not steady in the process o f
through focus imaging and domain overlapping at some regions) we chose different
areas but with the same thickness in Figure A. 10. However, attention was taken to make
sure both disordered and ordered region are included in each image in Figure A. 10. It
can be seen from Figure A. 10 that at each defocusing value, both simulated images
correspond very well with corresponding parts (ordered and disordered region) o f the
experimental images. This strongly indicates that the proposed Al-Ta ordered structure
is valid.
In summary, LSAT consists o f two types o f domains: one with a simple cubic
perovskite structure disordered (a = 0.3868 nm) and the other with an f.c.c. ordered
structure (a — 0.737 nm). The domain sizes range from 5 to 30 nm. There is no
compositional change across different domains. The simple cubic perovskite structure
has A sites randomly occupied by La and Sr and B sites randomly occupied by Al and
135
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Figure A. 10 Through focus HREM images and simulations
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Ta. The f.c.c. ordered structure is found to be prim arily Al-Ta ordering with an order
parameter o f 0.71. The simulated HREM images ag re e very well to the experimantal
images.
\
137
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