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Sol -gel composite hydrothermal processing of barium strontium titanate films for microwave frequency applications

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Sol-Gel Composite Hydrothermal Processing of
Barium Strontium T itanate Films for
Microwave Frequency Applications
by
K im Z e l o n k a
A thesis subm itted to the D epartm ent of Physics
in conformity w ith the requirements for
the degree of Doctor of Philosophy
Q ueen’s University
Kingston, Ontario, C anada
September 2004
Copyright ©
Kim Zelonka, 2004
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A b stra ct
Stoichiometric barium strontium titan ate (BST) films of composition Bao.7Sr0.3T i03
w ith thickness >2/im have been fabricated on various substrates including S i/S iC ^ /P t
and A 12 0 3 /A u by hydrotherm al sol-gel composite processing. This film deposition
technique involves the treatm ent of a spun-on sol-gel composite film in an alkaline
aqueous solution at tem peratures from 50-200°C and pressures of 1-15 atm . An initial
hydrolysis procedure eliminates dissolution of the dried sol-gel prior to hydrotherm al
processing. Glancing angle x-ray diffraction shows excellent crystallinity and stoi­
chiom etry in the BST films. Scanning electron micrography, atom ic force microscopy,
and transm ission electron microscopy are used to examine the m icrostructure of the
films. B oth the him morphology and electrical studies suggest th a t the m icrostruc­
ture of the films evolves by nucleation and growth of the sol-gel-derived BST on
the underlying powder, resulting in an interconnected m icrostructure in which the
sol-gel-derived m aterial forms bridges between the original powder particles.
The relative dielectric constant and loss tangent of th e BST films are measured
in the frequency range from 1 to 100 kHz using parallel plate capacitors. Changes
in the electrical characteristics of th e him upon variation of hydrotherm al process
param eters including tem perature, process duration, and th e concentration of the
hydrotherm al solution are examined. At 100 kHz relative perm ittivities of the hlms
range from er = 400-1200 and loss tangents he in the range 0.05 < ta n 8 < 0.10,
depending on the param eters of preparation. Complex impedance analysis is used
to examine the varying bulk and grain boundary contributions to the to tal him be­
haviour.
BST pellets of various thicknesses have also been produced. These pellets are
im pregnated w ith BST sol-gel which is subsequently hydrotherm ally processed. The
electrical characteristics of the pellets are evaluated and explained in term s of the
degree of penetration of the sol-gel into the pellets.
i
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The relative dielectric constant and loss tangent of th e films between 5 and 40
GHz are determ ined using a set of coplanar waveguides w ith spur-line filters. The
m axim um relative dielectric perm ittivity at 40 GHz was found to be 94. The loss
tangent of the him was found to increase from 3.5% to 6.0% from 10-15 GHz.
The perm ittivity of the films from 1 kHz to 40 GHz is explained in term s of a
fractal description of the him m icrostructure.
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A ck n ow led gm en ts
I would like to extend thanks to a num ber of people who have contributed to the com­
pletion of this project in various ways. Firstly, I would like to thank my supervisor,
Dr. Michael Sayer, who has provided guidance and advice throughout the project,
and who will despise the num ber of commas in this section.
I would also like to
express gratitude to Dr. A1 Freundorfer and Dr. Hany H am m ad w ithout whom none
of the high-frequency measurements reported here would have been possible. H any’s
test circuit design and willingness to run com puter simulations from halfway around
the world have been integral to this project. Additionally, I would like to thank Dr.
Joke H aderm an who donated her time to perform powder TEM studies. These re­
sults have given insight which could not have been obtained otherwise. Thanks are
also extended to the Centre for Inform ation Technology of O ntario (CITO) which
provided funding for this project from 1999 to 2002. Lastly, I would like to thank my
friends and family who have provided support in times of frustration and distraction
at the busiest of times.
iii
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S ta te m e n t o f O riginality
This work develops the technique of applying hydrotherm al processing to barium
strontium tita n a te (BST) sol-gel composite films. This encompasses several novel
ideas, including the production of a low -tem perature BST sol-gel composite, the hy­
drotherm al treatm ent of a BST sol-gel, and the use of hydrotherm al processing w ith
sol-gel composites.
The technique used for GHz frequency characterization of BST films is employed
for the first time in this work. This technique allows meaningful and reliable mea­
surem ents of film perm ittivity and loss tangents to be made at frequencies up to 40
GHz. Previously, it was difficult to obtain electrical characterization of films at these
frequencies. The obtaining of sensible and meaningful results from the use of this
novel characterization technique not only provides inform ation on the behaviour of
hydrotherm ally processed sol-gel composite BST films at GHz frequencies b u t also
provides support for the validity of the m easurem ent technique.
The recognition th a t sol-gel composite hydrotherm al processing is a possible
m ethod for the deposition of ceramics for use at GHz frequencies is unique to this
work. Conventionally processed sol-gel composite films have poor electrical character­
istics due to the large number of boundaries inherent to th e film. At high frequencies
the effect of these boundaries becomes more significant. It has been shown here for
the first tim e th a t replacing conventional therm al sintering of sol-gel composite films
with a chemical hydrotherm al treatm en t gives rise to a unique m icrostructure w ith
few barriers which yields films w ith excellent electrical characteristics even at GHz
frequencies.
Gallium arsenide (GaAs) is a preferred su b strate for use in monolithic microwave
integrated circuits (MMIC) for operation at GHz frequencies, b u t it cannot be sub­
jected to tem peratures over 200°C while retaining optim al m aterial characteristics.
Thus, the development of the technique of hydrotherm al processing of sol-gel comiv
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posites for the first tim e reports a technique which is both com patible w ith th e tem ­
perature lim itations of GaAs and also produces BST films w ith excellent electrical
characteristics at GHz frequencies.
It is dem onstrated for the first tim e here th a t hydrotherm al processing of sol-gel
composite BST films is able to produce films w ith perm ittivity as high as or higher
th a n conventionally deposited films. This is the first technique which is able to do so
at tem peratures below 200°C.
The effect of varying hydrotherm al processing param eters including tem perature,
process duration, and concentration of the hydrotherm al solution is exam ined here.
The application of hydrotherm ally processed sol-gel to bulk m aterials is also
dem onstrated here.
Previously, sol-gels were used only to precipitate powders or
to fabricate films. In this work bulk BST pellets are im pregnated w ith BST solgel and then hydrotherm ally processed. The perm ittivity of th e pellets increases far
beyond w hat is predicted by the minim al increase in density of the pellets. The ap­
plication of hydrotherm ally processed sol-gel composites may be extended to include
an adhesion layer between circuits and structures such as dielectric resonators. Con­
ventionally air gaps between the su b strate and the resonator contribute significantly
to the losses of the structure. As in the bulk BST pellets, hydrotherm ally processed
sol-gel composites could be used to grow an adhesion layer w ithout such gaps.
The m icrostructure of hydrotherm ally processed sol-gel composite films is unique
in the fact th a t it is virtually barrier-free, and results from a process which does
not allow for film densification via trad itio n al therm al sintering processes.
The
recognition of the mechanism of form ation of this m icrostructure and th a t it is
this highly-connected m icrostructure w ith few barriers, which results from dissolu­
tion/redeposition of th e surface of the BST powder particles and epitaxial growth of
the sol-gel derived BST on the surface of th e particles, which gives rise to th e excellent
electrical behaviour of the films is unique to this work.
v
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This work also proposes for the first time th a t hydrotherm al processing of sol-gel
composites may be applicable to a wide range of ceramic m aterials. This would allow
for low -tem perature deposition of various m aterials on substrates whose tem perature
lim itations previously made them poor candidates for substrates for ceramic films.
These substrates include such m aterials as GaAs, polymers, and substrates w ith pre­
patterned elements which are tem perature sensitive. The technique may be useful in
such applications as flexible circuits and flat-panel displays.
Unless stated otherwise, this thesis is the original work of th e author.
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C ontents
A b s t r a c t .........................................................................................................................
i
A cknow ledgm ents........................................................................................................
iii
Statem ent of O r ig in a lity ...........................................................................................
iv
List of T a b l e s ...............................................................................................................
x
List of F ig u re s...............................................................................................................
xi
List of Acronyms and Common U n i t s ...................................................................
xvii
1 Introd u ction
1.1
Project G o a l........................................................................................................
2
1.2
Barium Strontium T i t a n a t e ...........................................................................
3
1.2.1
Characteristics
....................................................................................
3
1.2.2
Chemical Routes for BST P r o d u c tio n ............................................
5
1.2.3
Doping of B S T ....................................................................................
6
H ydrotherm al P ro c e ssin g .................................................................................
7
1.3
1.3.1
2
1
Conventional H ydrotherm al Production of BST from Inorganic
P re c u rs o rs ...............................................................................................
7
1.3.2
H ydrotherm al Processing w ith Organic P re c u rs o rs ....................
8
1.3.3
Sol-Gel-Hydrothermal Synthesis of C e r a m ic s ..............................
9
1.4
Sol-Gel Composite H ydrotherm al P r o c e s s in g .............................................
10
1.5
Outline of T h e s i s ..............................................................................................
10
E xperim ental M eth od
12
vii
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2.1 Sol-Gel Composite P reparation
....................................................................
13
2.2 Film D e p o sitio n ..................................................................................................
15
BST Pellet F a b ric a tio n .......................................................................
15
2.3 H ydrotherm al P ro ce ssin g ..................................................................................
16
Purging of the H ydrotherm al Vessel w ith N itro g e n ....................
17
2.4 Film P a tte r n in g ..................................................................................................
19
2.5 Analysis Techniques
........................................................................................
20
2.5.1
X-ray Diffraction A n a ly s is ...............................................................
20
2.5.2
Film Thickness D e te rm in a tio n .........................................................
22
2.5.3
Imaging T ech n iq u es.............................................................................
22
2.5.4
Low-Frequency Electrical C h a ra c te riz a tio n .................................
22
2.5.5
High-Frequency Electrical Test S t r u c t u r e s .................................
23
2.5.6
Complex Im pedance A n a l y s i s .........................................................
25
2.2.1
2.3.1
3
M icrostructural Changes D uring H ydrotherm al P rocessin g
3.1
A ttem pted Fabrication of BST T hin Films from M etallic T itanium Films 29
3.2
Powder F a b ric a tio n ..........................................................................................
31
3.3
BST Sol-Gel to which Powder Has Not Been A d d e d .............................
32
3.4
Benefits of Using a Sol-Gel Com posite over a Simple S o l- G e l..............
33
3.5
M icrostructure
.................................................................................................
37
3.6
Advantages of the H ydrotherm al Sol-Gel Composite Processing Tech­
nique
4
28
55
3.7
Lim itations on H ydrotherm al Processing Param eters ............................
56
3.8
Film T h i c k n e s s .................................................................................................
57
3.9
Initial Film H y d ro ly s is ...................................................................................
57
Low-Frequency E lectrical C haracterization
59
4.1
60
Acetic Acid and 2-m ethoxyethanol Based S o l-G e ls ................................
viii
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4.2
5
6
Variation of er and ta n 5 w ith Process Param eters for Sol-Gel Com­
posite F i l m s ........................................................................................................
60
4.3
Complex Impedance A n a l y s i s ......................................................................
67
4.4
Bulk Ceramic P e l l e t s ......................................................................................
71
4.5
Effective Perm ittivity Calculations for Pellets
........................................
72
4.6
Complex Impedance Analysis of BST p e l l e t s ...........................................
78
H igh-Frequency Electrical C haracterization
82
5.1
The Test S tru c tu re s .........................................................................................
83
5.2
S im u la tio n s .......................................................................................................
85
5.3
Uncovered C PW lin e s ......................................................................................
86
5.4
BST coated l i n e s .............................................................................................
88
P h ysical B asis for Film B ehaviour
100
6.1
Frequency Dependence of P e r m i t t i v i t y ....................................................
101
6.2
High Frequency P e rm ittiv ity .........................................................................
102
6.3
A Model for Film P erm ittivity from 1 kHz to 40 G H z .........................
103
7
C onclusions
112
8
Suggested Fhrther W ork
116
B ibliography
119
ix
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List o f Tables
2.1
Reagent masses used to fabricate BST sol-gel.............................................
4.1
T he variation of bulk and grain boundary resistances and capacitances
13
w ith process tem perature as derived from complex impedance analysis.
All films processed for 2 hours in 0.5 M (B a,S r)(0 H )2-8H20 solution.
4.2
70
The variation of bulk and grain boundary resistances and capacitances
w ith process duration as derived from complex im pedance analysis. All
films processed in 0.5 M (B a,S r)(0 H )2-8H20 solution at 150°C.
...
70
4.3 T he variation of bulk and grain boundary resistances and capacitances
w ith concentration of the hydrotherm al solution as derived from com­
plex impedance analysis. All films processed for 2 hours at 150°C in
(B a,S r)(0 H )2-8H20 solution.............................................................................
71
4.4 The variation of bulk and grain boundary resistances and capacitances
for pellets of various thicknesses w ith and w ithout sol-gel as derived
from complex impedance analysis...................................................................
80
6.1 Param eters used to fit model to experim ental d a ta ....................................
109
6.2 Percentages of film constituents as derived from th e model fit given
above.......................................................................................................................
x
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110
List of Figures
1.1
The perovskite structure of barium strontium tita n a te (B ST )...............
4
2.1
Flowchart of BST sol-gel composite production.........................................
14
2.2
Schematic of circular and cross-sectional pellet faces................................
16
2.3
Schematic of the autoclave used for hydrotherm al processing................
17
2.4
Purging the hydrotherm al system of CO 2 ....................................................
18
2.5
The lift-off photolithography process for patterning of films..................
21
2.6
Top view of the coplanar waveguide structure used for microwave fre­
quency characterization of BST films.............................................................
2.7
Equivalent circuit model for BST films and pellets used to calculate
complex im pedances...........................................................................................
3.1
23
XRD peaks of a hydrotherm ally processed Ti film.
26
BST peaks are
evident, b u t so are peaks from residual Ti, and th e underlying P t layer. 30
3.2
Structure used to determ ine th e residual conductivity of hydrother­
mally treated titan iu m .......................................................................................
3.3
30
Formation of a barrier layer during the hydrotherm al processing of
titan iu m ..................................................................................................................
xi
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31
3.4
The effect of hydrotherm al processing on the structure of non­
composite sol-gel BST films. Each film is processed at 150°C for 2
hours. The concentration of the hydrotherm al solution is varied, a)
OM b) 0.1M c) 0.2M d) 0.3M e) 0.5M. Circles indicate BST peaks. Tri­
angles indicate (B a,S r)C 0 3 peaks. Vertical offset of p attern s is arbitrary. 33
3.5
The effect of hydrotherm al processing on the stru ctu re of composite
and non-composite sol-gel BST films.
All films processed in 0.3 M
solution at 150°C for 2 hours, a) sol-gel in Sr(0H )2-8H 20 solution,
b) sol-gel composite in S r(0 H )2-8H20 solution, c) sol-gel composite in
B a (0 H )2-8H20 solution. d) sol-gel in B a (0 H )2-8H20 solution. Vertical
offset of pattern s is arbitrary ............................................................................
3.6
34
The effect of hydrotherm al processing on the stru ctu re of BST powders.
All films processed in 1.0M (B a,S r)(0 H )2-8H20 solution at 200°C. Du­
ration time: a) 5h b) 24h c) 48h. Vertical offset of p attern s is arbitrary. 35
3.7
The m aintenance of structure of sol-gel com posite films in various
concentration solutions (top to bottom :
0.1, 0.3, 0.5, and 1.0 M
(B a,S r)(0 H )2-8H20 solution), processed for 48h at 200°C. Vertical off­
set of p attern s is arb itrary .................................................................................
3.8
36
SEM image of the surface of a BST sol-gel composite film as deposited,
before hydrotherm al treatm ent. B oth the powder phase and the sur­
rounding sol-gel m atrix are evident................................................................
3.9
38
SEM images of the surface of BST films showing th e variation of BST
film m icrostructure w ith process time. All samples are processed in
0.5M (B a,S r)(0 H )2-8H20 solution at 150°C................................................
39
3.10 SEM images of the surface of BST films showing th e variation of BST
film m icrostructure w ith hydrotherm al solution concentration.
All
samples are processed for 2h at 150°C in (B a ,S r)(0 H )2-8H20 solution.
xii
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41
3.11 SEM images of the surface of BST films showing the variation of BST
film m icrostructure w ith process tem perature.
All samples are pro­
cessed for 2h in 0.5M in (B a,S r)(0 H )2-8H20 solution..............................
43
3.12 AFM image of raw films. Powder loading 1:2. 2 gm square, height
variation 100 nm ..................................................................................................
45
3.13 AFM images showing variation of m icrostructure w ith powder loading
and process tim e..................................................................................................
3.14 TEM images of a hydrotherm ally processed BST film.
46
This image
shows a wide view in which several particles joined by sol-gel derived
m aterial are evident. The sample was processed for 2 h at 150°C in
0.1M (B a,S r)(0H )2-8H20 solution..................................................................
4.1
50
Relative dielectric constants of raw and processed acetic acid- and 2methoxyethanol-based sol-gels.............................................................................
4.2
61
T he variation of er of BST films w ith process tem perature. All films
processed in 0.5 M (B a,S r)(0 H )2-8H20 solution for 2 hours, a) raw
film b) 50°C c) 100°C d) 150°C e) 200°C.........................................................
4.3
62
The variation of er of BST films w ith process time. All films processed
in 0.5 M (B a,S r)(0 H )2-8H20 solution at 150°C. a) raw film b) 1 h c)
2 h d) 5 h e) 20 h ................................................................................................
4.4
63
The variation of er of BST films w ith concentration of th e hy­
drotherm al solution.
All films processed for 2 hours at 150°C in
(B a,S r)(0 H )2-8H20 solution, a) raw film b) 0 M c) 0.1 M d) 0.5 M e)
1 M ..........................................................................................................................
4.5
The variation of ta n 5 of BST films w ith process tem perature.
64
All
films processed for 2 hours in 0.5 M (B a,S r)(0 H )2-8H20 solution, a)
raw film b) 50°C c) 100°C d) 150°C e) 200°C.............................................
xiii
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65
4.6
The variation of tan S of BST films with process time. All films pro­
cessed in 0.5 M (B a,S r)(0 H )2-8H20 solution at 150°C. a) raw film b)
1 h c) 2 h d) 5 h e) 20h ...................................................................................
4.7
66
The variation of ta n 5 of BST films with concentration of the hy­
drotherm al solution.
All films processed for 2 hours at 150°C in
(B a,S r)(0H )2-8H20 solution, a) raw film b) 0 M c) 0.1 M d) 0.5 M e)
1 M..........................................................................................................................
67
4.8 Complex impedance of raw and processed films showing semicircle due
to grain boundary contribution disappearing for films processed at
higher tem peratures. A similar p a tte rn is evident for films processed
for longer times and w ith higher concentrations of the hydrotherm al
solution...................................................................................................................
69
4.9 Effective perm ittivities of sol-gel im pregnated pellets of various thick­
nesses. W ithout sol-gel th e p erm ittivity of the pellet is independent of
pellet thickness.....................................................................................................
72
4.10 M ulti-cylinder model of sol-gel im pregnated BST p ellet..........................
73
4.11 SEM image of BST pellets w ith and w ithout sol-gel. The dep th of
penetration of the sol-gel is not dependent on thickness. The porosity
of the volume containing sol-gel is less th an th a t of th e central volume
w ithout sol-gel. a) pellet w ithout sol-gel (1.10 mm thick) b) 1.55 mm
thick pellet w ith sol-gel c) 0.64 m m thick pellet w ith sol-gel..................
74
4.12 Growth of sol-gel in pores of BST pellets after hydrotherm al crystal­
lization. a) w ithout sol-gel b) w ith sol-gel after hydrotherm al treatm en t. 75
4.13 Typical derived values for th e volume of the pellet containing sol-gel.
This particular case is for th e 0.79 mm thick pellet. The same values
for the perm ittivity of th e volume containing sol-gel is obtained for all
pellets......................................................................................................................
xiv
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77
4.14 Typical loss tangents of pellets w ith and w ithout sol-gel of various
thicknesses............................................................................................................
78
4.15 Typical complex impedance plots for pellets w ith and w ithout sol-gel.
The thinner pellets show a smaller contribution from grain boundaries.
5.1
79
Simulation of the shift in the position of the centre frequency of one
test structure on the thickness of gold used to form the structure.
. .
84
5.2
Cross-section of leg of coplanar waveguide p attern ed in gold on alumina. 85
5.3
The cross-sectional geometry of test structures used to sim ulate re­
sponses in HFSS..................................................................................................
85
5.4
M easured responses of C PW w ith no BST top-layer................................
87
5.5
Comparison between m easured response for one C PW line and the
sim ulated response of the line w ith consideration of conductor losses.
Each colour represents the d ata obtained from m easurem ents using one
of the eight test lines..........................................................................................
5.6
88
Typical prim ary resonance responses for the test structures w ith a
2.6 fxm top layer of BST. This particular film had a powder to solgel mass ratio of 1:1. Each colour represents the d a ta obtained from
measurem ents using one of the eight test lines...........................................
5.7
Sim ulated shifts in the centre frequency of the S2 1 notch for the 8 test
structure lines due to films w ith various dielectric constants..................
5.8
90
91
Sim ulated relationship between test film dielectric constant and shift
in S2 1 resonance center frequency to be used to determ ine dielectric
constant for test films. All 8 test lines follow approxim ately the same
relationship............................................................................................................
xv
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92
5.9
V ariation of relative perm ittivity of raw and processed BST films w ith
different powder to sol-gel ratios. The legends give the powder to solgel mass ratio of the sol-gel composite used to produce the film under
te s t..........................................................................................................................
93
5.10 V ariation of relative perm ittivity of raw and processed BST: 5 at%
Mn films w ith different powder to sol-gel ratios. The legends give the
powder to sol-gel mass ratio of th e sol-gel composite used to produce
the film under te st...............................................................................................
95
5.11 Typical simulated and measured d a ta used in determ ining the loss
tangent of the BST layer. This particular sample is a BST film w ith
powder to sol-gel ratio of 1:1............................................................................
98
5.12 Loss tangent of BST w ith powder to sol-gel ratio of 1:1 not considering
conductor losses due to factors such as surface roughness. The values
here are therefore m aximum values for the loss of the BST layer. . . .
6.1 Fractal model of film m icrostructure...............................................................
99
106
6.2 Nom enclature for grain boundary and bulk contributions at scale level
j= 3 ...........................................................................................................................
107
6.3 F itting the model to experim ental d ata. The solid line represents the
model fit and the points are experim ental d a ta ..........................................
xvi
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110
L ist o f A cron ym s and C om m on U n its
AFM
Atomic Force Microscopy
BST
Barium Strontium T itan ate
CPW
Coplanar Waveguide
CVD
Chemical Vapour Deposition
DRAM
Dynamic Random Access Memory
er
Relative Dielectric C onstant
HFSS
High-Frequency Sim ulation Software
JC PD S
Joint Com m ittee on Powder Diffraction Standards
LCR
Impedance Capacitance Resistance M eter
M BE
Molecular Beam Epitaxy
MMIC
Monolithic Microwave Integrated Circuit
MOCVD
M etallorganic Chemical Vapour Deposition
MOD
M etallorganic Decomposition
PLD
Pulsed Laser Deposition
PZT
Lead Zirconium T itan ate
Q
Q uality Factor, Q = l / t a n S
SEM
Scanning Electron Microscopy
SLF
Spur-Line Filter
ta n 5
Loss Tangent, ta n J = l / Q
TEM
Transmission Electron Microscopy
TR L
Through-Reflect-Line VNA C alibration
VNA
Vector Network Analyzer
XRD
X-ray Diffraction
GHz
109 s” 1
/rm
10-6 m
e0
8.85xl(T 12 C2/N m 2
xvii
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C hapter 1
Introduction
1
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1.1
P r o je c t G oal
There is currently a desire to be able to deposit high perm ittivity ceramic films
on novel substrates such as gallium arsenide (GaAs) and plastics for various appli­
cations. This presents challenges since conventional ceramic fabrication techniques
involve high processing tem peratures which the new substrates cannot w ithstand.
New techniques for the deposition of such films m ust be developed if these substrates
are to be exploited.
In high frequency applications such as m onolithic microwave integrated circuits
(MMIC) GaAs is often preferable to silicon for use as a substrate due to its high
electrical carrier mobility. In GaAs carriers react to high frequency microwaves and
effectively switch electrical currents in com munications systems faster th a n do silicon
devices. GaAs can be exposed to tem peratures less th a n 200°C for extended periods
of time, and to tem peratures as high as 350°C for tim es less th an 10 minutes. If
exposed to tem peratures over 350°C for longer periods, ohmic contacts and m aterial
stoichiom etry begin to degrade. At 400°C th e contacts degrade rapidly so heat cycles
have to be on the order of 30 seconds at this tem perature. Because of this lim itation, a
technique for depositing ceramic films at tem peratures below 200°C is desirable. The
development of such a low -tem perature technique would also allow th e deposition of
ceramic films on other tem perature-lim ited substrates such as polymers. This could
be useful for applications in flexible electronic circuits and flat panel displays.
Many applications of ceramic films require a m aterial w ith a high dielectric con­
stant and low loss tangent. Barium strontium tita n a te (BST) is a m aterial which has
been shown to have good behaviour in these areas. The dielectric constant has re­
ported to be as high as 5000 at kHz frequencies in bulk BST [1], Applications include
capacitors, tunable microwave devices, electronically tunable mixers, delay lines, fil­
ters, oscillators, resonators, phase shifters[2], therm istors, capacitative sensors[3], re­
duction of voltage fluctuations on bypass capacitors [4, 5], DRAMS [5], and reduction
2
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of lead inductance by placing structures on chip [5]. Lead inductance becomes espe­
cially im portant at high frequencies, since Z^ocujL (where
is the im pedance of the
inductor, L is the inductance, and u is the angular frequency of operation). Limited
chip space discourages on-chip integration, bu t w ith the high er value of BST, element
size can be reduced.
Concerns exist about the integration of BST into current clean-room environ­
ments, as it is considered an exotic m aterial, and contam ination and safety are of
issue. W ith a closed-system process, such as the one developed here, these issues can
be addressed.
1.2
B ariu m S tro n tiu m T ita n a te
1 .2 .1
C h a r a cter istics
Barium strontium tita n a te (BST, B a^Sri-^TiO a) is a m aterial of interest due to
its high relative dielectric constant (er ), which provides a high capacitance per unit
volume. This allows for m inim ization of th e size of capacitative elements on integrated
circuits in tu rn reducing cost. W ith x=0.7, B a^Sri.^T iO s is cubic and paraelectric at
room tem perature. Ceramic compositions w ith x> 0.7 are ferroelectric and tetragonal
at room tem perature, and those w ith x ^ 0 .7 have lower relative dielectric constants [5].
At room tem perature, er is a m axim um at x=0.7, and ta n h is a minim um at x= 0.5 (as
low as 0.0015), but has a reasonably low value at x= 0.7 (as low as 0.006). T he value
of er can be as high as 5000 [1] for bulk BST. The BST end-member, B a T i0 3 (barium
titan ate), has a pronounced m axim um in er at its Curie tem perature, T c, which is
395 K. Below T c, barium tita n a te is ferroelectric, and above, it is paraelectric. For
many applications, it is desirable to have a high relative dielectric constant near room
tem perature. S ubstitution of strontium (Sr) for some of the barium ions in B a T i0 3
has the effect of shifting the Curie tem perature. Since th e other BST end-mem ber,
S rT i0 3 (strontium titan ate), has a Curie tem p eratu re of T c ~ 20 K; depending on
3
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the Ba:Sr ratio the Curie tem perature of BST can be anywhere between 20 K and
395 K.
The electrical resistivity of BST is fairly constant over the full compositional range.
This is due to the fact th a t B a T i0 3 and S rT i0 3 have the same crystal structure, and
Ba2+ and Sr2+ have comparable ionic radii [3]. A slight decrease in resistivity for
x ^ l and x^O may be attrib u ted to m igration of additional point defects due to
compositional inhomogeneity[3].
BST crystallizes in the perovskite structure ABX3 shown in Fig. 1.1. The high
dielectric constant of BST is a result of ionic displacement, unlike m aterials w ith
lower dielectric perm ittivity such as SiC>2 , which exhibit electronic displacement only
as a result of a changing applied voltage [5].
Titanium
£
O xygen
Barium / Strontium
Figure 1.1: The perovskite structure of barium strontium tita n a te (BST).
As shown in Fig. 1.1, when free of applied voltage th e titan iu m ions are centered
4
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w ithin th e six surrounding oxygen, which are in an octahedral formation.
Under
these conditions, the dipole moments cancel. W ith an applied voltage, however, the
titan iu m ions are displaced, and a dipole moment p =q<5 (where q is the charge, and
8 is the separation between the charge centres) is induced.
X -ray diffraction studies of BST powders of various compositions prepared by
conventional solid-state powder processing techniques from BaTiOa and SrTiCU pow­
ders show th a t in all cases where x ^ l and x^O in B a^ S rp -^ T iO a, the B a T i0 3 and
S rT i0 3 peaks either disappeared (usual for B a T i0 3 peaks) or split w ith reduced inten­
sity (sometimes for SrTiCU peaks). This is explained by the fact th a t the form ation
of solid solutions in this case is governed by th e preferential diffusion of Sr2+ ions into
B a T i0 3, rath er th an diffusion of B a2+ [3].
The effect of average grain size on Bao.7Sr0.3T i0 3 powders produced by a sol-gel
technique has been examined [6]. It was found th a t at 273 K at 100 kHz, er was largest
when the average grain size was 1 gm. W ith larger grains there was a slight decrease
in er w ith increasing grain size. For grain size smaller th a n 1 //m, there was a sharp
decrease in er w ith decreasing grain size. T he Curie tem perature of BST decreased as
the grain size decreased. In another study, th e highest value of the dielectric constant
(5000) was obtained for fine-grained bodies, w ith grain sizes between 0.7 and 1 n m
[7]-
1 .2 .2
C h e m ica l R o u te s for B S T P r o d u c tio n
There are many different approaches to th e fabrication of BST in powder and him
form. BST powder may be formed via sol-gel processes [6], precipitation from catecholate precursors [8], solid-state techniques, and hydrotherm al techniques.
BST films m ay be deposited via m etal-organic decomposition (MOD) [5], pulsed
laser deposition [9], sol-gel techniques, chemical vapour deposition (CVD, M OCVD)
[10, 11], reactive sputtering [12], molecular beam epitaxy (MBE) [9], and radio fre-
5
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quency sputtering [13]. These techniques generally require high tem peratures of 700
to 800°C to crystallize the film a n d /o r remove im purities and organic residues.
M etallorganic decomposition (MOD) techniques involve high tem peratures, but
have the advantage of easy deposition, and stoichiometric control. Sputtering has
the disadvantage th a t stoichiometric control is more difficult. Oxides also have low
sputtering rates, and resputtering effects are of concern. Precursor control in chem­
ical vapour deposition (CVD) processes can be difficult. Laser ablation techniques
are difficult to scale up, and often result in a large num ber of particles comprising
the film [5]. Sol-gel techniques have also been used to deposit BST, b u t these typi­
cally require a high-tem perature (>500°C) firing stage to crystallize the ceramic, and
remove residual organic contam inants and solvents.
Conventional hydrotherm al processing of BST in which a titan iu m or T i 0 2 layer is
converted to BST at high pressure, is able to produce crystalline BST at tem peratures
below 300°C. Fundam ental lim itations of the process, however, limit th e reaction to
part of the precursor leaving m ost of the film as Ti or T iO x even for films as th in as
0.05 /im.
1 .2 .3
D o p in g o f B S T
There have been attem pts to increase the perm ittivity a n d /o r lower the loss tangent
of BST by doping the compound w ith various elements. One of the m ost promising
dopants is manganese.
The precise m ethod by which Mn doping affects BST is
not known however it is reported th a t Mn doping changes BST electrical properties
(lowers er and ta n 8) and m icrostructure by acting as an effective acceptor dopant,
and tending to stabilize a hexagonal phase [14]. The behaviour of thin films can be
greatly affected by their interfaces w ith substrates and superstrates, as the interface
may constitute a large percentage of the film itself. In the case of BST in contact
w ith Pt, the Fermi levels of the two m aterials equilibrate by depleting carriers from
6
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the BST. This results in band bending, which shifts the core levels of the BST [15].
An undoped thin him sample of BST has a depletion w idth com parable to the him
thickness, while a sample w ith a few percent Mn has a depletion w idth much greater
th an the him thickness. Consequently, the core levels of th e undoped sample undergo a
large shift upon m etallization, whereas the core levels of the doped sample are already
at their m etallized position, and undergo very little shift upon actual m etallization.
This was observed by Copel et al. [15] in Mn doped BST th in hlms fabricated by
chemical solution deposition (CSD) and m etallorganic chemical vapour deposition
(MOCVD).
1.3
H y d ro th erm a l P r o cessin g
The term hydrothermal processing refers to th e treatm en t of a sample in an aqueous
solution at elevated tem peratures and pressures. This type of process is responsible
for the form ation of many minerals in n atu ral geologic settings, and has been adapted
for the synthesis of m aterials in the laboratory. In this study, hydrotherm al processing
is used to synthesize BST.
1 .3 .1
C o n v e n tio n a l H y d r o th e r m a l P r o d u c tio n o f B S T from
In o rg a n ic P recu rso rs
H ydrotherm al processing has been employed to produce BST as both powder
and films.
Powder precursors include anatase TiC >2 powder [16, 17] and mixed
an atase/ru tile T i 0 2 nanosized powder [17]. T hin film precursors include titan iu m
foils [18, 19, 20, 21], single crystal TiC>2 , single crystal SrTiC >3 w ith anatase TiC >2
powder in suspension [22, 16], and metallic T i thin films on various substrates includ­
ing SiO2/p-Si(100) [23], Si(100) [24], P t/S i [25], P t/T i-W /S i [26], n-Si(lOO) [27, 28],
and polypheylene sulphide [29]. It has been shown th a t when hydrotherm ally pro­
cessed in alkaline solutions containing B a2+ and Sr2+ ions, these precursors can be
7
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converted to BST.
XRD studies indicate th a t these m ethods do produce crystalline BST. In th e case
of th in films little stoichiometric and electrical d ata have been published, however.
Generally, BST thin films produced from metallic Ti remain highly conductive as a
result of excess Ti in the film. Similar astoichiom etry is expected in films produced
from TiC>2 .
1 .3 .2
H y d r o th e r m a l P r o c e ss in g w ith O rganic P re cu rso r s
BST has been synthesized by hydrotherm al means from organic precursors. These
m ethods combine chemically and therm ally induced reactions to synthesize the desired
oxides, to crystallize them , and to remove residual im purities such as organic m aterials
and solvents such as alcohols and water. For example, BST powder has been produced
using an alkoxide-hydroxide type reaction by Hyashi et al. B a(0H )2-nH 20 (n ~ 1)
and Sr(O H ) 2 were dissolved in m ethanol, then mixed w ith titan iu m isopropoxide
and refluxed at room tem perature.
Evaporation of the m ethanol then resulted in
the precipitation of a free-flowing white powder. This powder was then crystallized
and hydrolyzed at 100°C in an N2/w a te r vapour atm osphere [30]. W hile the raw
powder was amorphous and contained organic residues the hydrolyzed powder was
single-phase Ba0.7 Sro.3 T i 0 3.
Using the alkoxide-hydroxide route noted for powders above, Hayashi et al. pro­
duced thin film BST on P t/T i/S iC U /S i substrates [30], by spinning on the precursor
solution, and then treating the film in a mixed oxygen/w ater vapour atm osphere at
150°C, and then in oxygen at 650°C.
T h e C hem istry o f C rystallization w ith H ydroxides
In sol-gel processing of barium and strontium tita n a tes one m ajor problem is the
spontaneous self-condensation between the Ti-OH groups. This leads to th e form a­
tion of Ti-O-Ti clusters, and hence a heterogeneous distribution of Ba, Sr, and Ti
8
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ions. This may lead to precipitates consisting of hydrated TiC >2 and alkaline earth
carbonates, rath er th an the desired tita n a te products. This may be avoided by the
use of chelating agents to complex the Ti ions. This results in oxalate or citrate salts
which may then be therm ally decomposed to result in the desired oxides. U nidentate
ligands, such as alkoxy or carboxyl groups may also be used. Again, the resulting
compounds may be therm ally decomposed to produce the desired oxides.
An alternative to a therm al treatm ent to convert the complex organic precursors
to the final oxide is the use of a chemical treatm ent. The presence of a highly alkaline
solution can lead to direct condensation between Ti(OH)g- and Me2+ (M e=Ba, Sr)
ions to form the tita n a te compound. Again in this case, self-condensation between
Ti-OH groups m ust be carefully controlled, to prevent deviations from the desired
stoichiometry.
1 .3 .3
S o l-G e l-H y d r o th e r m a l S y n th e sis o f C era m ics
The ability to produce ceramic th in films from sol-gel precursors by way of a hy­
drotherm al treatm ent was dem onstrated in 1999 by Jianm ing Zeng et al. They were
able to produce crystalline P b (Z r0.52Tio.48)03 (PZT) [31, 32] and BaTiC >3 [33] at tem ­
peratures below 200°C. Films were deposited on platinized silicon. In th e case of
PZT, the films were processed in a 0.1 M solution of P b (O H )2 in a sealed autoclave,
between 100° C and 200° C for between 1 and 6 hours [34],
C rystallization P rocesses during H ydrotherm al P rocessin g o f Organic P re­
cursors
Work by Bucko et al. [35] on the hydrotherm al crystallization of zirconia powder gives
some insight into possible mechanisms by which crystallization of a sol-gel in an alka­
line aqueous solution may occur. In the case of zirconia, two possible mechanisms for
crystallization have been previously suggested. Nishizawa et al. [36] p o stu lated th a t
there occurred a spontaneous coalescence of highly ordered zirconia crystallites into
9
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elongated monoclinic crystals, w ith no dissolution/recrystallization occurring. A lter­
nately, Tani et al. [37] suggested th a t a dissolution/precipitation process is entirely
responsible. Work by Bucko et al. showed th a t both of these processes may act. A
zirconia gel, zirconia crystallites, and a zirconia gel containing zirconia crystallites
were separately treated hydrotherm ally in NaOH. The kinetics of the reaction in the
third (mixed) case were the fastest. Both growth of new crystallites, and dissolu­
tion/recrystallization of existing crystals were observed. It is hypothesized here th a t
a similar technique may be used to grow BST films hydrotherm ally in a gel. It was
expected th a t the tita n a te powders used in sol-gel composite processing may behave
similarly to the crystallites used to seed the zirconia gel, in th a t they will act as
dissolution/ recryst allization sites.
1.4
S o l-G el C o m p o site H y d ro th erm a l P r o cessin g
It is proposed th a t in addition to hydrotherm ally crystallizing sol-gels, it would be
advantageous to seed the precursor gel w ith crystalline powder of the desired ceramic.
This may enable the gel to crystallize more readily, as it prevents nuclei from having
to form spontaneously. The final film m ay also benefit from the presence of dense
particles which have properties th a t more closely approxim ate those of a bulk sample.
If epitaxial growth of sol-gel derived BST on th e surface of powder particles can be
induced, the contribution of grain boundaries to the behaviour of the final film will
be reduced.
1.5
O u tlin e o f T h esis
In this thesis the efficacy of hydrotherm al processing in producing high quality BST
films is evaluated. The effect of varying process param eters on th e m icrostructure and
electrical characteristics of the films is examined. T he perm ittiv ity and loss tangent
of the films at kHz frequencies are m easured using parallel plate capacitors. High
10
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frequency (GHz) electrical characterization is achieved by way of a series of coplanar
waveguide structures. The results are explained in term s of the evolution of a highlyconnected m icrostructure with few barriers unique to hydrotherm al processing of
sol-gel composites.
11
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Chapter 2
Experi mental Me t ho d
12
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2.1
S o l-G el C o m p o site P rep ara tio n
An acetic acid-based sol-gel w ith a barium to strontium ratio of 70:30 was used. The
precursor sol-gel was produced by dissolving appropriate am ounts of barium acetate
((CH 3C O O )2Ba, BDH Limited) and strontium acetate ((CH3COO)2Sr-0.5H2O, Alfa
Aesar) in deionized water. This solution was added to a m ixture of titanium butoxide
(T i[0 (C H 2)3CH3]4, Aldrich Chemical), acetic acid (Aldrich Chemical), and m ethanol
(Fisher Chemical), and agitated, producing a clear, colourless liquid. The sol-gel was
stable for three days. This stability tim e could be increased to seven days by a three­
fold increase in the am ount of m ethanol added. Table 2.1 shows the mass of each
reagent used. The flowchart in Figure 2.1 shows the order of mixing.
R eagent
T itanium (IV) Butoxide
Acetic Acid
M ethanol
Deionized W ater
Barium A cetate
Strontium A cetate (0.5 H20 )
M ass U sed (g)
3.66
8.00
3.00
6.00
4.03
3.39
Table 2.1: Reagent masses used to fabricate BST sol-gel.
The BST powder was prepared by combining appropriate am ounts of barium
carbonate (Aldrich Chemical Company), strontium carbonate (Fisher Chemical), and
titanium dioxide powders (Fisher Chemical). The powders were ball-milled dry with
alum ina balls to promote mixing, fired in air for 20 hours at 1100°C in an alum ina
crucible, and then ball milled again to break up the resulting mass of BST. This
produced a powder w ith particles w ith an average diam eter of 0.3 /mn, as determ ined
from SEM images.
Adding the BST powder to the sol-gel produced th e sol-gel composite. In this
study, unless otherwise stated, the ratio of th e mass of the powder to the mass of the
sol-gel is 1:1. The m ixture was agitated in an ultrasonic mixer for five hours in order
13
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to break up any agglomerated particles and to distribute the powder throughout the
sol-gel.
Films using a 2-methoxyethanol based sol-gel were also produced for comparison,
using a similar m ethod with 2-methoxyethanol in place of acetic acid as a solvent.
Sol-gel composites were also produced using powder and sol-gel doped w ith 5 at%
Mn. Powder doping was achieved by adding the appropriate am ount of manganese
carbonate (Acros) to the titanium dioxide and barium and strontium carbonates th a t
were fired to produce the tita n a te powder. Sol-gels were doped by adding manganese
acetate (Acros) w ith the barium and strontium acetates.
Titanium (IV)
Butoxide
Acetic
Add
Deionized
Water
Methanol
agitate
until
dear
agitate
until
dear
Aqueous
Solution
agitate
until
dear
BST Sol-Gel
ultrasonic
agitation
BST Sol-Gel
Composite
Figure 2.1: Flowchart of BST sol-gel composite production.
14
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2.2
F ilm D e p o sitio n
Films were fabricated by spin-coating the sol-gel composite onto substrates such as
platinized S i/S i0 2 and A120 3. Each layer deposited was dried on a hot plate at
150°C for 10 minutes, and hydrolyzed above a hot water b a th for 10 m inutes to
prevent dissolution upon immersion in the hydrotherm al solution.
For the sol-gel
composites w ith a mass ratio of powder to sol-gel of 1:1, a spin-rate of 3000 rpm
for one m inute produced a single layer 2.6 fxm thick. Variations in the constituents
of the sol-gel composites (such as varying the relative am ount of powder) required
the spin-rate used for deposition to be altered to m aintain a constant film thickness
between samples.
2 .2 .1
B S T P e lle t F a b rica tio n
Porous pellets of BST were produced from BST powder synthesized as outlined above.
The BST powder was mixed w ith 5% by mass m ethyl cellulose which acts as a binder.
The m ixture was pressed in a jig of 6.50 m m diam eter under a pressure of 1 to n /sq u are
inch. The pellets were allowed to dry overnight and then were fired at 300°C for 1
hour, at 500°C for 20 minutes, at 600°C for 20 m inutes, and finally at 1000°C for 3.5
hours, then were allowed to cool. The resulting pellets were of various thicknesses in
the range 0.5-2.0 mm.
Some of the pellets were immersed in a BST sol-gel overnight to allow the sol-gel to
perm eate the pores of the pellet. These pellets were th en dried on a hot plate at 150°C
for 20 minutes, and hydrolyzed over a hot w ater b a th for 10 m inutes. T hen th e pellets
were subjected to hydrotherm al processing at 150°C in a 0.3 M (B a,S r)(0 H )2-8H20
solution for 3 hours.
The circular faces of some of the pellets were coated w ith gold by sputtering to
allow electrical contacts to be made. O ther pellets were prepared for cross-sectional
exam ination by cleaving them perpendicular to th e circular face, as shown in Fig.
15
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2.2. T he cleaved samples were embedded in acrylic and polished to present a clear
cross-section. The samples were examined using a SEM.
cleaved pellet face
circular
pellet
faces ~
Figure 2.2: Schematic of circular and cross-sectional pellet faces.
2.3
H yd roth erm a l P r o cessin g
The hydrotherm al solution was prepared by dissolving appropriate am ounts of
B a (0 H )2-8H20 and S r(0 H )2-8H20 (Aldrich Chemical Company, Inc.) in deionized
w ater which had been boiled for 10 m inutes to remove dissolved C 0 2. The disso­
lution was carried out under a nitrogen atm osphere to prevent the precipitation of
B a2+ and Sr2+ from the solution as carbonates. Once dissolution of the hydroxides
was complete, the sample was transferred into the hydrotherm al solution, which was
contained in a Teflon vessel, and was sealed inside an autoclave, as shown in Fig.
2.3. The vessel was purged w ith nitrogen, again to prevent the precipitation of the
anions as carbonates. The pressure inside the vessel was autogeneous, and close to
the vapour pressure of pure water. The tem perature of the vessel was controlled via
a feedback loop to an external heater. Typical processing tem peratures were between
50°C and 200°C, yielding pressures between 1 and 15 atm ospheres. After th e allot­
ted processing tim e and cooling for 1 hour, the vessel was opened; the sample was
removed from the solution, rinsed in deionized w ater, and dried in a stream of air.
16
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Pressure
< 1 5 atm
Temperature
< 200°C
(Ba,Sr)(0H)2 -8H2 0
solution
Sample
Teflon
beaker
Heater
Figure 2.3: Schematic of the autoclave used for hydrotherm al processing.
2 .3 .1
P u r g in g o f th e H y d r o th e r m a l V e ss e l w ith N itr o g e n
To determ ine the time needed for nitrogen flow-through to adequately purge the
hydrotherm al vessel of carbon dioxide, the following analysis was used:
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Nitrogen in
at F I/s
G as mixture
out at F I/s
R
Hydrothermal
V essel
Nitrogen
Tank
Figure 2.4: Purging the hydrotherm al system of CO 2 .
Ignoring any transient pressure changes, at equilibrium, nitrogen flows from the
tank of compressed nitrogen at F i/ s , into vessel V (the vessel to be purged), and the
m ixture of nitrogen and air leaves vessel V at the same rate as in Fig. 2.4.
Assuming instant homogenization of the gases in vessel V, if X (t) is th e num ber
of litres of CO 2 in V at tim e t, then
dX(t)
dt
W ) iX
'■(?)
X(t)
X(t)
-F
V
( 2 . 1)
X 0e - 7 ‘.
( 2 .2)
=
-
=
where Xo is the initial num ber of litres of C O 2 in vessel V at tim e t= 0 .
In order to prevent precipitation of B a2+ and Sr2+ from the solution as carbonates,
the maximum allowable concentration of CO 2 in the atm osphere is 10~5 moles of CO 2
18
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per kilogram of other gases [38].
Air, by volume percent, consists of: 78.084 N2, 20.946 0 2, 0.033 C 0 2, and 0.934
other gases [39].
L etting there be c litres of C 0 2 in V at time t= 0 , and ignoring the 0.934 vol% of
other gases, the air in V consists of:
0 . 78(14 — c)
litres
N2
0.21(14 —c)
litres
02
c litres
C02
Determ ining the mass of N2 and 0 2 in V at tim e t= 0 ,
at a pressure of
1
and tem perature of 298 K, and R = 0 .08206 L- atm / K- mol, taking c ~ 0 ju st for this
calculation, as C 0 2 forms only a small percentage of the volume, gives 0.032-V mol
N2, and 0.0086-V mol 0 2. W ith the respective m olar masses npv2 = 28 g/m ol and
m o2 = 32 g/m ol, this gives a to tal mass of N2 and 0 2 of 1.17-Vg.
Using the fact th a t the maximum allowable concentration of C 0 2 in th e atm o­
sphere is 10-5 moles of C 0 2 per kilogram of other gases, this allows a m axim um of
1(U8-V mol C 0 2.
W ith the regulator set at 20 psi, the flow rate F is m easured with a M atheson
flowmeter to be 1.4 £/m in. In this study, th e pressure vessel has a volume of 1
and therefore can be adequately purged in 10 m inutes, including additional tim e to
account for the lack of instantaneous mixing of gases in the vessel.
2.4
F ilm P a ttern in g
In order to determ ine the high-frequency response of th e films, they were deposited on
a set of coplanar waveguides w ith spur-line filters. It was necessary to make contact
to the ends of each line, so a window had to be left in the BST film at these locations.
This was done via a lift-off photoresist technique, as outlined in Fig. 2.5. T he C PW
19
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
atm ospher
structure was first coated w ith HP 504 photoresist, spun on at 3000 rpm for 1 minute.
This film was dried on a hot plate at 120°C for 1 minute, and then exposed to UV
radiation through an appropriate mask for 2 minutes.
The photoresist was then
developed, leaving blocks only at the ends of the CPW lines. The BST film was then
deposited as outlined earlier. Once th e desired film thickness had been deposited, the
sample was immersed in acetone in a ultrasonic mixer, which caused th e photoresist
to dissolve, lifting off the ceramic film above. The sample was dried in a stream of
air, and hydrotherm ally processed as outlined earlier.
The exposure of the film to acetone has no discernible effect on the film. There is
no m easurable thickness change, and th e low-frequency behaviour of the films is the
same as the films not exposed to acetone. This makes the lift-off technique preferable
to etching the BST, as this requires exposure of the film to harsh etchants.
2.5
A n a ly sis T echniques
2 .5 .1
X -ra y D iffra ctio n A n a ly sis
X-ray diffraction (XRD) studies were carried out to examine the crystallinity and
composition of the powders and films. Powder studies were completed on a Phillips
X ’Pert XRD Analyzer with Cu K a radiation at a wavelength of 1.54 A. Film studies
were perform ed using a Rigaku XRD analyzer w ith Cu K a radiation or Cr K a radi­
ation with a wavelength of 2.29 A. In the case of films, a glancing angle of incidence
(2°) of the beam was used.
20
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deposit
photoresist
mask and expose
to UV radiation
develop
photoresist
deposit top layer
to be patterned
remove photoresist
by ultrasonic
agitation in acetone
Figure 2.5: The lift-off photolithography process for p attern in g of films.
Bragg angle conversion between Cu and C r radiation is achieved through the
formula
/3 6 0 \
2 0 Cu =
1a s m
1.54
( 2 0Cr
sin
,
2.29
\ 2 ' '
(2.3)
K ;
Peaks are fit w ith the analysis software Origin, using G aussian fits. Com pound
identification is achieved by comparison of the experim entally obtained peaks w ith
d ata from the Joint Com m ittee on Powder Diffraction S tandards (JC PD S) database.
Lattice constants are determ ined by indexing th e XRD peaks w ith the appropriate
(hkl) param eters. For a cubic structure (as is th e case w ith perovskite m aterials like
21
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
BST), one has
2dsinO =
nX,
(2.4)
(2.5)
VW TW +P’
where 29 is the Bragg diffraction angle, A is th e wavelength of the radiation used, d
is the spacing between lattice planes, and a is the lattice constant of the m aterial.
2 .5 .2
F ilm T h ick n ess D e te r m in a tio n
Film thickness measurements were made by a force feedback tip, the R ank Taylor
Hobson ’T alystep’ profilometer. The tip of the device is dragged over the surface of the
film, and the force on the tip is monitored. This is calibrated to give a m easurem ent
of the thickness of the film under test.
2 .5 .3
Im a g in g T ech n iq u es
Scanning electron microscopy (SEM), atomic force microscopy (AFM), and transm is­
sion electron microscopy (TEM) were used to examine the m icrostructure of the films.
Images were taken w ith a JEO L 740 SEM and a NanoScope M ultimode AFM . TEM
studies were perform ed by Dr. Joke H aderm an of The University of Antwerp.
2 .5 .4
L o w -F req u en cy E le c tr ic a l C h a r a c te r iz a tio n
The relative perm ittivity and loss tangent of th e BST films were determ ined by use
of parallel plate capacitors. A platinum layer on the su b strate served as a bottom
electrode, and a gold top electrode was deposited on the processed BST film under
test by vacuum evaporation through a shadow mask. The top electrodes were circular,
w ith a diam eter of 0.15 mm. Capacitance and loss tangent m easurem ents were made
between 1 and 100 kHz using a H ew lett-Packard 4284A Precision LCR Meter.
In the case of a parallel plate capacitor, the capacitance, C, is given by
er eoA
d
_
22
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
( 2 ,6 )
where er is the relative perm ittivity of the capacitative m aterial, eo is the perm ittivity
of free space, A is the area of the electrode and d is the spacing between th e electrodes.
2 .5 .5
H ig h -F req u en cy E le c tr ic a l T est S tr u c tu re s
A m ethod by which the dielectric constant of a thin film m aterial can be measured
up to 40 GHz has been developed by Hany F. Hammad of the Q ueen’s University
D epartm ent of Electrical Engineering [40]. The technique makes use of th e response of
C PW band-stop filters to estim ate the dielectric constant of the film. M easurem ents
can be made at frequencies up to 40 GHz.
CPV\K
Figure 2.6: Top view of the coplanar waveguide structure used for microwave fre­
quency characterization of BST films.
The configuration used is th a t of a C PW w ith spur-line band-stop filter, as shown
in Fig. 2.6. The signal is sent down the central line of th e structure, while th e two
outer lines act as grounds. The response of the structure is measured in term s of a
s-param eter test set. The power tran sm itted from port 1 to p o rt 2 is denoted s2i and
is the key to use of this structure for determ ining characteristics of dielectric films.
The structure can be modeled as a 50 Q transm ission line w ith a shorted quarterwavelength stub in the centre. At a signal frequency, F c, having wavelength equal to
the length of the quarter-w avelength stub, th e short moves to an open at th e tran s­
mission side end. At F c, the input signal is to tally reflected, and the in p u t/o u tp u t
ports are totally isolated.
23
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
The centre frequency of the filter can be accurately calculated from [41]
Ac p w
4
Aq
4\ / m
c
(2.7)
vV TxT)
where L is the spur-line length, Ac p w is the C PW guided wavelength, A0 is the
free space wavelength, c is the speed of light in vacuum, and ee/ / ( / ) is the frequencydependent effective dielectric constant. Rearranging the final equality in equation
2.7 for the case where the effective dielectric constant of the structure is known as a
function of frequency, the band-stop filter centre frequency can be calculated from
(2 . 8 )
The effective dielectric constant of the structure can also be determ ined using the
analysis software HFSS (High-Frequency Simulation Software) from Ansoft which uses
finite element analysis to determ ine the response of a given structure. Use of this tool
has several advantages over other m ethods as some (as in [42]) do not consider the
effect of the finite ground plane w idth of the CPW . O thers (as in [43]) do consider this
factor, b u t calculate the effective dielectric constant independent of the frequency of
operation. The intersection of the curve for er calculated by HFSS and the expression
for er given by equation 2.8 gives th e centre frequency of th e band-stop filter, F c.
The ceramic under test is deposited in a layer over th e C P W structure, shifting
the centre frequency from F c to F c'. The size of the shift is dependent on th e partic­
ular cross-section of the C PW structures and of the ceramic coating, as well on the
relative dielectric constant of the ceramic, eceramic. In order to determ ine eCeramic as a
function of F c', HFSS is used to simulate the structure. The m easured F c' can then
be compared w ith the values predicted by the sim ulation in order to determ ine the
V a lu e
of
^ceram ic-
The test structures are p attern ed in gold on alum ina by Nanowave Technologies
Inc. The cross-section of the gold p attern is exam ined by cleaving the sample through
the middle of the structure, perpendicular to th e length of th e C P W ’s. The sample
24
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
is th en m ounted in acrylic, and polished to present a clear cross-section under an
optical microscope.
N etw ork A nalyzer Calibration
It is necessary to calibrate the response of the network analyzer to account for
im pedances of the probes and leads used. In this case, a through-reflect-line (TRL)
type calibration is used. In this calibration, a short through line, an open reflect line,
and a longer line are probed. The response of these structures is determ ined, and is
used to calibrate the base response of the network.
Sim ulations
The response of the test structures is sim ulated in the program High Frequency Sim­
ulation Software (HFSS) which uses finite element analysis to determ ine the response
of the structures. The geometry of the structures is defined in three dimensions, ta k ­
ing into account the dimensions and cross section of each line. The alum ina substrate
is taken to be infinite in thickness and extent in the plane of the te st structures.
M aterials are defined in term s of their conductivity, perm ittivity, and permeability.
2 .5 .6
C o m p le x Im p e d a n c e A n a ly sis
The BST film can be modeled as a series com bination of two parallel RC elements,
as shown in Fig. 2.7. One of th e RC elements represents th e average contribution
of the bulk to the to tal impedance of the film. The other RC element represents the
average contribution of grain boundaries to th e to ta l impedance. O ther RC elements
representing the film-electrode interface or th e capacitance due to the porosity could
also be considered b u t are unnecessary in this case.
25
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
AAr
A
N
c gb
c bulk
Figure 2.7: Equivalent circuit model for BST films and pellets used to calculate
complex impedances.
T he to tal complex impedance of the film, Z = Z' + iZ" is given by
Z'
=
Z"
=
Rl
i?2
+
1 + {uiRiCi)2
1 + {U1R2C2)2
ujR\C\
ujR2C2
+
{uR^Ci
0UR 2C 2)2'
(2.9)
( 2 . 10)
The complex impedance is related to the complex modulus, M = M' + iM", via
M = iooCnZ
(2 .11)
g iv in g
M' =
M" =
(uRiCi
(UJR2C 2
Co
+ § i
C!
C N l + i u R ^ ) 2]
C2 \ 1 + {ojR2C2)2J'
ujR \C i
Cn
L0 R 2C 2
Co
+
Cx
(2 .12)
(2.13)
where C q is the vacuum capacitance of the cell. In the preceding equations, Ft,- and
C j, j = 1,2 are the grain and grain boundary resistance and capacitance, respectively.
The complex modulus can be calculated from the complex perm ittivity, e = e'+ie"
since
M = e-1 .
26
Reproduced with permission o f the copyright owner. Further reproduction prohibited without permission.
(2.14)
The real component of the perm ittivity, e', can be determ ined from measured
capacitance values and the geometry of the test structures used. In the case of the
parallel plate capacitors
where eo is the perm ittivity of free space, C is the measured capacitance value, d is
the film thickness, and A is the area of the top electrode.
The im aginary component of the perm ittivity, t" , can be determ ined from m ea­
sured loss tangent values and e' via
e"
tan5 = —.
e
(2-16)
If the im aginary component of the impedance for a single RC element is plotted
against the real p art of its im pedance the locus is a semicircle. A similar plot of the
im pedance for two RC elements connected in series yields two superim posed semicir­
cles. By varying the values of R and C for each component, a h t to measured d a ta can
be obtained. The R and C values giving the best fit indicate th e average resistance
and capacitance of the him component (bulk or grain boundary) represented by th a t
RC element.
27
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Chapter 3
Microstructural Changes During
Hydrothermal Processing
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
3.1
A tte m p te d F ab rication o f B S T T h in F ilm s
from M eta llic T ita n iu m Film s
The initial approach in developing a low -tem perature m ethod for the fabrication of
th in film BST was to hydrotherm ally treat a titanium m etal film in a solution of
barium and strontium hydroxides. T itanium films were deposited on various sub­
strates (including S i/S i0 2/P t , alumina, and glass) by RF sputtering, and bulk Ti foil
samples were also treated. H ydrotherm al treatm ent proceeded in a m anner similar
to th a t described for the sol-gel composite films. After hydrotherm al processing, the
films were dark and lustrous, w ith colours ranging from blue to yellow, depending
on the particular conditions of the hydrotherm al process used. Glancing angle XRD
studies of a typical film on S i/S i0 2/ P t produced by this m ethod (Fig. 3.1) show
characteristic BST peaks, as well as the P t ( l l l ) peak from the substrate, and the
Ti(101) peak characteristic of residual, unreacted titanium . Films produced by this
m ethod rem ained highly conductive supporting the idea th a t only a thin surface layer
of the film reacted w ith the m etal producing BST leaving the resulting film rich in
titanium . The variation in colour of the films is taken to be indicative of varying
the thickness of BST film. Longer reaction times, higher process tem peratures, and
higher concentration of the hydrotherm al solution produced films w ith colour closer
to the yellow end of the spectrum rath er th a n blue. This is interpreted as a thicker
layer of BST. Despite this tren d towards thicker films, even at an extended reaction
tim e of 120 hours in a 1 M solution at 200°C, not all of a 50 nm layer of titan iu m
was reacted and the film rem ained highly conductive.
As all etchants for BST also etch titanium , the residual Ti could not be exposed
simply by etching off any reacted BST. Instead, the fact th a t the film rem ained highly
conductive was taken as evidence th a t th e com position of th e film was Ti rich. The
conductivity of the film was determ ined by fabricating a stru ctu re as in Fig. 3.2.
29
Reproduced with permission o f the copyright owner. Further reproduction prohibited without permission.
> >
</>
c
0
4—»
c
o
CO
1—
CsJ
20
Figure 3.1: XRD peaks of a hydrotherm ally processed Ti film. BST peaks are evident,
b u t so are peaks from residual Ti, and the underlying P t layer.
Titanium / BST
Gold Electrode
Gold Electrode
Alumina Substrate
Figure 3.2: S tructure used to determ ine th e residual conductivity of hydrotherm ally
treated titanium .
Even with the reaction conditions considered above, the gold electrodes in such a
structure could not be isolated from one another w ith th e reacted layer.
30
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
It is believed th a t the problem w ith this m ethod of BST production results from
the in itial high-density of the titan iu m him and the diffusion-limited ra te of reaction.
As th e layer of Ti in contact with the solution reacts, it forms BST. This layer
effectively seals off the rest of the titanium from the solution. Reaction of the rest of
the layer would require either diffusion of B a2+, Sr2+, and oxygen through the BST
into th e titanium , or diffusion of the titanium outw ard into the solution, as indicated
in Fig. 3.3.
Because of these lim itations production of BST films by hydrotherm al treatm ent
of m etallic titanium was deemed ineffective.
It is expected th a t similar problems
would arise in attem pts to produce BST beginning w ith TiOy.
Ba2+
*
1 1 1* U ^ m
*1* *
M I H I liB
substrate
Figure 3.3: Form ation of a barrier layer during the hydrotherm al processing of tita ­
nium.
3.2
P ow d er F abrication
The solid state technique described in the previous chapter used to produce BST
powder successfully fabricated a fine, white-yellow powder. The XRD p a tte rn of this
powder (Fig. 3.6) shows it to be BST. There are no crystalline carbonate nor TiCb
residues evident in the powder. If small am ounts of these im purities do remain, then
the acidic sol-gel will dissolve th e carbonates, and th e TiCb will be converted (at
31
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
least in part) to BST by the hydrotherm al process. A ddition of MnCC >2 produced
M n-doped BST powder, which was a brown colour. There were no additional peaks
over those on undoped BST powder evident in the XRD pattern.
3.3
B S T S ol-G el to w hich P ow d er H as N o t B ee n
A d d ed
XRD p atterns of non-composite sol-gel BST films hydrotherm ally processed in solu­
tions of various concentrations are shown in Fig. 3.4. All films were processed at
150°C for 2 hours. At concentrations of 0.1-0.3 M, the B S T ( lll) peak is evident.
The film processed at 0.3 M also shows additional BST peaks, indicating a greater
degree of crystallization over films processed in lower concentration solutions. Only
one BST peak is evident in the p a tte rn of the film processed at 0.5 M, as th e film
experienced significant desorption, likely due to the rapid attack of hydroxide ions on
the gel, not allowing sufficient tim e for redeposition of species before tra n sp o rt from
the substrate/solution interface occurred.
In all films except for the one treated in pure water, carbonate peaks (JC PD S
5-418, 5-378) th a t are large in comparison to th e BST peaks (JC PD S 13-522, 34-411,
39-1395) are evident. This indicates th a t the crystalline carbonates arise prim arily
through precipitation of carbonates from the solution ra th e r th an from th e residual
carbon in the sol-gel.
32
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c r —
m rn
•
CO
00
? = ---------------------- "
^
—
I
T_"
CM O
w
c o w
TCVJ
|—
\—
CO
,i
--------- ....................
• “
o CNI
CNI CNI
l IT lU T
cn
c
CD
cc
i—
-I—*
■
_Q
S_
<
^
T
b
a
20
30
40
50
60
70
80
20
Figure 3.4: The effect of hydrotherm al processing on th e structure of non-composite
sol-gel BST films. Each film is processed a t 150°C for 2 hours. The concentration of
the hydrotherm al solution is varied, a) 0M b) 0.1M c) 0.2M d) 0.3M e) 0.5M. Circles
indicate BST peaks. Triangles indicate (B a,S r)C 0 3 peaks. Vertical offset of p attern s
is arbitrary.
3.4
B en efits o f U sin g a S o l-G el C o m p o site over a
Sim p le S ol-G el
Fig. 3.5 shows a comparison between the effects of hydrotherm al processing on the
structure of composite and non-composite BST films. W hile th e composite films show
33
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
no shift in peaks away from th a t of the powder alone, the non-com posite films show
a definite peak shift. The sample treated in a B a(0 H )2-8H20 solution shows peaks
shifted to lower 26 values, while the sample treated in a S r(0 H )2-8H20 solution has
peaks shifted to higher angles. This is consistent with the film becoming more Ba or
Sr rich in composition during the hydrotherm al treatm ent, depending on the contents
of the solution. It is expected th a t the shift in peaks of the non-composite samples is
a result of a compositional change rath er th an residual stresses induced in the lattice
during crystallization.
CM
O
pi
S'
CO
c
2
§
< .
~
h*
C/3
m
QQ
s
CD
o
o
O
0) Sl
a
O
CM
CM
H
(0
00
h*
8
CM
CM
8
i
CO
u
-i—•
L_
<C
20
30
40
50
60
70
80
20
Figure 3.5: The effect of hydrotherm al processing on th e structure of composite and
non-composite sol-gel BST films. All films processed in 0.3 M solution at 150°C for
2 hours, a) sol-gel in S r(0 H )2-8H20 solution, b) sol-gel composite in S r(0 H )2-8H20
solution, c) sol-gel composite in B a (0 H )2-8H20 solution, d) sol-gel in B a (0 H )2-8H20
solution. Vertical offset of p attern s is arbitrary.
34
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Were the shift due to stress in the lattice, the shift in peaks would be expected
to be all in the same direction, which they are not. In the case of th e composite,
the powder does not change in composition, even at extended reaction tim es in a
high-concentration solution (1.0 M B a (0 H )2-8H20 or S r(0 H )2-8H20 ) , at a high tem ­
perature (200°C), as shown in Fig. 3.6. Thus, the overall composition of the sol-gel
composite films remains constant, as shown in Fig. 3.7, unlike the composition of
simple sol-gel films.
o
o
eg
CM
\—
to
CD
h*
o
to
i CD
to
CO
CM
CM
*'w"
CM
O
CM
( /)
c
H
to
CD
O
O
0
-t— *
_c
I—
H
w
m
«,
t:
05
L—
I
-t—»
\—
O
eg
to
w
CD
VvVK' tV y^ ■
■
.Q
L—
V
i
M
^
<C
'
S
A
20
30
40
50
60
70
80
20
Figure 3.6: The effect of hydrotherm al processing on th e structure of BST powders.
All films processed in 1.0M (B a,S r)(0 H )2-8H20 solution at 200°C. D uration time: a)
5h b) 24h c) 48h. Vertical offset of p attern s is arbitrary.
35
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
CM
•O
oCM
0
0
^
CO
c
CM
CM
^
O
DQ
£
“
CO
1
J
*8
CD
CO
CD
O
CM
s
O
CO
©
CM
CO
CD
o
CM
CO
to
CM
CM
H
CD
CD
CM
w
5,
hCO
GQ
CO
£0
CO
CO
<D
o
XhjhmQjhyt
L
S
_Q
L_
to jw M to v * *
'W
w w
C
, 'W
20
30
40
50
60
70
'v J w
80
2 0
Figure 3.7: The m aintenance of structure of sol-gel com posite films in various con­
centration solutions (top to bottom : 0.1, 0.3, 0.5, and 1.0 M (B a,S r)(0 H )2-8H20
solution), processed for 48h at 200°C. Vertical offset of p attern s is arbitrary.
Control of th e stoichiom etry of BST is im portant for control of its electrical be­
haviour. The Curie tem perature of BST is strongly dependent on the ratio of B a to
Sr, as B a T i0 3 and S rT i0 3 have widely differing Curie tem peratures of 395 K and 20
K respectively. T he Curie tem perature of th e BST him in tu rn determines its room
tem perature perm ittivity. The ratio of Ba to Sr also affects th e loss tangent of the
him although at high frequencies stru ctu ral factors and internal barriers probably
36
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
have th e m o st significant effect.
3.5
M icrostru ctu re
T he m icrostructure of the raw sol-gel composite film is examined by SEM in Fig. 3.8.
T he pow der phase is clearly surrounded by the dried sol-gel m atrix. In the following
SEM images of processed films (Figures 3.9 to 3.11) showing m icrostructural changes
as a function of process time, solution concentration, and process tem perature, this
am orphous phase is no longer evident, indicating th a t it has been removed or con­
verted to crystalline BST. SEM images indicate th a t as th e conditions are enhanced to
facilitate crystallization, the density of th e overall layer increases. If the sol gel com­
ponent were ju st removed or dissolved by the hydrotherm al process, the powder would
not adhere to form a coherent film and th e observed increase in density would not
take place. Experim ents also show th a t crystalline BST is present in hydrotherm ally
tre a ted non-composite BST films. This suggests th a t th e sol-gel phase is converted
into crystalline BST formed on the underlying powder by the hydrotherm al process.
N ucleation of crystalline BST from the sol-gel is most favoured on the surface of the
seed BST powder particles, rath er th an in the inter-particle sol-gel m atrix. This is
further supported by the AFM and TEM images contained here.
W hile the concentration of the hydrotherm al solution and the processing tem per­
ature are kept constant, an increase in process tim e prom otes the growth of finer
structures in the film (Fig. 3.9). This suggests th a t in addition to the direct conver­
sion of the sol-gel to BST in place, there is also a dissolution-recrystallization process
occurring. At 1 hour there is no am orphous phase evident between the crystalline
elements, b u t at later times this space is filled. This is hypothesized to be crystalline
BST th a t has been dissolved and recrystallized to form the new m icrostructure. A
more concentrated hydrotherm al solution prom otes th e growth of denser, finer stru c­
tures in the film (Fig. 3.10). The condensation of th e sol-gel to crystalline BST is
37
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prom oted in high pH atmosphere due to increased attack on the sol-gel by OH“ ions.
A higher process tem perature tends to result in more extensive growth of the film
(Fig. 3.11), suggesting th a t reaction kinetics are faster at higher tem peratures.
Powder Particle
Amorphous Sol-Gel
Figure 3.8: SEM image of the surface of a BST sol-gel composite film as deposited,
before hydrotherm al treatm ent. Both the powder phase and the surrounding sol-gel
m atrix are evident.
38
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a) Film processed for 1 hour.
b) Film processed for 2 hours.
Figure 3.9: SEM images of th e surface of BST films showing the variation of
BST film m icrostructure w ith process time. All samples are processed in 0.5M
(B a,S r)(0H )2-8H20 solution at 150°C.
39
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c) Film processed for 5 hours.
d) Film processed for 20 hours.
Figure 3.9 continued: SEM images of the surface of BST films showing th e variation
of BST film m icrostructure w ith process time. All samples are processed in 0.5M
(B a,S r)(0H )2-8H20 solution at 150°C.
40
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a) Film processed in 0 M solution.
b) Film processed in 0.1 M solution.
Figure 3.10: SEM images of the surface of BST films showing th e variation of BST film
m icrostructure w ith hydrotherm al solution concentration. All samples are processed
for 2h at 150°C in (B a,S r)(0 H )2-8H20 solution.
41
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c) Film processed in 0.5 M solution.
d) Film processed in 1 M solution.
Figure 3.10 continued: SEM images of the surface of BST films showing th e variation
of BST film m icrostructure w ith hydrotherm al solution concentration. All samples
are processed for 2h at 150°C in (B a,S r)(0 H )2-8H20 solution.
42
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a) Film processed at 50° C.
b) Film processed 100°C.
Figure 3.11: SEM images of the surface of BST films showing the variation of BST
film m icrostructure w ith process tem perature. All samples are processed for 2h in
0.5M in (B a,S r)(0 H )2-8H20 solution.
43
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c) Film processed at 150°C.
d) Film processed at 200° C.
Figure 3.11 continued: SEM images of th e surface of BST films showing the variation
of BST film m icrostructure w ith process tem perature. All samples are processed in
0.5M (B a,S r)(0H )2-8H20 solution for 2h.
44
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The m icrostructure of the raw sol-gel composite film is examined by AFM in Fig.
3.12. In this case, the mass ratio of powder to sol-gel is 1:2. The powder particles
are surrounded by the amorphous sol-gel m atrix as in the SEM image of the raw him
(Fig. 3.8).
/ f
i
100 nm
'#
F ^ o w d e 3 a r t ic le
*mm,
4
W N9tr
0 nm
Figure 3.12: AFM image of raw films. Powder loading 1:2. 2 pm square, height
variation 100 nm.
Figure 3.13 shows AFM images of the progressive growth of bridging structures
in films w ith various powder loadings and process times. All films except for (b)
are processed for 3 hours in 0.3M (B a,S r)(0 H )2-8H20 solution at 150°C. The sample
in (b) is processed for only 1 hour. The powder to sol-gel ratios of the samples in
Fig. 3.13 are: a) 1:10 b) 1:2 c) 1:2 d) 1:1. Bridging between the powder particles
is evident in all of these images. In the cases of higher powder loadings and longer
process times, the connectivity of the powder phase becomes greater.
45
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t
^
100 nm
n
.SK:
0 nm
a) Film processed for 3 hours in 0.3 M (Ba,Sr)(0H)2-8H20 solution at 150°C. Powder to
sol-gel mass ratio is 1:10.
100 nm
0 nm
b) Film processed for 1 hour in 0.3 M (Ba,Sr)(0H)2-8H20 solution at 150°C. Powder to
sol-gel mass ratio is 1:2.
Figure 3.13: AFM images showing variation of m icrostructure w ith powder loading
and process time.
46
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100 nm
id g in g S tr u c t ir i|is
liy F o r m e d
t
J
0 nm
^
£
.*
*
*
m
c) Film processed for 3 hours in 0.3 M (Ba,Sr)(0H)2-8H20 solution at 150°C. Powder to
sol-gel mass ratio is 1:2.
100 nm
d g in g S t r u c t u n s
rtially F o r m e d
d) Film processed for 3 hours in 0.3 M (Ba,Sr)(0H)2-8H20 solution at 150°C. Powder to
sol-gel mass ratio is 1:1.
Figure 3.13 continued: AFM images showing variation of m icrostructure w ith powder
loading and process time.
Figure 3.14 shows TEM images of a hydrotherm ally processed BST film. These
images were obtained by Dr. Joke H aderm an of th e University of Antwerp.
Fig.
3.14 shows a wide view in which several particles joined by sol-gel derived m aterial
47
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are evident. Particle size is consistent w ith SEM and AFM images. Fig. 3.14 (a)
shows an enlarged portion of Fig. 3.14 (as indicated by the white rectangle) in which
an interface between crystalline powder particles and the sol-gel derived bridging
structure is evident. Areas of Fig. 3.14 (a) outlined in black are crystalline and show
lattice lines at higher magnification indicating th a t crystallization of th e sol-gel occurs
during hydrotherm al processing. This is consistent w ith XRD data.
The corner denoted A is the same in Figs. 3.14 and 3.14 (a) for orientation. Figs.
3.14 (a .l), (a.2), and (a.3) show enlarged sections of Fig. 3.14 (a) as denoted by
num bers 1, 2, and 3. The contrast in these areas in Fig. 3.14 (a) has been enhanced
to indicate the region enlarged. In Fig. 3.14 (a.l) lattice lines are evident in a section
of th e sol-gel derived m aterial far away from the interface w ith the powder. This
may indicate th a t crystallization of this region of sol-gel began far from a powder
particle, or th a t the powder particle where crystallization began was removed during
preparation of the sample for imaging. Fig. 3.14 (a.2) shows a crystalline portion
of the sol-gel derived m atrix in close proxim ity to a powder particle. In this case
there is a large degree of lattice m ism atch between the powder and the sol-gel derived
m aterial. Again, this may be due to nucleation of crystallites occurring away from
the sol-gel:powder interface, or crystallization of this region may have begun on the
surface of a powder particle not imaged here.
Fig.
3.14(a.3) shows lattice lines extending from the powder particle into the
sol-gel derived m aterial. This indicates th a t grow th of the sol-gel derived crystalline
BST is at least in p art epitaxial on th e surface of the powder particles. The interface
between the powder and the sol-gel-derived region is very sm ooth in this case, w ith
no boundary layer evident. It is this lack of boundaries which is thought to give
rise to the excellent electrical characteristics seen in hydrotherm ally processed sol-gel
composite BST films. Fig. 3.14 (a.4) shows an am orphous region of the film.
Grain boundaries typically have much lower dielectric perm ittivities th an do bulk
48
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dielectrics.
Looking at the com bination of the bulk and the grain boundary as a
series com bination of two capacitors, if the bulk region has dielectric constant eB
and thickness dB, and the grain boundary has dielectric constant egb, and thickness
dgb, then assuming the bulk and grain boundary have the same area, A, the effective
capacitance of the combination, C, can be w ritten as
c
=
_
T f y
£p£BegbA
(s .i)
(3.2)
tBdgb + Cgbds
Letting egb = O.lee, if CB is the capacitance of the bulk region, then
C
CB
dB
10 dgb + dB
(3.3)
In this case, if dgb = O.Olde then the capacitance of th e bulk-grain boundary
com bination is 91% of the capacitance of the bulk structure. If the grain boundary
is thicker or has a lower dielectric constant, then the capacitance of the combined
structure will be even lower. This analysis indicates th a t even a thin low -perm ittivity
grain boundary significantly decreases the p erm ittivity of the structure as a whole.
49
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Figure 3.14: TEM images of a hydrotherm ally processed BST film. This image shows
a wide view in which several particles joined by sol-gel derived m aterial are evident.
The sample was processed for 2 h at 150°C in 0.1M (B a,S r)(0 H )2-8H20 solution.
50
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Figure 3.14 a: An enlarged portion of 3.14 as indicated by the white rectangle. The
corner denoted A is the same in each image. Areas outlined in black show evidence
of lattice lines at higher magnification.
51
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PiSHr(
at this 3 i4 a‘1: P
0 la® « c a ( i " '
0[
exioted
(aJ- laatt;
ttice ljn
52
0oPyright
°wnei
erre^ c „ 0„
proh'bite<j
w<thou,
Permhlssio n
es are
evH an.
Figure 3.14 a.2: Enlargem ent of region 2 as denoted in (a). This region shows the
interface between a powder particle and th e sol-gel derived bridging structure. A
m ism atch in the lattice is evident at this interface.
53
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Figure 3.14 a.3: Enlargem ent of region 3 as denoted in (a). This region shows the
interface between a powder particle and the sol-gel derived bridging structure. Con­
tinuation of lattice lines from the powder into the bridging stru ctu re is evident at this
interface, indicating epitaxial growth on th e surface of the powder.
54
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Figure 3.14 a.4: An enlargement of an amorphous region of the bridging structure in
(a).
3.6
A d van tages o f th e H y d ro th erm a l
C o m p o site P r o ce ssin g T echnique
S ol-G el
The technique of hydrotherm al sol-gel composite crystallization outlined here has
several significant advantages over other film deposition techniques. It does not in­
volve tem peratures in excess of 200°C like m any other deposition techniques (such as
CVD, metallorganic decomposition, and conventional sol-gel processing). This makes
it compatible w ith many tem perature-lim ited substrates, such as GaAs and polymers.
The technique outlined here also allows for b e tte r stoichiom etric control, b e tte r adhe­
sion, and (as outlined in the next chapter) b e tte r electrical characteristics th a n films
55
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fabricated by other low-tem perature techniques (such as hydrotherm al processing of
Ti or simple sol-gels).
3.7
L im ita tio n s on H y d ro th erm a l P r o cessin g P a ­
ram eters
The hydrotherm al conditions under which the him is crystallized have a significant
im pact on the m icrostructure of the final him. In particular, crystallization and densihcation of the hlms are prom oted by a hydrotherm al process w ith higher tem perature,
higher concentration of the hydrotherm al solution, and a longer process tim e. An in­
crease in the perm ittivity of the him is also seen under these conditions. There are,
however, limits placed on the hydrotherm al processing param eters as a result of other
concerns. Firstly, the tem perature at which the him is processed cannot exceed 200°C
in order to ensure com patibility of the process w ith tem perature-lim ited substrates
such as GaAs. Secondly, if the concentration of the hydrotherm al solution exceeds 0.5
M, then the adhesion of the BST him to the substrate is compromised, making the
repeatable deposition of large-area hlms difficult. Lastly, extended process tim es tend
to compromise the adhesion of the BST him, and may have detrim ental effects on the
substrate m aterial or other pre-patterned com ponents subjected to the hydrotherm al
process. Film adhesion tends to become an issue for hlms processed for longer th an
3 hours. This may be due to continued dissolution and recrystallization of the him
th a t may weaken the bond between the him and th e substrate.
The mass ratio of powder to sol-gel in the sol-gel composite also affects the mi­
crostructure of the hnal him. The higher the relative am ount of powder, the denser
and more highly interconnected the hnal him, and th e higher the relative perm ittivity.
If, however, the mass ratio of powder to sol-gel exceeds 1:1, it becomes increasingly
difficult to distribute the powder evenly in th e sol-gel, and th e him obtained by the
spin-on process is not of uniform thickness.
56
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3.8
F ilm T hick n ess
T he thickness of the deposited film may be controlled in several ways. The viscosity
of the sol-gel composite is determ ined by the constituents of th e sol-gel and by the
am ount of powder added. These factors in tu rn affect the thickness of the final film.
The spin rate used to deposit the sol-gel composite may also be used to determ ine
the thickness of the film. M ultiple layers of sol-gel composite may be deposited to
build up a thicker film, as long as they are hydrolyzed between depositions to prevent
dissolution. The thicker the layer deposited in one coat, the more likely the film is to
crack during drying.
The lim itation on the maximum thickness of the film is prim arily imposed by the
effect of the hydrotherm al process on the film. Films w ith thickness in excess of 5
pm tend to lift off the substrate during the hydrotherm al process. The lim itation on
the minimum thickness of the film is determ ined by th e size of th e powder used in the
sol-gel composite. In this study, the BST powder had an average diam eter of 0.3 pm,
which lead to films with thickness of less th an 1 pm not having uniform thickness.
In conventional therm al processing of a sol-gel composite a decrease in film thick­
ness occurs upon firing. If, however, the sol-gel composite is treated by a hydrotherm al
process, the thickness after processing is the same as th e thickness of the dried b u t
unprocessed film. This is a convenient feature, as deposition param eters may be op­
tim ized for a desired film thickness w ithout having to hydrotherm ally crystallize each
film. It is hypothesized th a t this lack of shrinkage is due to th e in-situ conversion of
the amorphous sol-gel to a crystalline form by a chemical process.
3.9
In itial F ilm H y d ro ly sis
An im portant aspect of successful film deposition by the hydrotherm al sol-gel compos­
ite m ethod is the partial hydrolysis of the film in w ater vapour prior to hydrotherm al
57
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processing. If this is not done, then the sol-gel composite film is removed by the next
layer deposited, or by the hydrotherm al solution. The details of the effect of water
vapour on the raw film has not been studied here, but the effect of w ater vapour
on other films indicates th a t it does affect the crystallization behaviour of sol-gel
films in many cases. For instance, work by Imai et al. [36] on the preparation of
anatase coatings from titan iu m dioxide and titanium dioxide-silica sol-gels indicates
th a t exposure of a gel to a high hum idity environment affects the crystallization be­
haviour of the ceramic. Similarly, M atsuda et al. [37, 44] reported stru ctu ral changes
in sol-gel-derived SiC>2 and SiC>2 containing TiC>2 in a high hum idity environment
at tem peratures below 100°C. The crystallization process in hum id atm ospheres is
hypothesized to be a hydrolysis reaction due to the w ater vapour, which causes a
rearrangem ent of the gel network w ith cleavage of Ti-O -Ti bonds, followed by a con­
densation reaction which gives rise to th e crystalline film. C rystallization of T i02 in
a solvent or of gel films is thought to occur through dissolution in adsorbed water,
migration, and subsequent recrystallization [35]. It has also been shown th a t curing
in a humid atm osphere prom otes the removal of alkoxy groups over curing in a dry
environment, at tem peratures as low as room -tem perature [45]. S tructural changes
similar to those outlined here are suspected to occur in th e raw BST sol-gel composite
films upon exposure to a high-hum idity environment.
58
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C hapter 4
Low-Frequency Electrical
C haracterization
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The low frequency (1-100 kHz) perm ittivity and loss tangent of BST films and pel­
lets are determ ined by use of parallel plate capacitors. The low-frequency behaviour
of the films gives some insight into th e possible high-frequency behaviour, and is used
to determ ine the optim al processing conditions under which samples to be tested at
high frequency will be fabricated. Complex impedance analysis is used to determ ine
the contributions of bulk grains and grain boundaries to the to tal film resistance and
capacitance. The influence of grain boundaries is minimized in films w ith the highest
perm ittivity. The behaviour of bulk BST pellets im pregnated with hydrotherm ally
treated sol-gel provides further evidence th a t linking of the powder in hydrotherm ally
tre a ted sol-gel composites gives rise to high perm ittivity ceramics.
4.1
A c e tic A cid and 2 -m eth o x y eth a n o l B a sed SolG els
Figure 4.1 shows the frequency dependence of the perm ittivity and loss tangent for
non-composite BST films made from acetic acid and 2-methoxyethanol based sol-gels.
The acetic acid based sol-gel yields a film w ith a higher perm ittivity and lower loss
tangent. Acetic acid is also less toxic th an 2-methoxyethanol. For these reasons acetic
acid based sol-gels are used in the rest of this study.
4.2
V ariation o f er and ta n 5 w ith P r o cess P a ra m ­
eters for S ol-G el C o m p o site F ilm s
The variation of er and ta n S w ith processing param eters including tem perature,
reaction duration and concentration of th e hydrotherm al solution has been examined.
Figures 4.2, 4.3, and 4.4 show the variation of er w ith these variables, respectively.
The relative dielectric constant of th e film increases w ith the increase of process
tem perature, process duration, or concentration of the hydrotherm al solution, while
the other param eters are held constant.
60
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120
Acetic Acid-Based Sol-Gel
24 h
100
80
Raw Sol-Gel
to 60
40
2-Methoxyethanol-Based Sol-Gel
20
0
1000
Raw Sol-Gel
10000
100000
Frequency (Hz)
Figure 4.1: Relative dielectric constants of raw and processed acetic acid- and 2m ethoxyethanol-based sol-gels.
The increase in dielectric constant w ith process tim e, process tem perature, and
concentration of the hydrotherm al solution corresponds to the changes in film mi­
crostructure with these param eters reported in the previous chapter. A higher di­
electric constant corresponds w ith a denser, more finely structured film. G row th is
prom oted at higher tem peratures due to increased reaction kinetics. Longer process
duration allows more tim e for growth to occur. Higher solution concentration pro­
vides higher pH levels which prom otes attack of the sol-gel by OH~ ions, prom oting
faster reaction kinetics.
61
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All films except the one processed in 1 M solution show a relatively flat frequency
response in the dielectric constant.
The sample processed in 1 M solution shows
a sharp decrease in dielectric constant over the entire range studied. This sample
showed a high degree of desorption from the substrate, likely due to the rapid attack
of the high-pH solution on the sol-gel. This desorption may be the reason for the
anomalous frequency dependence of the perm ittivity in this case.
1600
CO
1200
-
1000
-
OQQ
j e X K K M X
W~9 m
400 -
1000
b
a
10000
Frequency (Hz)
100000
Figure 4.2: The variation of er of BST films w ith process tem perature. All films
processed in 0.5 M (B a,S r)(0 H )2-8H20 solution for 2 hours, a) raw film b) 50°C c)
100°C d) 150°C e) 200°C.
62
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Figures 4.5, 4.6, and 4.7 show the variation of tan S with various process param e­
ters. In all cases the loss tangent decreases w ith increasing frequency. Exam ining the
loss tangent values at 100 kHz shows th a t most of the processed films have higher loss
tangents th a n the unprocessed film. Only under the conditions yielding films with
the highest perm ittivities is the loss tangent smaller th an th a t of the raw film. It is
shown later th a t in these cases the effect of grain boundaries in the film is minimized.
In all cases, at 100 kHz the loss tangents lie in the range from 0.05 to 0.10.
1200
1000
800
to
600
400-
i » 0 » » » » 4
200
0
1000
10000
Frequency (Hz)
100000
Figure 4.3: The variation of er of BST films w ith process tim e. All films processed in
0.5 M (Ba,Sr)(0H )2-8H 20 solution at 150°C. a) raw film b) 1 h c) 2 h d) 5 h e) 20 h.
63
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1600
1400
1200
1000
CO
N I! IIII X >
800
e
d
600
b
a
400
r r
200
0
1000
10000
100000
Frequency (Hz)
Figure 4.4: The variation of er of BST films w ith concentration of the hydrotherm al
solution. All films processed for 2 hours at 150°C in (B a ,S r)(0 H )2-8H20 solution, a)
raw film b) 0 M c) 0.1 M d) 0.5 M e) 1 M.
64
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Frequency (Hz)
Figure 4.5: The variation of ta n 8 of BST films w ith process tem perature. All films
processed for 2 hours in 0.5 M (B a,S r)(0 H )2-8H20 solution, a) raw film b) 50°C c)
100°C d) 150°C e) 200°C.
65
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
0.8
0.7
0.6
0.5
0.3 -
0.2
-
0.0
1000
10000
100000
Frequency (Hz)
Figure 4.6: The variation of ta n S of BST films w ith process time. All films processed
in 0.5 M (B a,S r)(0 H )2-8H20 solution at 150°C. a) raw film b) 1 h c) 2 h d) 5 h e) 20
h.
66
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0.7
0.6
0.5
to 0.4
c
(0 0.3
0.2
0.1
0.0
1000
10000
100000
Frequency (Hz)
Figure 4.7: The variation of ta n 5 of BST films w ith concentration of the hydrotherm al
solution. All films processed for 2 hours at 150°C in (B a,S r)(0 H )2-8H20 solution, a)
raw film b) 0 M c) 0.1 M d) 0.5 M e) 1 M.
Furnace heating of hydrotherm ally processed BST films at 400°C for 12 hours
did not change the perm ittivity or loss tangent of th e films. This indicates th a t any
residual species in the film which affect the electrical behaviour of the film cannot be
removed by heating to this tem perature.
4.3
C om p lex Im p ed a n ce A n a ly sis
The complex im pedance for each film has been determ ined. The film is well modeled
as two parallel RC elements connected in series. The semicircle appearing at low
67
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values of the real part of the im pedance (corresponding to higher frequency mea­
surem ents) disappears in films processed under conditions yielding higher dielectric
constants (high tem perature, high solution concentration or long process time). For
this reason, and the fact th a t tita n a te ceramics tend to have low-capacitance grain
boundaries, this component is considered to represent the grain boundary contribu­
tion to th e film impedance. The resistance and capacitance of the bulk contribution
increase as the process tem perature is increased, as th e solution concentration is in­
creased, and as the duration of the process is increased. Capacitance of the grain
boundary contribution also increases under these conditions while the resistance of
the grain boundary contribution decreases. This is indicative of the volume of the
film comprising grain boundaries decreasing under favourable processing conditions.
Figure 4.8 shows typical complex im pedance plots. The semicircle resulting from
grain boundary contributions is evident in the raw films and those films w ith lower
relative perm ittivities. Only the bulk contribution is evident in the hlms processed
under conditions yielding the highest perm ittivities. T he values of the bulk and grain
boundary contributions to him resistance and capacitance as they vary w ith process
tem perature, process duration, and concentration of the hydrotherm al solution are
shown in Tables 4.1, 4.2, and 4.3, respectively.
68
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160
140
120
G 100
LO
o
ZV 1 0 5 ( Q )
a) Film prior to hydrothermal processing.
8070— 60G
r 50-
o
s: 40N
■ 30 20
-
10
-
40
Z V 10 5(Q )
b) Film processed at 50° C.
Figure 4.8: Complex im pedance of raw and processed films showing semicircle due to
grain boundary contribution disappearing for films processed at higher tem peratures.
A similar p attern is evident for films processed for longer tim es and w ith higher
concentrations of the hydrotherm al solution.
69
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40
a
to
O
0
1
2
3
4 5 6 7
Z7105 (Q)
8
9
10
c) Film processed at 200°C.
Figure 4.8 continued: Complex impedance of raw and processed films showing semi­
circle due to grain boundary contribution disappearing for films processed at higher
tem peratures. A similar p attern is evident for films processed for longer times and
w ith higher concentrations of the hydrotherm al solution.
Param eter
Rbulk (MO)
C bulk (nF)
Rgft (MO)
Cgb (nF)
R aw Film
55
0.056
1.0
0.160
100°C
19
0.140
0.7
0.200
50° C
20
0.100
0.8
0.160
150°C
18
0.150
0.5
0.500
200°C
14
0.220
0
0
Table 4.1: The variation of bulk and grain boundary resistances and capacitances
w ith process tem perature as derived from complex im pedance analysis. All films
processed for 2 hours in 0.5 M (B a,S r)(0 H )2-8H20 solution.
Param eter
Rbulk (Mf2)
Qmik (nF)
Rgb (M il)
Cgb (nF)
R aw Film
55
0.056
1.0
0.160
1 h
19
0.110
0.6
0.30
2 h
18
0.150
0.5
0.50
5 h
11
0.170
0
0
20 h
9
0.180
0
0
Table 4.2: The variation of bulk and grain boundary resistances and capacitances w ith
process duration as derived from complex im pedance analysis. All films processed in
0.5 M (B a,S r)(0H )2-8H20 solution at 150°C.
70
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Param eter
Rbulk (MU)
C'bulk (nF)
Rgb (Mf2)
Cgb (nF)
Raw Film
55
0.056
1.0
0.160
0 M
20
0.090
0.7
0.170
0.1 M
19
0.145
0.6
0.180
0.5 M
18
0.150
0.5
0.500
1.0 M
7
0.240
0
0
Table 4.3: The variation of bulk and grain boundary resistances and capacitances
w ith concentration of the hydrotherm al solution as derived from complex im pedance
analysis. All films processed for 2 hours at 150°C in (B a,S r)(0 H )2-8H20 solution.
4 .4
B u lk C eram ic P e lle ts
The perm ittivity of the bulk BST pellets increased significantly upon their impreg­
nation w ith sol-gel and subsequent hydrotherm al treatm ent. This increase cannot be
accounted for by increase in density alone, as the increase in density of the pellets is
less th a n 1%. This supports the idea th a t the high perm ittivity of hydrotherm ally
processed sol-gel composite films is due to a change in the m icrostructure similar to
w hat occurs in the pellet upon im pregnation w ith processed sol-gel.
The perm ittivity of the im pregnated thinner pellets was higher th a n th a t of the
thicker pellets, while the perm ittivity of the unprocessed pellets did not depend on
thickness. This can be explained due to the fact th a t the larger surface to volume
ratio of the smaller pellets allowed for more complete penetration of th e sol-gel into
the pellet. Figure 4.9 shows the m easured perm ittivity for pellets w ith and w ithout
sol-gel of various thicknesses.
71
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500
450
400
thickness
l- 350
to
pellets with sol-gel
^ 300
(mm)
0.64
0.73
0.79
0.90
1.04
1.55
£250
75 200
O
~ 150
100
50
pellets without sol-gel
0 . 71 , 1.23
0
0
50000
100000
Frequency (Hz)
Figure 4.9: Effective perm ittivities of sol-gel im pregnated pellets of various thick­
nesses. W ithout sol-gel the perm ittivity of the pellet is independent of pellet thick­
ness.
4.5
E ffective P e r m ittiv ity C a lcu la tio n s for P e lle ts
The sol-gel-treated BST pellet can be modeled as two concentric cylinders, as shown
schematically in Fig. 4.10. The inner layer consists of the volume not reached by
the sol-gel. This region has the same dielectric perm ittivity as determ ined from the
untreated pellet, e2. The outer layer consists of the region im pregnated w ith sol-gel.
This region has a dielectric perm ittivity
T he effective perm ittivity of the pellet,
eef f depends on ti and e2, as well as the depth to which th e sol-gel penetrates the
pellet. The pellet can be considered as two capacitors in parallel; one capacitor, CQ
72
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represents the outer region, and one capacitor, Cj represents the inner region. The
inner capacitor can be represented by three capacitors in series such th a t w ith C\ and
C2 as defined in Fig. 4.10
C XC2
(4.1)
C x + 2 C2
e0eie27rr2
(4.2)
e2(T —t) -f- e\t
Since C = Ci + C2, this gives
C =
€0fLiTv{R2 - r 2)
eo*4??xr2
(4.3)
T
2R
/ V
1
2r
Figure 4.10: M ulti-cylinder model of sol-gel im pregnated BST pellet.
Since it is also the case th a t
C =
e0ee ff -KR2
T
(4.4)
the two preceding equations can be combined and rearranged to give
e\{R2 - r 2) + ei[e2r 2T + e2( R 2 - r 2)(T - t) - eeff R 2t] - eef f e2R 2(T - t) = 0. (4.5)
The preceding quadratic equation can be solved for e\.
The root which gives
<fi < T // is rejected.
73
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Figure 4.11: SEM image of BST pellets w ith and w ithout sol-gel. The d ep th of
penetration of the sol-gel is not dependent on thickness. The porosity of the volume
containing sol-gel is less th an th a t of the central volume w ithout sol-gel. a) pellet
w ithout sol-gel (1.10 mm thick) b) 1.55 m m thick pellet w ith sol-gel c) 0.64 m m thick
pellet with sol-gel.
74
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Figure 4.12: Growth of sol-gel in pores of BST pellets after hydrotherm al crystalliza­
tion. a) w ithout sol-gel b) w ith sol-gel after hydrotherm al treatm en t.
75
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SEM images (Fig. 4.11) indicate th a t for pellets w ith a particular porosity the
depth to which the sol-gel penetrates is independent of the pellet thickness, and th a t
for the pellets studied here the depth of penetration is 0.21 mm. This suggests th a t
thicker sol-gel-treated pellets should have a lower perm ittivity due to the fact th a t a
larger volume fraction of the pellet is unaffected by th e sol-gel. Fig. 4.12 shows pores
in the pellet w ith and w ithout sol-gel.
The effective perm ittivity for each pellet is shown in Fig. 4.9. As predicted, the
thicker pellets had a lower effective perm ittivity.
The use of the above model to
determ ine the effective perm ittivity of the sol-gel im pregnated portion of the pellet,
ex yields a consistent value between pellets. D ata for a typical pellet is shown in
Fig. 4.13. The value of e\ is significantly higher th an the relative perm ittivity of the
pellets w ithout sol-gel.
Fig. 4.14 shows typical loss tangent values for the pellets. All are relatively high,
however there is a distinct decrease in loss for the sol-gel im pregnated pellets.
76
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450
400
350
300
250
co
200
total pellet
150
100
50
0
volu m e without so l-g e l
0
50000
100000
Frequency (Hz)
Figure 4.13: Typical derived values for the volume of the pellet containing sol-gel.
This particular case is for th e 0.79 mm thick pellet. The same values for th e p erm it­
tivity of the volume containing sol-gel is obtained for all pellets.
77
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0.8
0.7 -
0.6 0 .5 without sol-gel
(1.10 mm)
0 .4 0.3-
0.2
0.0
-
0
with sol-gel
1.55 mm
0.64 mm 50000
100000
Frequency (Hz)
Figure 4.14: Typical loss tangents of pellets w ith and w ithout sol-gel of various thick­
nesses.
4.6
C om p lex Im p ed a n ce A n a ly sis o f B S T p e lle ts
The complex im pedance of the BST pellets has been determ ined as was done for the
films. Again, the system is modeled as a series connection of two parallel RC elements,
representing the bulk and grain boundary contributions, respectively. Fig. 4.15 shows
the results. As for the case of the films processed under favourable conditions, the
thinner pellets (having a smaller region not reached by the sol-gel) have a smaller
contribution from grain boundary elements to their to tal behaviour. This is consistent
w ith the sol-gel im pregnated region containing fewer grain boundaries th a n the region
not containing sol-gel. The values of the bulk and grain boundary contributions to
78
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pellet resistance and capacitance for the three pellets whose complex im pedances are
plotted in Fig. 4.15 are shown in Table 4.4.
250
200
£ 150in
O
F
100
-
50-
0
20
40
60 80 100 120
Z 7 1 0 5 (Q )
140
a) 1.10 mm thick pellet without sol-gel.
160
140120
-
o
80-
Fsl
604020
-
0
10 20
30 40 50 60
Z 7 1 0 5 (Q )
70 80 90
b) 1.55 mm thick pellet with sol-gel.
Figure 4.15: Typical complex im pedance plots for pellets w ith and w ithout sol-gel.
The thinner pellets show a smaller contribution from grain boundaries.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
50
4540_ 35£ 30in
© 25-
£
'
2° 1510
-
0 -
ZV 105 (O )
c) 0.64 mm thick pellet with sol-gel
Figure 4.15 continued: Complex im pedance of raw and processed films showing semi­
circle due to grain boundary contribution disappearing for films processed at higher
tem peratures. A similar p attern is evident for films processed for longer tim es and
w ith higher concentrations of the hydrotherm al solution.
Param eter
Rftu/fc (Mf2)
Cbuik (nF)
Rgb (Mfi)
Csl (nF)
1.10 mm pellet
w ithout sol-gel
55
0.05
7
0.03
1.55 mm pellet
w ith sol-gel
52
0.07
5
0.07
0.64 mm pellet
with sol-gel
46
0.10
4
0.09
Table 4.4: The variation of bulk and grain boundary resistances and capacitances
for pellets of various thicknesses w ith and w ithout sol-gel as derived from complex
impedance analysis.
Low-density films typically produce films w ith low effective perm ittivities, as the
signal passes through air-filled, low perm ittivity regions. It is therefore quite sur­
prising th a t hydrotherm ally crystallized sol-gel composite BST films, which have a
high level of porosity due to the in-situ conversion of sol-gel to crystalline tita n a te
and lack of conventional densification mechanisms, should have such high dielectric
perm ittivities. It is suggested th a t this may be due to th e highly-connected n atu re
80
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of the m icrostructure in which few barriers exist.
81
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C hapter 5
H igh-Frequency Electrical
C haracterization
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
The high-frequency (up to 40 GHz) perm ittivity and loss tangent of the BST films
have been determ ined employing a novel technique designed by Hany F. H am m ad of
the Q ueen’s University departm ent of Com puting and Electrical Engineering [40]. As
described in an earlier chapter, this technique makes use of the dependence of the
response of C P W ’s on the characteristics of a top layer of BST. The fact th a t sensible
and meaningful results have been obtained via this technique not only provides in­
form ation on the characteristics of hydrotherm ally processed BST sol-gel composite
films, b u t also validates this m ethod of high frequency electrical characterization.
5.1
T h e T est S tru ctu res
The test structures are pattern ed in gold on alum ina by Nanowave Technologies
Inc. The physical shape of the p attern ed test structures affects their behaviour, and
m ust be modeled accurately to obtain meaningful results. For instance, the effect of
changing the thickness of the gold layer on the centre resonance frequency is shown
in Fig. 5.1.
The alum ina substrate w ith the p attern ed gold test stru ctu re is cleaved perpen­
dicular to the C PW lines. The sample is then m ounted in acrylic, and polished to
present a clear cross-section under an optical microscope, as shown in Fig. 5.2. The
processed BST film fills well between the legs of the C PW , and has a uniform height
above the CPW . This height is equal to the height m easured before processing, and
to th a t measured far from the C PW structures, allowing for easy determ ination of the
height of other BST samples. The to tal w idth of the gold structures and th e spacing
between them is as was designed, bu t the edges are not vertical, presum ably due to
the etching process used to produce the p attern . The cross-sectional shape, however,
is consistent from leg to leg, and thus can reasonably be taken into account in the
design of a model for the structure whose response is to be simulated.
83
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28.5
N
X
o
uncovered line
&
c
0)
3
57
2
Li.
0
27.5
27
d)
O
26.5
T
G o ld T h ic k n e s s (|im )
a)
17.5
N*
i.
with 2.6 jim
17
BST, 8= 30
c 16.5
a
CT
o
16
15.5
15
0
b)
2
4
G o ld T h ic k n e s s ( jim )
Figure 5.1: Sim ulation of th e shift in the position of the centre frequency of one test
structure on the thickness of gold used to form the structure.
84
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Figure 5.2: Cross-section of leg of coplanar waveguide p attern ed in gold on alumina.
1
a i2o 3
(not to scale)
all measurements in microns
Figure 5.3: The cross-sectional geometry of test structures used to sim ulate responses
in HFSS.
5.2
S im u lation s
Sim ulations have been run using HFSS from Ansoft by Hany F. Hammad. The values
used for the gold test structures are e^u= l , Hau= 0.99996/io> cr/iu= 4 .1 x lO ~ 7S/m . For
the conductor, the loss tangent is given by
tanSAu = aAu
(5-1)
where uj is the angular frequency of operation. The alum ina substrate is considered
to be lossless and to have a relative perm ittivity of 9.8 and n aiumina=HoSimulations of the test structures w ithout a BST top layer were com pleted first.
This allowed for an assessment of the agreem ent between the results of the sim ulations
and the m easured response of the uncovered test structures. Subsequently a 2.6 ^im
thick layer of BST was added to th e stru ctu re to be sim ulated, as in Fig. 5.3. As
described in a previous chapter, the addition of the BST layer has the effect of shifting
the centre frequency of the filter to a lower frequency. The dependence of the shift
85
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on the perm ittivity of the top layer is determined. This allows for the perm ittivity of
actual films to be determined from their measured response.
In the case of one him the loss tangent has also been determined. Simulations
indicate th a t the addition of a loss tangent of a few percent does not significantly
shift the centre frequency of the filter, b u t changes the depth of the resonance notch.
The loss tangent is adjusted to best fit th e shape of the m easured curve.
5.3
U n covered C P W lines
The m easured response of the C PW structures w ithout a BST top layer is shown in
Fig. 5.4. The lines w ith the longest resonant wavelengths show m ultiple notches in
s2i, unlike the prediction of the simulation. W ithout the inclusion of conductor losses
in the simulations, the structure acts as an ideal filter giving rise to an infinitely deep
notch at the centre frequency. Sim ulations of th e response of th e structures including
conductor losses show little shift in th e position of th e notches however the depth of
the notches is reduced, as in the m easured results, as the structure no longer acts
as an ideal filter. Because of th e fact th a t losses do not greatly affect the position
of the centre frequency it is possible to vary th e value of the dielectric constant and
loss tangent in the sim ulated structure separately to best fit th e sim ulation to the
measured response. The model can give a value for b o th the dielectric constant and
the loss tangent.
As is evident in Fig. 5.5 the conductor losses of th e gold structure do not entirely
account for the measured losses. The m easured s2i curve is shallower th an the sim ­
ulated response. The additional losses may be due to surface roughness of the gold,
losses due to the alum ina substrate, or other non-ideal behaviour of the structure
which has not been taken into account in th e simulations. These additional losses are
not accounted for in the rest of this analysis, and thus th e loss values for the BST
films obtained are maximal values. A ctual loss tangent values for BST film are lower
86
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th a n reported here, as the values reported here include the extra losses due to the
test structures.
0
Frequency (GHz)
20
40
4
CM
-12
Figure 5.4: M easured responses of C PW w ith no BST top-layer.
87
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Frequency (GHz)
20
25
30
measured
m
- io
■o
CM
W -15
simulated
-20
-25
Figure 5.5: Comparison between m easured response for one C PW line and the simu­
lated response of the line w ith consideration of conductor losses. Each colour repre­
sents the d a ta obtained from m easurem ents using one of the eight test lines.
5.4
B S T co a ted lin es
Films of BST and BST doped w ith 5 at% Mn w ith thickness of 2.6 /im were deposited
on the test structures and p attern ed as described in earlier chapters.
were hydrotherm ally processed.
The films
Films were processed for 2 h at 150°C in 0.5 M
(B a,S r)(0H )2-8H20 solution.
The effect of placing a dielectric layer on top of th e C PW structures is to shift
88
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the position of the notch to a lower frequency. The size of this shift is related to the
dielectric constant of the m aterial in the top layer, and its geometry. The m easured
prim ary resonance notches of typical test structures with a 2.6 fim top layer of BST are
shown in Fig. 5.6. The relationship between the size of the shift in centre frequency
and the perm ittivity of the BST layer is m apped out in Figures 5.7 and 5.8. This
allows th e dielectric perm ittivity of unknown films to be determ ined. For films w ith
dielectric perm ittivities outside the range of the sim ulation, th e perm ittivities are
extrapolated given the relationship in Fig. 5.8.
Films produced from sol-gel composite films of several compositions have been
examined in this m anner. Films consisting of BST powder in a BST sol-gel, or of
BST:M n powder in BST:M n sol-gel (5 at% Mn) have been produced w ith different
powder loadings. The mass ratio of powder to sol-gel is 1:1, 1:2, 1:10, or pure sol-gel
(no powder). The spin rate during deposition is adjusted in each case to produce a
film 2.6 /im in thickness. In the case of pure sol-gel, repeated depositions w ith an
interm ediate exposure to a high hum idity environment were necessary to achieve a
thickness of 2.6 /rm.
The resulting dielectric constants are shown in Figures 5.9 and 5.10. The processed
films have a much higher dielectric constant th an their raw counterparts. T he Mn
doped films exhibit slightly lower dielectric constants th an th e undoped films, which
is consistent w ith the work of others. There is a strong dependence of th e perm ittivity
on the relative am ount of powder in the film w ith those films containing more powder
exhibiting higher dielectric constants.
89
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0
Frequency (GHz)
5
10
15
20
-10
-12
-14
-16
Figure 5.6: Typical prim ary resonance responses for th e test structures w ith a 2.6
/im top layer of BST. This particular film had a powder to sol-gel mass ratio of 1:1.
Each colour represents the d a ta obtained from m easurem ents using one of th e eight
test lines.
90
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Film Relative
160
4-1
c 140
(0
iM
to 120
o 100
o
o
80
L.
o
0)
0
Q
Center Frequency
of s Resonance (GHz)
Figure 5.7: Sim ulated shifts in the centre frequency of the s2i notch for th e 8 test
structure lines due to films w ith various dielectric constants.
91
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141
s r=
121
I
c
o
o
-3976.5x5 + 14942x4 - 22441x3 +
17032x2.6683.8x + 1128.2
101
81
o
o
0)
61
<D
Q
41
21
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Center Frequency with Test Film/
Center Frequency of Uncovered Lines
Figure 5.8: Sim ulated relationship between test film dielectric constant and shift in
S2 1 resonance center frequency to be used to determ ine dielectric constant for test
films. All 8 test lines follow approxim ately th e same relationship.
92
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20
18
16
14
a
• 1:10
12
to
1:2
♦ sol-gel
10
8
6
4
♦
2
0
0
20
40
Frequency (GHz)
a) Films prior to hydrothermal processing.
Figure 5.9: V ariation of relative perm ittivity of raw and processed BST films w ith
different powder to sol-gel ratios. The legends give the powder to sol-gel mass ratio
of the sol-gel composite used to produce th e film under test.
93
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400
a
1:2
• 1:10
♦ sol-gel
to- 300
200
■■
0 j -------------------------------- —
0
------------------------------------
20
40
Frequency (GHz)
b) Films processed for 2 hours at 150°C in 0.5 M (Ba,Sr)(0H)2-8H20 solution.
Figure 5.9 continued: Variation of relative perm ittivity of raw and processed BST
films with different powder to sol-gel ratios. The legends give the powder to sol-gel
mass ratio of the sol-gel composite used to produce th e film under test.
94
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20
18
16
14
12
a
1:2
•
1:10
♦ sol-gel
w 10
8
6
4
♦
2
♦
▼
0
0
20
40
Frequency (GHz)
a) Films prior to hydrothermal processing.
Figure 5.10: V ariation of relative p erm ittivity of raw and processed BST: 5 at% Mn
films with different powder to sol-gel ratios. The legends give the powder to sol-gel
mass ratio of the sol-gel composite used to produce the film under test.
95
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600
500
400
1:10
♦ sol-gel
•
w"300
200
100
0
10
20
30
Frequency (GHz)
b) Films processed for 2 hours at 150°C in 0.5 M (Ba,Sr)(0H)2-8H20 solution.
Figure 5.10 continued: Variation of relative perm ittiv ity of raw and processed BST:
5 at% Mn films w ith different powder to sol-gel ratios. The legends give the powder
to sol-gel mass ratio of the sol-gel composite used to produce the film under test.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure 5.11 shows the sim ulated and measured S2 1 resonance of a typical test
structure.
The simulated curve includes conductor losses.
The second sim ulated
curve also includes losses of the BST film under test. Figure 5.12 shows the losses of
th e processed BST film w ith powder to sol-gel ratio of 1:1 as a function of frequency.
Since th e simulations used to obtain these values did not include the necessary losses
of the test structure in addition to conductor losses, these values for th e loss tangent
of the BST film are maximal values.
97
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Frequency (GHz)
5
6
7
8
9
10 11 12 13 14 15
0
-2
-4ffl
6
S -8 •
^ ■ 1° -
12
-
-14-16_____
-18
Measured
^^Simulated (BST Loss Tangent =0)
— Simulated (BST Loss Tangent = 0.034)
Figure 5.11: Typical sim ulated and m easured d a ta used in determ ining th e loss ta n ­
gent of the BST layer. This particular sample is a BST film w ith powder to sol-gel
ratio of 1:1.
98
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0.07
0.06
c
o
O)
c
,2 0.05
<0
(0
o
0.04
0.03 "'
10.00
1
11.25
1
12.50
13.75
15.00
Frequency (GHz)
Figure 5.12: Loss tangent of BST w ith powder to sol-gel ratio of 1:1 not consider­
ing conductor losses due to factors such as surface roughness. The values here are
therefore m axim um values for th e loss of the BST layer.
Typically, good quality dielectric m aterials require high tem peratures for densification. Normally, the quality of the m aterial varies directly w ith its density. It is there­
fore surprising th a t hydrotherm ally crystallized BST should exhibit th e favourable
dielectric properties dem onstrated here. M icrostructural studies indicate th a t this
processing m ethod produces a highly porous film. This film is, however, also highly
connected. It is believed th a t it is this connectivity and small num ber of barriers in
the m icrostructure which gives rise to the high dielectric constant and relatively low
loss tangent found in these films.
99
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*
C hapter 6
P h ysical Basis for Film Behaviour
100
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T he values obtained for the perm ittivity of hydrotherm ally processed BST films
are som ew hat surprising. Since the films are not processed at high tem peratures,
there is no mechanism for densification via traditional sintering. The low tem per­
ature of processing is also expected to leave non-BST residues in th e film in the
form of organic compounds, hydroxides, and water. This would typically be expected
to lower the dielectric constant and not give rise to the constant values for p erm it­
tivity w ith frequency in the 1-100 kHz range which have been exhibited. The m ost
obvious feature of the m icrostructural changes in the film upon hydrotherm al process­
ing is th e form ation of partially crystallized bridges between powder particles and a
sm ooth interface between the powder particles and the interconnecting bridges. Here,
the increase in dielectric constant upon hydrotherm al processing and its frequency
dependence is described in term s of the formation of this m icrostructre in which a
connected network of BST is formed w ith few barriers.
6.1
F req uency D e p e n d en ce o f P e r m ittiv ity
In the 1-100 kHz range, the films studied here exhibit essentially constant values
for dielectric perm ittivity w ith frequency. Conversely, at GHz frequencies, the per­
m ittivity exhibits an exponential decrease w ith frequency. The general form of this
behaviour can be described in term s of films comprised of elements exhibiting a wide
range of relaxation times. Such a distribution of relaxation tim es is suggested by the
m icrostructure of the films, as there are elements of m any different sizes comprising
the films. Bisquert and Garcia-Belmonte [46] derive th e distribution of relaxation
times for a m aterial w ith a fractal dimension D to be
G (t ) =
a
fo r r < t0,
G (r)
0
f o r t > t 0.
=
(6-1)
where a = 2 (l-D /3 ) and r 0 is the RC tim e constant for th e largest element of the film.
101
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The relaxation function is defined as
o
1 + iu r
a
r To
(6*2)
which for G (r) as given in 6.1 yields
At frequencies in excess of r0 ,
r a_1
(6,3)
is given by
(6.4)
The relaxation function is related to the complex perm ittivity via
^0
Cqo
(6.5)
where e(u>) is the frequency-dependent complex perm ittivity, eo is the static value of
the complex perm ittivity, and
is the high-frequency value of the complex p erm it­
tivity.
For frequencies in excess of r 0 1 the frequency dependent complex perm ittivity can
thus be w ritten
( 6 .6 )
This gives an essentially constant value for perm ittivity at frequencies below To,
and an exponential decrease in perm ittivity above such frequency. This is consistent
w ith experim ental results.
6.2
H igh F requency P e r m ittiv ity
At GHz frequencies there is a large difference between the perm ittivity of hydrothermally processed films and of the unprocessed sol-gel composite films. This disparity
can be explained in term s of the elim ination of low -perm ittivity boundary layers in
the processed films. Figure 5.9 (b) indicates th a t the high-frequency perm ittivity of
102
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the film produced from a sol-gel composite with a 1:1 powder to sol-gel ratio is 94.
Figure 5.9 (a) indicates th a t the perm ittivity of this same film before processing is 8.
Ignoring the porosity of the film (as it is similar in the raw and processed films),
the loosest bounds on the m ixture of two dielectrics are the W iener bounds [47] given
by
£ eff,m a x
f
~I- (1
/)^ei
(6.7)
( 6 .8 )
fce // ,m in
where a m aterial with perm ittivity ee contains / volume percent m aterial w ith per­
m ittivity ti
If the boundaries of the film are assumed to be present only prior to hydrotherm al
processing, and these boundary layers are assumed to have a p erm ittivity of 1, then
the lower W iener bound indicates th a t to agree w ith experim ental perm ittivity values,
11% of the non-pore volume of the film m ust consist of boundary. For a spherical
particle w ith diam eter 0.3 \im this is equivalent to a boundary on th e outer surface
of 6 nm.
This analysis indicates th a t even a relatively thin low -perm ittivity barrier can re­
sult in a significant reduction in the overall perm ittivity of the film. This, combined
w ith the sm ooth interfaces shown in TEM images tends to indicate th a t hydrotherm al
processing of sol-gel composites does result in a uniquely well-connected m icrostruc­
ture with few barriers which results in the ability to deposit extrem ely high quality
films at very low tem peratures.
6.3
A M o d el for F ilm P e r m ittiv ity from 1 kH z to
40 G H z
A more detailed m ethod of exam ining the effect of m icrostructure on the dielectric
perm ittivity of a porous m edium such as hydrotherm ally processed sol-gel com posite
103
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BST films has been developed by S. Thevanayagam [48]. The m ethod was establiished
in order to describe the behaviour of sedim entary rocks, which neutron experiments
have shown to have pore surfaces and skeletal structures which may be character­
ized by fractals [49], however it is equally applicable to the connected structure of
hydrotherm ally processed sol-gel composite films resulting from the in situ form ation
of sol-gel derived bridges joining powder particles.
In this model the porous skeleton and pore surface are considered to be express­
ible as a series of subm atrix structures at different scale levels. The effect of grain
boundaries can also be included since the charcteristics of the two constituents of
each subm atrix element may be different from the constituents of elements at other
scale levels.
The m ost basic subm atrix element can be considered to consist of a solid skeleton
(bulk BST) phase and a grain boundary phase. These subm atrix elements are com­
bined to form the ’solid’ phase of a larger subm atrix element which also consists of
a contribution from the pore structure. Subm atrix elements may be thus combined
indefinitely until the whole film structure is modeled. At each stage the subm atrix
consists of two phases; one phase is the entire subm atrix element from the previous
scale level, and one phase may be defined independently as is dem anded by the phys­
ical structure being modeled. In this analysis a three level structure is considered.
At each scale level an electric field propagating through the medium can be con­
sidered to encounter three paths: The ’solid’ (bulk BST at the lowest level or the
bulk and grain boundary combined stru ctu re at the next level), the ’surrounding’
(grain boundary at the lowest level or pore at the next level), or a combination of the
two. At scale level i, let the probabilities of encountering the three paths described
above be q , bi, and
respectively. In this case a,i+bi+Ci=1. In the case th a t the
p ath consisting of both the solid and surrounding phase is encountered, let the prob­
ability of encountering the solid phase in this p ath be
and thus the probability of
104
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encountering the surrounding phase is 1-dj. Assuming th a t the above probabilities
are proportional to the cross-sectional area of each p ath encountered, a schematic of
how a m edium is constructed from subm atrix elements and a representation of the
probabilities described above is given in Fig. 6.1
T he m icrostructure of the medium at scale level % is thus represented by the
probabilities cp, bi, q , and di. These probabilities need not be single valued. For
instance, in an anisotropic medium the probabilities will differ for different directions.
Each phase of a subm atrix element may be represented as a parallel RC element.
Given the above description of the medium the probabilities of discrete paths being
encountered can be determ ined in term s of the above probabilities. Network analysis
may be used to determ ine the equations for the perm ittivity (ej) and conductivity (cr,)
of m edium at level j . In term s of the characteristics of the m aterial at the previous
level this gives
d j)S j . 1
4?(1
4
u>2^2
e,o / c/ i cJ +
dj
Oi =
4/
(6.9)
+ b'ji tG - i
( 6 . 10 )
di
dj{ I - d j)S j
1 —d-i
■ ef i ai -1 |
d;
+
da
+
bj CTj - 1
+
Cj CTfj ,
where
a fj
a3~l
dj
+
11 efj
— di
€ j -1
(6 . 11)
and
dj + bj + Cj — 1;
The meaning of the probabilities
dj < 1 .
(6 . 12)
, bi, Ci, and di can be interpreted in term s of
the connectivity of regions of the solid phase of th e medium. This can give further
insight into the physical indications of the probabilities. Let rij be the region filled
105
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by solid a t scale level j. The to tal region filled by solid, n, is given by
n=
£
nr
(6,13)
j= l ,2 .. m
1 -d
..w?:
-v
!. - ■- - J►
T
grain
boundary
■
j =2
pore
Figure 6.1: Fractal model of film m icrostructure
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
d3
Figure 6.2: N om enclature for grain boundary and bulk contributions at scale level
j= 3 .
The distribution of solid regions for a three level stru ctu re is depicted in Fig. 6.2.
At each level continuous regions have a subscript c and discontinuous regions have a
subscript d.
The types of solid regions may be organized according to th e scale level w ith which
they are associated. For a three level system this gives rii as th e regions associated
w ith the first level, n 2 as the regions associated w ith the second level, and n 3 as
107
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the regions associated with the th ird level. These regions m ay be w ritten in term s
of the smaller regions which comprise them. This allows the probabilities a*, bi, Ci,
and di, z= l,2 ,3 to be w ritten in term s of the regions of solid with different levels
of connectivity. This allows for the effect of changing the size of a region w ith a
particular type of connectivity on the effective dielectric constant to be examined.
The solid region for level 1 is given by
ni
=
n'cl
=
0>3d3a2d2b]_,
n'di
=
a3d3a2d2aid\.
(6.14)
The solid regions for level 2 are given by
n2
= n 'c2 + r 4 + n"2 + r 4 ;
(6.15)
n'c2
= h a 2d2bl ,
(6.16)
n'd2
= bza2d2a\d\,
n"2
= a3d3b2b1 ,
n 'd2
= o,3d3b2a\d\.
The solid regions for level 3 are
n3
given by
= rics + rids;
nc 3 = 636261,
Tid3
(6.17)
( 6 -18 )
= b3b2a\di.
The preceding equations may be combined and rearranged to express the prob­
abilities a,i, bi, and q , i = l ,2,3 to be w ritten in term s of th e solid regions and the
param eter di.
The to tal connected structure, n c, may be expressed as th e sum of th e elements
with subscript c. Similarly the to tal disconnected structure, n d, may be expressed
108
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j
1 (processed)
1 (raw)
2
3
cij
h3
0.910
0.100
0.65
0.66
0.069
0.063
0.32
0.25
dj
0.020
0.250
0.90
0.80
cj
0.021
0.837
0.03
0.09
efj
10
10
1
1
afj
5
5
0
0
Table 6.1: Param eters used to fit model to experim ental data.
as the sum of the elements w ith subscript d. The to tal grain boundary, gb, may be
expressed as the sum of the partial grain boundaries as shown in Fig. 6.2. This gives
nc
= n c 3 + n'c2 + 77.^2 + Tl'ci
=
nd
~ h 6 3 (2 2 ( 6 2 6 1
+
® 3 (6 3 6 2 6 1
+ ^ 3 (6 3 (2 2 (6 2 6 1 ,
= rid3 + n'd2 + n d2 + n dl
=
gb
636261
(6.19)
6 3 6 2 0 1 (6 1
+
6 3 0 2 (6 2 (2 1 ( 6 1
(6.20)
+
0 3 (6 3 6 2 0 1 ( 6 1
+
0 3 (6 3 0 2 (6 2 0 1 (6 1 ,
= gbc3 -P gbd3 + gb'c2 + gb'd2 + gb"2 + gbd2 + gb>'cl + gbdl
=
63
&2 C1 +
+
0 3 (6 3 6 2 0 1 ( 1
6362
^ 1 ( 1 — di) + b3a2d2C\ +
— (6 1 ) +
0 3
(6 3 0
2 (6 2 0 1
+
( ^ 1 ( 1 — d\) +
6 3 0 2 62
0 3 (6 3 0 2 ( 6 2 0 1 ( 1
(6 .2 1 )
0 3 (6 3 6 2 0 1
— (6 1 ).
For the BST film produced from a sol-gel composite w ith a powder
of 1:1,
to sol-gel ratio
the m easured perm ittivity from 1 kHz to 40 GHz can be fit well using the
model described above w ith the param eter values as indicated in Table 6.1. The BST
powder is assumed to have a relative perm ittivity of 250 and a conductivity of 0. The
GHz frequency d a ta points obtained from extrapolation of th e curve shown in Fig.
5.8 are not included as they do not fit well w ith th e model described here. This may
indicate th a t extrapolation to these points was not accurate or th a t they represent
the results of phenom ena which are not accounted for in this model. The fit between
measured d a ta and th a t predicted by the model is shown in Fig. 6.3.
109
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P rocessed Film
0.734
0.001
0.071
0.193
Film Elem ent
Connected Bulk
Disconnected Bulk
G rain Boundary
Porosity
Raw Film
0.081
0.013
0.713
0.193
Table 6.2: Percentages of film constituents as derived from the model fit given above.
900
800
700
600
w 500
400
300
processed
raw
200
100
3
5
7
9
,11
Frequency (Hz)
Figure 6.3: F itting the model to experim ental data. The solid line represents the
model fit and the points are experim ental data.
The sizes of regions of the film comprised of various constituents as calculated from
equations 6.20, 6.21, and 6.22 are given in Table 6.2. The processed film consists of
a much smaller region occupied by grain boundaries and a much larger region of the
film occupied by bulk BST (the porosity of th e raw and processed films are taken to
110
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be the sam e in this analysis). The region of the processed film occupied by connected
bulk ra th e r th a n disconnected bulk is also much larger in the processed him th a n in
the raw him.
The param eters used here to h t the model to the experim ental d a ta are not the
only set which give a reasonable ht. The lack of experim ental d ata in the midrange
of frequencies makes a more precise dehnition of the param eters difficult. The pa­
ram eters used to give the ht here are physically reasonable. The h t is sufficient to
dem onstrate th a t the model presented here can adequately describe th e physical be­
haviour of the him in term s of the frequency response of the dielectric constant. The
h t shown here also dem onstrates th a t the proposed mechanism by which hydrotherm al
processing affects the dielectric constant of the sol-gel composite hlms is reasonable
in th a t the grain boundaries in hlms are elim inated and m icrostructure consisting of
connected bulk is formed.
Ill
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C hapter 7
C onclusions
112
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It has been shown th a t the conventional hydrotherm al processing of titan iu m films
is not a viable technique for the fabrication of BST films. W hile XRD studies indicate
th a t crystalline BST is formed by such a process, the films rem ain highly enriched
in tita n iu m and are highly conductive. The technique of hydrotherm ally processing
sol-gel BST films is taken as a second approach to the problem.
XRD studies indicated th a t sol-gel BST films may be crystallized via hydrotherm al
processing, however the composition of the processed film is highly dependent on the
concentration of the solution used in hydrotherm al processing. Films produced from
acetic acid based sol-gels are found to have higher dielectric constants and lower loss
tangents th a n films produced from 2-methoxyethanol based sol-gels so acetic acid is
the preferred solvent.
It has been found th a t it is necessary to subject sol-gel and sol-gel composite films
to a high-hum idity atm osphere before hydrotherm al processing or the deposition of
another sol-gel or sol-gel composite layer. If this is not done then th e already deposited
film is dissolved and removed from the substrate. This has been explained in term s
of a hydrolysis of the film.
Sol-gel composite BST has been produced, and used to deposit films via spin
coating. It has been shown th a t this film may be hydrotherm ally processed w ithout
com positional changes, unlike the non-composite sol-gel derived films. The final stoi­
chiometry of the film is determ ined prim arily by the powder constituents of the film,
resulting in a b e tte r ability to control the stoichiom etry of the film th an in the case of a
simple sol-gel w ithout powder. The effects of varying process tim e, tem perature, and
concentration of the hydrotherm al solution on th e m icrostructure and low-frequency
electrical behaviour of the films have been examined. Longer process durations, higher
process tem peratures, and increased concentration of the hydrotherm al solution are
found to produce denser films w ith higher perm ittivity.
Relative perm ittivities of
er =400-1300 have been measured in the frequency range 1-100 kHz. Loss tangents
113
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at 100 kHz lie in the range 0.05 < tan S < 0.10. The maximum dielectric constant
achieved at 100 kHz was 1264.
SEM, AFM, and TEM imaging has been used to examine the m icrostructure of
the films. All techniques indicate th a t the morphology of the him evolves during
hydrotherm al processing via dissolution/redeposition of the surface of the powder
particles and epitaxial growth of sol-gel derived bridges between powder particles.
This results in the formation of a highly-connected m icrostructure w ith very few
barriers. The disappearance of barriers is dem onstrated through complex impedance
analysis of the hlms in the 1-100 kHz frequency range.
Bulk BST pellets have been im pregnated w ith BST sol-gel and subsequently hy­
drotherm ally processed. The sol-gel has been shown to hll pores in th e pellets well
and to form bridging structures across gaps. The perm ittivity of the pellets increased
dram atically from the pellets w ithout sol-gel to the hydrotherm ally processed sol-gel
pellets. T he increase was signihcantly greater th a n predicted by the increase in pellet
density alone. This result supports the conclusion th a t th e high p erm ittivity of the
hydrotherm ally processed sol-gel composite films is a result of the unique m icrostruc­
ture th a t results from this deposition technique.
The dielectric constant and loss tangent of BST th in films made by hydrother­
mally crystallizing a sol-gel composite film have been determ ined in the 5 to 40 GHz
frequency range by use of a novel technique involving the use of coplanar waveguides
w ith spur-line filters.
For a particular set of processing conditions, the dielectric
constant has been shown to increase w ith increased powder loading. T he m axim um
projected perm ittivity at 40 GHz is 94. Doping with 5 at% Mn has been shown to
decrease the dielectric constant slightly. O btaining sensible and meaningful results
from this measurem ent technique not only provides inform ation on th e characteris­
tics of hydrotherm ally processed sol-gel com posite films at GHz frequencies bu t also
validates the m easurem ent technique.
114
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The dependence of the perm ittivity of the films on frequency of operation and on
the effects of hydrotherm al processing has been explained in term s of the form ation
of a highly-connected m icrostructure containing few barriers via the hydrotherm al
processing of sol-gel composites.
115
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C hapter 8
Suggested Further Work
116
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There are many variables which affect the final characteristics of a hydrotherm ally
crystallized sol-gel composite film. These include, but are not lim ited to, constituents
and chem istry of the sol-gel, quality and size of powder used, deposition conditions,
substrate, and hydrotherm al processing param eters.
Due to the large num ber of
variables involved, exhaustive studies for the optim ization of the hydrotherm al process
for a particular application has not been performed here. There is a great potential
for work to be done in this area.
The implications of the ability to deposit high-quality ceramic films at tem pera­
tures below 200°C are wide-reaching. This particular study has been lim ited to the
hydrotherm al crystallization of sol-gel composite BST, however there is no reason th a t
the techniques developed here cannot be extended to include other compounds. There
are many ceramics which have been synthesized hydrotherm ally in powder form. Of
these many have also been fabricated by sol-gel routes. In principal, any com pound
which can be synthesized hydrotherm ally from organic precursors is a candidate for
production via a sol-gel composite hydrotherm al process. In particular, hydrotherm al
processing of sol-gel composites may be applicable to th e deposition of electrolumi­
nescent m aterials. Electrolum inescent m aterials have been deposited by b o th sol-gel
[50, 51] and hydrotherm al [52, 53] methods.
As has been dem onstrated by way of im pregnating porous BST pellets w ith solgel and then hydrotherm ally treatin g them , the application of hydrotherm al crys­
tallization of a sol-gel is not necessarily lim ited to th e production of ceramic films.
A nother possible application deals w ith th e adhesion of ceramic resonators to inte­
grated circuits. Conventional techniques leave air spaces between the resonator and
the substrates. These gaps contribute significantly to the lossiness of the circuit el­
ement. As seen in the m icrostructure of films produced here, as well as in the pore
filling of the BST pellets, hydrotherm ally processed sol-gel tends to fill in gaps and
m atch well w ith the initial ceramic powder elements. It m ay therefore be possible to
117
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grow a layer between the circuit and the resonator by hydrotherm ally crystallizing a
sol-gel or sol-gel composite layer which would improve th e loss characteristics of the
resonator.
In order to asses the applicability of this process to the deposition of films on
various substrates GaAs, Si w ith benzocyclobutene (BCB, a common passivation
layer), high density polyethylene and high density polypropylene were hydrotherm ally
processed. In the case of the polymers, BST sol-gel composite films were deposited
on top of the substrate prior to processing. Q ualitatively these substrates appear
unchanged after processing for 5 h at 200°C in 0.5 M (B a,S r)(0 H )2-8H20 solution.
No quantitative characterization of th e effect of hydrotherm al processing on these
substrates has been completed, however. This needs to be done in order to gauge the
feasibility of hydrotherm al processing of sol-gel composites as a practical deposition
technique for use w ith these substrates.
The hydrotherm al process is widely applicable, however it does have lim itations.
It is inherently a batch process due to the need for elevated pressures.
The use
of a highly alkaline solution also limits th e substrates which may be subjected to
hydrotherm al processing w ithout the use of protective coatings. Despite these few
lim itations hydrotherm al processing of sol-gel composites provides the first technique
by which high-quality ceramic films may be deposited at extrem ely low tem peratures.
118
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