ABSTRACT
AYGÜN, SEYMEN MURAT. Processing Science of Barium Titanate. (Under the direction of Jon-Paul Maria.)
Barium titanate and barium strontium titanate thin films were deposited on base metal foils via chemical solution deposition and radio frequency magnetron sputtering. The films were processed at elevated temperatures for densification and crystallization. Two unifying research goals underpin all experiments: 1) To improve our fundamental understanding of complex oxide processing science, and 2) to translate those improvements into materials with superior structural and electrical properties.
The relationships linking dielectric response, grain size, and thermal budget for sputtered barium strontium titanate were illustrated. (Ba0.6Sr0.4)TiO3 films were sputtered on nickel foils at temperatures ranging between 100-400 °C. After the top electrode deposition, the films were co-fired at 900 °C for densification and crystallization. The dielectric properties were observed to improve with increasing sputter temperature reaching a permittivity of 1800, a tunability of 10:1, and a loss tangent of less than 0.015 for the sample sputtered at 400 °C. The data can be understood using a brick wall model incorporating a high permittivity grain interior with low permittivity grain boundary. However, this high permittivity value was achieved at a grain size of 80 nm, which is typically associated with strong suppression of the dielectric response. These results clearly show that conventional models that parameterize permittivity with crystal diameter or film thickness alone are insufficiently sophisticated. Better models are needed that incorporate the influence of microstructure and crystal structure. This thesis next explores the ability to tune microstructure and properties of
chemically solution deposited BaTiO3 thin films by modulation of heat treatment thermal profiles and firing atmosphere composition. Barium titanate films were deposited on copper foils using hybrid-chelate chemistries. An in-situ gas analysis process was developed to probe the organic removal and the barium titanate phase formation. The exhaust gases emitted during the firing of barium titanate films were monitored using a residual gas analyzer (RGA) to investigate the effects of ramp rate and oxygen partial pressure. The dielectric properties including capacitor yield were correlated to the RGA data and microstructure. This information was used to tailor a thermal profile to obtain the optimum
-13 dielectric response. A ramp rate of 20 °C/min and a pO2 of 10 atm resulted in a
permittivity of 1500, a loss tangent of 0.035 and a 90 % capacitor yield in 0.5 mm dot
capacitors. Yield values above 90% represent a significant advantage over preexisting reports
and can be attributed to an improved ability to control final porosity.
Finally, the dramatic enhancement in film density was demonstrated by
understanding the processing science relationships between organic removal, crystallization,
and densification in chemical solution deposition. The in situ gas analysis was used to
develop an each-layer-fired approach that provides for effective organic removal, thus pore
elimination, larger grain sizes, and superior densification. The combination of large grain
size and high density enabled reproducing bulk-like dielectric properties in a thin film. A
room temperature permittivity of 3000, a 5 μF/cm2 capacitance density, and a dielectric
tunability of 15:1 were achieved.
By combining the data sets generated in this thesis with those of comparable literature
reports, we were able to broadly rationalize scaling effects in polycrystalline thin films. We show that the same models successfully applied to bulk ceramic systems are appropriate for thin films, and that models involving parasitic interfacial layers are not needed. Developing better models for scaling effects were made possible solely by advancing our ability to synthesize materials thus eliminating artifacts and extrinsic effects. Processing Science of Barium Titanate
by Seymen Murat Aygun
A dissertation submitted to the Graduate Faculty of North Carolina State University in partial fulfillment of the requirements for the degree of Doctor of Philosophy
Materials Science and Engineering
Raleigh, North Carolina
2009
APPROVED BY:
______Jon-Paul Maria Zlatko Sitar Associate Professor Professor Materials Science and Engineering Materials Science and Engineering Committee Chair
______Gregory Parsons Yuntian Zhu Professor Associate Professor Chemical Engineering Materials Science and Engineering DEDICATION
To my family
ii BIOGRAPHY
Seymen Aygün was born on August 11, 1980 to parents Baykut and Sezer Aygün in
Ankara, Turkey. He graduated from METU (Middle East Technical University) High School and enrolled at the Metallurgical and Materials Science Department of METU. He received his B.S. in 2002. After that, he decided to continue his journey in the US and he worked with
Dr. David Cann at Iowa State University of Science and Technology where he received his master’s degree in 2005. After spending a year and a half as a postmaster researcher under supervision of Dr. Jon-Paul Maria at North Carolina State University, he decided to pursue
Ph.D. and received his degree in 2009.
iii ACKNOWLEDGEMENTS
First I would like to thank my mentor and friend Professor Jon-Paul Maria for the opportunities, guidance, and convincing me to pursue Ph.D. I am grateful for the four years I have spent at NCSU. I would also like to thank my friends at MSE; Jon Ihlefeld, Brian
Laughlin, Mark Losego, Dipankar Ghosh, Spalding Craft, Patrick Daniels, Peter Gaifun Lam,
Jimster, Erin Gross, Michelle Casper, Elizabeth Paisley, Jesse Jur, James Steel, and Tony
Rice. I would like to acknowledge the help of Dr. Bill Borland with my research. I would like to thank Dick Parham and Edna Deas for their help and patience with my administrative problems.
Also to my friends Metin, Eren, Erdem, Berna, and Arun. To Utkan for her love and support. Finally, and most importantly, I would like to express my gratitude to my family.
Thank you for your constant love, support and patience. I could not have accomplished this without you.
iv TABLE OF CONTENTS
LIST OF FIGURES...... viii
LIST OF TABLES ...... xiii
CHAPTER 1. INTRODUCTION ...... 1
CHAPTER 2. LITERATURE REVIEW...... 3
2.1 Dielectrics ...... 3
2.2 Classification in Terms of Crystal Symmetry...... 11
2.3 Ferroelectricity ...... 13
2.3.2 Theory of Ferroelectricity ...... 14
2.3.3 Dielectric Properties of Ferroelectrics ...... 21
2.4 Perovskite Structure and The Archetypical Ferroelectric BaTiO3 ...... 31
2.4.1 Crystal Structure and Phase Transitions...... 31
2.4.2 Dielectric Properties...... 35
2.4.3 Compositional Modification with SrTiO3 ...... 38
2.4.4 Stress-Strain Effects...... 40
2.5 Scaling Effects in BaTiO3 ...... 43
2.5.1 Scaling Effects in Bulk BaTiO3 ...... 44
2.5.2 Scaling Effects in Thin Film BaTiO3 ...... 49
2.6 Processing of BaTiO3 – (Ba,Sr)TiO3 Thin Films ...... 57
2.6.1 Magnetron Sputtering...... 58
2.6.2 Chemical Solution Deposition...... 63
v 2.6.3 Firing of Thin Films on Base Metal Substrates...... 81
References...... 85
CHAPTER 3. EXPERIMENTAL PROCEDURES ...... 104
3.1 Barium Strontium Titanate Sputtering on Base Metal Foils...... 104
3.2 Chemical Solution Deposition of Barium Titanate ...... 107
3.3 Low pO2 Processing of Thin Films ...... 109
3.3.1 Firing of Sputtered BST Thin Films ...... 109
3.3.2 Firing and Probing the Phase Evolution of CSD Barium Titanate Thin Films.112
3.3.3 Reoxidation Anneals ...... 116
3.3.4 Physical Characterization of the Thin Films ...... 119
3.3.5 Electrical Characterization of The Thin Films ...... 120
References...... 122
CHAPTER 4. HOT SPUTTERING OF BARIUM STRONTIUM TITANATE ON
BASE METAL FOILS ...... 124
4.1 Hot Sputtering of Barium Strontium Titanate on Nickel Foils...... 124
4.1.1 Introduction ...... 125
4.1.2 Experimental Procedure ...... 127
4.1.3 Results and Discussion...... 130
4.1.4 Summary...... 143
4.2 Hot Sputtering of Barium Strontium Titanate on Copper Foils...... 143
References...... 148
vi CHAPTER 5. PROCESS-PROPERTY RELATIONSHIPS IN CHEMICAL
SOLUTION DEPOSITED BARIUM TITANATE THIN FILMS ...... 154
5.1 Abstract...... 154
5.2 Introduction...... 155
5.3 Experimental Procedure...... 158
5.4 Results and Discussion ...... 161
5.5 Summary...... 176
References...... 177
CHAPTER 6. HIGH DENSITY CHEMICAL SOLUTION DEPOSITED BARIUM
TITANATE THIN FILMS...... 182
6.1 Experimental ...... 194
References...... 195
CHAPTER 7. CONCLUSIONS AND FUTURE WORK ...... 198
7.1 Conclusions ...... 198
7.2 Future Work ...... 199
References...... 200
vii LIST OF FIGURES
Figure 2.1 Schematic representation of dielectric polarization...... 4
Figure 2.2 Schematic representation of the frequency dependence of complex
permittivity in the presence of various polarization mechanisms...... 9
Figure 2.3 Schematic representation of the spontaneous polarization as a function of
temperature for a first order (a) and a second order (b) phase transition...... 16
Figure 2.4 Schematic representation of the polarization with a finite wavelength and
infinite wavelength...... 19
Figure 2.5 Schematic representation of (a) 180° and (b) 90° domain walls...... 20
Figure 2.6 Polarization vs. electric field curves for a single crystal ferroelectric, a
polycrystalline ferroelectric, and a ferroelectric in the paraelectric state...... 22
Figure 2.7 Relative permittivity vs. electric field curves for a ferroelectric and a
paraelectric material...... 25
Figure 2.8 Schematic representation of frequency dependencies of (1) three-quantum, (2)
four quantum, and (3) quasi-Debye mechanisms. o and o are the soft-
mode frequency and damping...... 30
Figure 2.9 Perovskite unit cell shown with the BO6 octahedron...... 32
Figure 2.10 Cubic and tetragonal unit cells of BaTiO3...... 34
Figure 2.11 Schematic potential wells...... 35
Figure 2.12 Dielectric constants Ka and Kc for single crystal BaTiO3...... 36
Figure 2.13 Relaxation of ferroelectric BaTiO3...... 37
viii Figure 2.14 Curie temperature dependence of BaxSr1-xTiO3 on Ba concentration...... 39
Figure 2.15 Dielectric constant of BaTiO3 as a function of grain size...... 46
Figure 2.16 Temperature dependence of permittivity of BaTiO3 with changing
thickness...... 47
Figure 2.17 Temperature dependence of permittivity of BST films with changing
thickness...... 55
Figure 2.18 Schematic depiction of magnetron sputtering...... 59
Figure 2.19 Schematic plot of an amorphous CSD film, the supercooled liquid, and the
crystalline perovskite phase...... 73
Figure 2.20 TTT and sintering curves for an amorphous material...... 76
Figure 2.21 Nucleation (Iv) and growth (u) rate data for anorthite...... 77
Figure 2.22 pO2 versus temperature diagram for the oxidation of metals...... 83
Figure 3.1 Atomic force microscopy images of Cu and Ni foils...... 105
Figure 3.2 (a) Schematic illustration of the sputtering system and (b) nickel and copper
samples on a quartz plate...... 106
Figure 3.3 Process flow for barium titanate chemical solution deposition...... 109
Figure 3.4 Illustration of the system used for low pO2 firing...... 112
Figure 3.5 Physical and chemical processes that occur during firing of a chemical
solution deposited thin film...... 113
Figure 3.6 Schematic illustration of the system used for in-situ experiments...... 114
Figure 3.7 Defect concentrations in undoped-BaTiO3 as a function of pO2...... 118
ix Figure 4.1 pO2 vs. temperature diagram showing the processing window in which the
oxides of Ba, Sr, and Ti are stable with metallic Ni...... 128
Figure 4.2 X-Ray diffraction patterns of the samples for (a) as-deposited and (b) fired at
900 °C...... 130
Figure 4.3 Capacitance and loss tangent vs. field curves for the as-deposited samples
sputtered at 100 °C and 400 °C...... 131
Figure 4.4 (a) Capacitance and loss tangent vs. field curves for the samples sputtered in
the range 100-400 °C (b) Tunability vs. sputtering temperature plot...... 133
Figure 4.5 SEM surface image of the sample, which was sputtered at 400 °C (de-wetted
light colored areas are Pt)...... 134
Figure 4.6 Field dependency of (a) Dielectric constant and (b) Leakage current density
of the sample sputtered at 400 °C...... 135
Figure 4.7 Atomic force microscopy images of the samples sputtered at (a) 100 °C, (b)
200 °C, (c) 300 °C, and (d) 400 °C...... 136
Figure 4.8 Temperature dependency of dielectric constant and loss tangent for the
samples sputtered at 100-400 °C...... 138
Figure 4.9 Comparison of dielectric constant values as a function of crystal dimension
taken from several reports...... 141
Figure 4.10 XRD patterns of the (a) as-deposited samples and (b) those fired at 900
°C...... 145
Figure 4.11 Optical microscope image of a 0.5 mm diameter Pt electrode...... 146
x Figure 4.12 Permittivity and loss tangent vs. field curves for the samples sputtered in the
range of 100-300 °C...... 147
Figure 5.1 Changes in the partial pressure of carbon dioxide as a function of time and
temperature for different flow rates...... 162
Figure 5.2 (a) X-Ray diffraction patterns and (b) Raman spectra of the barium titanate
thin films...... 165
Figure 5.3 Changes in the carbon dioxide partial pressure as a function of time and
temperature for the ramp rates of (a) 3 °C/min and (b) 1 °C/min...... 166
Figure 5.4 Plane view images of the samples fired with (a) 20 °C/min, (b) 1 °C/min, and
(c) rapid ramp rates...... 168
Figure 5.5 Cross-sectional images of the samples fired with (a) 20 °C/min, (b) 1 °C/min,
and (c) rapid ramp rates...... 169
Figure 5.6 Permittivity versus applied bias curves for the samples fired with a ramp rate
of (a) rapid, (b) 20 °C/min, (c) 3 °C/min, and (d) 1 °C/min...... 170
Figure 5.7 Changes in the carbon dioxide partial pressure as a function of time and
temperature for the oxygen partial pressures of (a) 10-15 atm and (b) 10-11 atm
above 700 °C...... 173
Figure 5.8 Plane view images of the samples fired at a pO2 of (a) 10-15 atm and (b) 10-11
atm above 700 °C...... 175
Figure 5.9 Cross-sectional images of the samples fired at a pO2 of (a) 10-15 atm and (b)
10-11 atm above 700 °C...... 175
-15 Figure 5.10 Permittivity versus applied bias of the samples fired at a pO2 of (a) 10
xi atm and (b) 10-11 atm above 700 °C...... 176
Figure 6.1 Plane view images of (a) one-step, (b) two-step, and (c) each-layer-fired
samples...... 185
Figure 6.2 Cross-sectional images of (a) one-step, (b) two-step, and (c) each-layer-fired
samples...... 186
Figure 6.3 Fracture images of (a) one-step, (b) two-step, and (c) each-layer-fired
samples...... 188
Figure 6.4 (a) Permittvity vs. applied bias and (b) temperature dependent permittivity
curves for the three firing conditions...... 190
Figure 6.5 Grain size dependence of permittivity comparison for pertinent data sets in
the literature...... 192
xii LIST OF TABLES
Table 4.1 Summary of the atomic force microscopy results...... 137
Table 5.1 Summary of the SEM and yield studies...... 172
Table 6.1 Summary of the scanning electron microscopy results...... 187
xiii CHAPTER 1. INTRODUCTION
The ever-increasing advancements in electronic systems require continuous
miniaturization of electronic circuits. As the sophistication and functionality of commercial and industrial electronics increase, the number of active circuit components such as integrated circuits (ICs) and passive components (resistors, inductors, and capacitors) must scale similarly and the price for each component must go down. For instance, the number of capacitors in a modern cellular phone has surpassed 500, while the average price has remained constant. This technology trend cannot be sustained using the conventional surface mounting approach. One avenue to shrink the size of these circuits is embedding passive components such as thin film capacitors within the printed wiring board. There are three main advantages of this method. First, surface space can be freed allowing more ICs; second, the inductive losses from metallization are reduced since the passive components can be located directly underneath the ICs, and third; the low cost of planar parallel processing compared to the series pick-and-place assembly. However, the lack of a reliable process for integration, insufficient capacitance density, and the cost issues stemming from expensive electrode materials has slowed down the progression of this approach.
This thesis discusses the research efforts to understand the structure-process-property relationships that regulate ferroelectricity in thin layers, and to develop high quality ferroelectric thin films suitable for embedded applications. The research was conducted through collaboration between North Carolina State University and DuPont Microelectronics.
Methods for sputtering and chemical solution deposition of BaTiO3 and (Ba,Sr)TiO3 (BST)
1 thin films directly on base metal foils are discussed in addition to an expanded understanding
of scaling effects in ferroelectric thin films. Process-property relationships are investigated
by systematic selection and variation of three principle synthesis parameters: (i) thermal
budget, (ii) atmosphere control, and (iii) thermal profiles for organic removal.
Chapter 4 focuses on the sputtering of BST on copper and nickel foils. The ability to observe large permittivity in fine grain ceramic films is demonstrated and a hypothesis is supported which attributes scaling effects to crystal mosaicity as opposed to crystal
dimension. Chapter 5 explores the processing of BaTiO3 deposited on copper foils via
chemical solution deposition and specifically how heat treatment profiles influence the
evolution of crystal structure, microstructure, and the dielectric properties. An In-situ
experimental capability is developed to enable our study of process-property relationshiops.
In Chapter 6, we use the information learned by our in situ experiments and develop an each-
layer-fired approach which optimizes BaTiO3 properties and produces thin layers with permittivity values of 3500 .
2 CHAPTER 2. LITERATURE REVIEW
2.1 Dielectrics
Dielectrics, also called insulators, are materials with a small number of charge
6 - 3 carriers (<10 e /m ) and large band gaps, Eg > 2.5 eV [1]. These materials can store energy
by neutralizing charges at the dielectric/electrode interface in a capacitor [2]. This phenomenon is known as polarization, which arises from a finite displacement of positive and negative charges, i.e. formation of dipoles, under applied electric field. This is different from conduction, where there is a finite average velocity of charge motion under applied electric field.
If a dielectric material is inserted between the plates of a capacitor, it increases the charge storage ability per unit voltage by a factor of r, where r is the relative permittivity
(or dielectric constant). Faraday was the first to recognize this increase in capacitance due to
the polarization of the dielectric medium between the capacitor plates in the 1830s [3]. This
can be pictured as the free ends of dipole chains neutralizing the opposite charges on the
terminating metal plates, as shown in Figure 2.1. The dielectric material between the metal
plates responds to the applied electric field by forming dipoles. Each dipole, which is a pair
of opposite charges +q and –q, creates a dipole moment, which is given by
v pv qd Eq. (2.1) =
3 v where q is the charge and d is the charge separation (vector). Polarizability, which is the ability of an atom or molecule to become polarized, relates the dipole moment to the applied field through
v pv E Eq. (2.2) =
where is the polarizability. The sum of all the dipole moments gives the polarization, which is defined by
v P N pv Eq. (2.3) =
where N is the number of dipoles per cubic meter. Ideally, the applied field, polarization, dipole moment, and separation vectors are parallel. v E applied + - + - + - + - + - + - dipole + - + - + - + - + - - + + - pv + - + - + - + - + - v P Figure 2.1. Schematic representation of dielectric polarization.
4 In dielectrics, the material’s ability to polarize is quantified by the dielectric constant
(or relative permittivity) or the dielectric susceptibility. The material polarizes by either
creating dipoles or modifying existing fixed dipoles in linear dielectrics, or by reorienting re-
orientable dipoles in non-linear dielectrics. The relationship between polarization and electric field is given by
v v v v P = oE or P = ( 1) E Eq. (2.4) r o
where is the dielectric susceptibility, o is the permittivity of vacuum, and r is the relative
permittivity.
It is also important to differentiate between free and bound (polarization) charges [4].
In Figure 2.1, the charges stored on the plates are free, since they are the electrons in the
metal. On the other hand, the polarization charges in the dielectric are bound to the parent
ion/atom cores. The free charge on the capacitor plates is Qo when there is no dielectric in
between them. Under the application of an electric field, we may divide by the electrode area to define the electric flux density (or the dielectric displacement) as
v Qo v D = =oE Eq. (2.5) A
When a dielectric material is inserted, the free charges on the electrodes increase. This
increase is due to the neutralization of the polarization charges, QP. Therefore, the final free
5 charge on the plates is Q= Qo+ QP. The free surface charge density on the plates after the
dielectric inserted is given by v v v D P E Eq. (2.6) = +o
If the thickness of the dielectric is t, then the net capacitance is
A C = Eq. (2.7) o r t
At the microscopic level there are 4 main contributions to the polarization. These are
(i) electronic polarization, which arises from the deformation of electron cloud surrounding
the nucleus, (ii) ionic polarization, which arises from the displacement of lattice ions from their equilibrium positions, (iii) dipolar (orientational) polarization, which arises from the
orientation of a permanent dipole, and (iv) space charge (interfacial) polarization, which
arises from the migration of charge carriers within a heterogeneous material. The electronic
polarization mechanism is present in all materials, since there will always be electron clouds
around individual atoms/ions or electrons participating in covalent bonds. Ionic polarization
is present in most of the materials except covalent crystals as Si and Ge. In both electronic
and ionic polarization there are no dipoles if there is no applied field. Dipolar polarization is
observed in molecules with reorientable permanent dipoles such as H2O (l), BaTiO3 and NO2
(g). Finally, space charge polarization occurs whenever there is a possibility for field-induced
charge accumulation at an interface or boundary. For instance, these could be
6 dielectric/electrode interfaces or grain boundaries in the material. The dielectric constant of a
material is the sum of all polarization mechanisms
= + + + Eq. (2.8) r r,el r,ion r,dip r,sc 14 4 2 4 4 3 if present
In general, covalently bonded materials, which only have electronic polarization, have very
low permittivities (r<10), ionic bonded materials, which have electronic and ionic
polarization mechanisms, have permittivities in the range 10-40, while materials with dipolar
5 or space charge contributions can have permittivities exceeding 10 . The magnitude of r also depends on the electronic structure, stiffness of the lattice, density, and defects.
When there is an alternating field (i.e. a sinusoidal wave, E=Eo sin(t)) applied across
the capacitor, which is mostly the case in electrical circuits, the polarization of the dielectric
leads to an ac permittivity. This complex permittivity is given by
* = r i r Eq. (2.9)
The real part r corresponds to polarization in response to an electric field and is used as the
relative permittivity in calculating the capacitance. The imaginary part r corresponds to the
finite energy loss associated with the physical polarization process. It is usually quantified by
the term loss tangent,
7 tan = r Eq. (2.10) r
The phase difference between capacitor charging and discharging under an ac field (or the phase angle between the imaginary and the real components of permittivity) is 90o for perfect insulators with no loss and 0o for perfect conductors. Real capacitors have phase angle values in between these end points. Loss tangent is proportional to the heat generated per cycle.
Therefore, at high frequencies this can become an issue.
As it can be seen from the above equations, both relative permittivity and loss tangent are frequency dependent. The frequency response of permittivity and loss tangent depends on the active polarization mechanism in that frequency range. The frequency dependencies in the presence of space charge, dipolar, ionic, and electronic polarization are shown in Figure
2.2.
8 Figure 2.2 Schematic representation of the frequency dependence of complex permittivity in the presence of various polarization mechanisms (adapted from Kasap [4]).
Electronic and ionic polarization mechanisms can be thought as simple harmonic
oscillators in which the driving force is the oscillating electric field and the restoring force is
the Coulombic attraction between the species. These two mechanisms are active up to their resonant frequencies (el and ion), the point after which the oscillation of the electric field is
too fast for them to respond. Electronic polarization is active up to very high frequencies,
1015-1016 Hz, since electrons have very low mass. Above the electron resonance frequency
the material behaves no different than a vacuum (r~1). The ionic polarization is able to keep
up with the oscillating field up to ~1012 Hz, the lattice vibration frequency, above which the restoring force and the mass of ions are too large to support a dipole formation that fast.
Dipolar polarization can be generically visualized as charged species jumping
between the sites in a lattice. In the absence of an applied field these sites are equivalent,
9 however when a bias is applied a preference between the sites is generated. The collective of
preferential jumps will then result in net dipole formation [5]. There are mainly two factors opposing the alignment of dipoles with the applied field. The first one is friction due to the dipole’s interaction with the neighbors during its rotation in a viscous medium. So, at high enough frequencies, megahertz to gigahertz region, the dipoles cannot follow the field, above this frequency range relaxation occurs. The reciprocal of the frequency (r) at which the
polarization process can no longer respond is called the relaxation time (). This corresponds
to the average time spent in each dipole orientation. The complex permittivity equations for
dipolar polarization are given by the Debye relationships which include the relaxation time,
o r = + r = (o ) Eq. (2.10) 1+ 2 2 1+ 2 2
where the real part of the permittivity r is a constant equal to o for frequencies << r and
equal to for frequencies above r. The Debye-model assumes one unique relaxation time
for the system which is a good approximation for crystals but not for glasses [6].
The second factor is thermal agitation. When the temperature is low an applied
electric field can orient the dipoles, however as the temperature increases there is enough
thermal energy to randomize dipole orientation despite the presence of an ac field. In this
situation, the effective polarizability, thus permittivity decreases. Since the dipole reorientation rate is temperature dependent, the relaxation is also thermally activated thus
temperature dependent. It is important to note that this is in contrast to the electronic and
10 ionic polarization mechanisms, which are temperature independent. The reason is that dipolar polarization requires microscopic diffusion, in the electronic and ionic mechanisms, the
charge displacement distances are so short that diffusion concerns can be effectively ignored.
Space charge polarization occurs when the motion of charged defects can create net
charge separation. There is no motion with an average velocity, however there is a finite
displacement of charges since continuous current is impeded by insulating barrier(s). Often
times this is the result of a heterogeneous structure such as combinations of an insulating
phase & a conducting phase or insulating grain boundaries & conducting grains. All materials contain defects, impurities, various charge carriers, and heterogeneities, hence
space charge is always present to a certain extent. Space charge gives rise to very high
dielectric constants on the order of 104-106, however it is limited to low frequency
applications (102-104 Hz). One common application of space charge polarization is the barrier
layer capacitor. These are based on the limited reoxidation of a reduced material to obtain
conducting grains and insulating grain boundaries [7]. As in the case of dipolar mechanisms,
polarization involves a diffusional process, thus the temperature dependence is pronounced
and a relaxation mechanism describes the frequency dependence.
2.2 Classification in Terms of Crystal Symmetry
All crystals can be divided into 32 point groups, where a point group is defined as the
minimum combination of symmetry elements required to describe the crystal’s symmetry.
Among these, there are 21 non-centrosymmetric point groups 20 of which are piezoelectric.
11 The word “piezo” is derived from the Greek “piezein” meaning press or squeeze, hence
piezoelectricity is the generation of a charge displacement under applied mechanical stress.
This is known as the direct piezoelectric effect. The direction of the polarization (charge
displacement) depends on the direction of the applied stress. The direct piezoelectric effect is
defined using the tensor notation by,
P = d X Eq. (2.11) i ijk jk
where Pi is the polarization (a first rank tensor), dijk is the piezoelectric coefficient (a third rank tensor), and Xjk is the mechanical stress (a second rank tensor). These crystals also produce mechanical strain when they experience an electric field, which is known as the converse effect. Centrosymmetric crystals cannot be piezoelectric, because even under stress the center of positive and negative charges in a unit cell will still coincide and result in zero
net polarization.
Classifying further, 10 out of the aforementioned 20 groups have a spontaneous and
permanent polarization in the absence of an applied field or a mechanical stress. This polarization also changes with temperature, hence these crystals are called pyroelectric. They
are also called polar due to their spontaneous polarization. A subgroup of pyroelectrics is
ferroelectrics, in which the spontaneous polarization is strongly nonlinear and can be
reoriented by an applied electric field.
12 2.3 Ferroelectricity
2.3.1 A Brief History
The observation of polar materials possibly reaches back to Ancient Greece. More
than 23 centuries ago, philosopher Theophrastos noted that lyngourion (possibly the mineral
tourmaline) attracts wood particles [8]. The detailed work began with the advent of
formalized crystallography in the 18th century, and pyroelectricity and piezoelectricity was
th discovered in Rochelle salt (NaKC4H4O64H2O) in the 19 century [9]. These findings
enabled the discovery of ferroelectricity, when in 1921 Valasek reported that the spontaneous
dipole moment in Rochelle salt can be reoriented by an external electric field [10]. The term
ferroelectricity, which indicates polarization hysteresis with applied electric field, is used in
analogy to ferromagnetism, which exhibits magnetization hysteresis with applied magnetic
field.
In the early 1940s, critical steps were taken in understanding piezoelectricity and
ferroelectricity with the work on BaTiO3, as indicated by Jaffe [11]. These were (1) the
discovery of the unusually large dielectric constant, (2) the discovery that this high value was
due to ferroelectricity, and (3) the discovery of the reorientation of the dipoles with a process
called poling. There were concurrent studies in the United States, USSR, Japan, and England.
The publications started to appear after the World War II. In the United States, Thurnauer
and Deaderick synthesized ceramics with a dielectric constant of 1100 [12]. The reports of
Wainer and Salomon from 1943 show the temperature dependence of permittivity and the
effects of compositional modification [13], however these were not published since 1946
13 [14]. The work of Wul and Goldman in the USSR and von Hippel in the US discovered that
the origin of the high dielectric constant was ferroelectricity [15, 16]. There were also
independent discoveries in Japan by Ogawa in 1944 and in England by Coursey and Brand in
1946 [17, 18]. The third significant step was the discovery of the poling process. Gray
showed that a sufficiently high voltage can reverse the dipole moments of a ferroelectric
ceramic [19]. These were followed by single crystal and then thin film studies. Today,
ferroelectric materials find many application areas including high density capacitor applications, piezoelectric transducers, positive temperature coefficient resistors, and microwave filters with their interesting dielectric, piezoelectric, thermal, and optical properties.
2.3.2 Theory of Ferroelectricity
The two important criteria for ferroelectricity are the presence of spontaneous
polarization and the reversibility of this polarization with an applied electric field. This is
different in the parent analogue, ferromagnetism, where the presence of spontaneous
moments also means that they can be reversed by an external field [20]. Another
precondition is that the ferroelectric phase arises from a structural transition from a high
symmetry phase to a low symmetry phase. The temperature at which this transition occurs is
known as the Curie point and the temperature dependence of the dielectric constant above
this temperature is given by the Curie-Weiss law,
14 C r =o + Eq. (2.12) T To
where r is the relative permittivity, o is the permittivity of vacuum, C is the Curie constant, and To is the Curie temperature. Above the transition temperature, the crystal is in the paraelectric state, which is the non-polar state with no net dipole in the unit cell. Below the transition temperature, the material undergoes a phase transition into the ferroelectric state, a polar state with spontaneous polarization. If the transition is due to the displacement of the ions, then this is called a displacive transition. For example in BaTiO3, which has a cubic perovskite structure in the paraelectric state, the displacement of the Ti4+ ion from the cell center creates a dipole moment.
Ferroelectric transitions are generally classified into first and second order phase transitions. In a first order transition, spontaneous polarization exhibits a discontinuity at the transition temperature (Figure 2.3a), also there is a volume change and a latent heat associated with the transition. In a second order transition, the spontaneous polarization decreases continuously as the temperature decreases and reaches zero at the transition temperature as shown in Figure 2.3b. There is no volume change and no latent heat associated with the transition.
15 Figure 2.3 Schematic representation of the spontaneous polarization as a function of temperature for a first order (a) and a second order (b) phase transition.
There are two main approaches to explain the microscopic origin of ferroelectricity
and the ferroelectric phase transition [21]. The first one is the “polarization catastrophe”
approach. In this model, at a critical temperature the local electric field caused by the dipole
moment in the unit cell becomes larger than the restoring force stabilizing the polarization.
Polarization is given by,
v v P = NE Eq. (2.13) loc
where Eloc is not the external field, but the microscopic electric field felt by the polarizing
atom. This Lorentz local field is given by,
v v 1 v E = E + P Eq. (2.14) loc 3 o
16 v v Substituting Equation 2.14 into 2.13 and using Equation 2.4 to eliminate E and P , a
relationship between r and is obtained,
1 N r = Eq. (2.15) r + 2 3o
This relationship is called the Clausius-Mossotti equation. Rearranging this gives,
2N 1+ 3 = o Eq. (2.16) r N 1 3o
This expression shows that when N 3o, r approaches infinity. So, when the product of number density and polarizability of the dipoles are at a critical level, the material becomes
infinitely polarizable. This physically means that the dielectric will polarize even in the
absence of an applied electric field. Neglecting electronic and ionic contributions the total
polarizability is equal to the dipolar polarizability,
pv 2 dip = Eq. (2.17) 3kT
17 Substituting into Equation 2.16 we get,
C r Eq. (2.18) T To
which is the Curie-Weiss law for the dielectric constant. This dipolar model predicts that as
the temperature approaches the transition temperature from above, the permittivity becomes
infinite, the system becomes unstable and a phase transition occurs. This divergence at To is called the polarization catastrophe.
Even though this dipolar model leads to the Curie-Weiss law for a ferroelectric transition, it has shortcomings when it is applied to polar liquids. For instance, according to this model the water should become ferroelectric at To = 1100 K [5]. However, water even
does not become ferroelectric below its freezing temperature.
The other approach to explain ferroelectricity is associated with ionic polarizability.
In ionic polarization, the permittivity can be related to the vibration mode frequency using a
simplified version of the Lyddane-Sachs-Teller relationship by [22],
1 r Eq. (2.19) 2 TO
18 This relation suggests that if the lattice vibration frequency which produces polarization goes
to zero, the permittivity reaches infinity. A specific transverse optic mode, known as the
ferroelectric soft mode, displays a decrease in frequency as temperature decreases, and at the
point that it becomes zero the host lattice becomes unstable and the ferroelectric phase
transition occurs. When the frequency is non-zero (finite wavelength) the vibration of the
ions will result in transient dipoles. However, the net instantaneous polarization will be zero
since the oppositely oriented dipoles will cancel each other. The implication of the zero
frequency is that when the wavelength becomes infinite, all the ions will be shifted from their
equilibrium high temperature positions. The high temperature structure will be distorted into
another structure and result in a net instantaneous polarization at any time as shown in Figure
2.4.
Figure 2.4 Schematic representation of the polarization with a finite wavelength and infinite wavelength.
19 In the ferroelectric phase, the direction of polarization is not necessarily uniform throughout the material. The dipole moments in neighboring unit cells align themselves into regions of uniform polarization which are called ferroelectric domains. In the absence of an applied electric field, each domain will have a net polarization, however the average of all domain orientations will sum to zero. The polarization can be made uniform by the application of an external field in the paraelectric state and cooling with the field applied.
This process is called poling, which can potentially reorient domains in the direction of the applied field. When an electric field is applied, the domains reorient so that there is a net polarization parallel to the applied field. Domain walls separate domain states and have a thickness that is dependent on wall orientation and material quality – in the absence of
extrinsic factors, domain walls are only ~ 2 unit cells thick. The types of domain walls in a
ferroelectric crystal depend on the symmetry. For example, while in a tetragonal perovskite
180° and 90° domain walls can occur, in the rhombohedral phase the polarization along the
body diagonals result in 180°, 71°, and 109° domain walls [23]. The walls which separate the
oppositely oriented domains are called the 180o walls (Figure 2.5a) and the ones which
Figure 2.5 Schematic representation of (a) 180°and (b) 90° domain walls.
20 separate the perpendicularly oriented domains are called the 90o (Figure 2.5b) domain walls.
Key difference between them is the strain associated with the 90o domain walls.
Ferroelectric domains form to minimize the electrostatic energy due to depolarization
fields and the elastic energy associated with spontaneous strain. Depolarization fields are
required by any change in or gradient in polarity. This could be due to a change polarization
near the surface or a gradient across a grain boundary. When the material experiences a phase
transition mechanical constraints can increase the elastic energy by confining the
spontaneous strain associated with the structural change. The formation of domains reduces
the energy associated with both effects, however, 180 ° domain walls are only ferroelectric,
while other domain wall orientations (like 90° walls) have also a ferroelastic component.
2.3.3 Dielectric Properties of Ferroelectrics
2.3.3.1 Polarization Hysteresis
The unique characteristic of a ferroelectric is the polarization switching with an applied electric field. This results in a hysteresis loop when the polarization in the material is measured as a function of the applied electric field. This is a large signal measurement during
which a strong ac field with a frequency ~100 Hz is applied to the material. The hysteresis
arises from the energy needed to reorient ferroelectric dipoles during each field cycle. In the
paraelectric state there are no domains but the material exhibits a non-linear response without
hysteresis. Polarization vs. electric field loops for a single crystal ferroelectric, a
polycrystalline ferroelectric and a paraelectric are depicted in Figure 2.6. In polycrystalline
21 ferroelectrics there is usually a large amount of stress in the material. This stress is relieved by 90o domain walls which results in lower switchable polarization values.
Figure 2.6 Polarization vs. electric field curves for a single crystal ferroelectric, a polycrystalline ferroelectric, and a ferroelectric in the paraelectric state.
As the applied electric field is increased the domains start to align with the field and the measured polarization increases until all the domains become parallel to the field. This
22 point is called the saturation. When the applied field strength is decreased to zero, some of
the domains switch back, however there is still a net polarization, which is called the
remanent polarization, Pr. As the field is applied in the reverse direction, more domains
switch back and zero polarization is reached when the electric field is at EC, coercive field,
the amount of field needed to switch the polarization. Nevertheless, this is not an absolute
value. If a lower electric field is applied for a sufficient amount of time, the polarization will
eventually switch [24]. Spontaneous polarization can be found from the figure by drawing a
tangent to the saturation and finding the polarization intercept. Since the P-E relation is hysteretic and the Equation 2.4 does not hold for the non-linear response, a definition in terms of the change in polarization could be written,
P =o(r 1)E Eq. (2.20)
Since the derivative P /E gives the permittivity, the slope at any point gives the large
signal permittivity. The area of the loop represents the energy dissipated as heat. For this
reason, the experiment is usually run at low frequencies (~100 Hz) [11]. The shape and the
position of the hysteresis loop give additional information about the material. For instance,
an off-centered loop indicates an internal field which could be caused by space charge or
aging [23]. The magnitude of the coercive field can be an indication of the grain size (e.g.
large coercive field means smaller grain size), while the loop squareness and sharpness are
indicative of general material quality and high resistivity [9].
23 2.3.3.2 Dielectric Permittivity and Tunability
The dielectric permittivity of a ferroelectric material can be parameterized by Landau
theory which is based on an expansion of the Helmholtz free energy with respect to
polarization [25]. The first two terms of this expansion is given by,
F = P2 + P4 Eq. (2.21) 2 4
Using the equation of state, F /P = E , taking the derivative of the above expression,
E =P + P3 Eq. (2.22)
Then, the dielectric permittivity can be written as,
1 P 1 1 Eq. (2.23) r = = 2 o E o + 3P
This equation describes the permittivity both in the absence and presence of an applied field.
When there is no field, polarization is set to zero and in the presence of a field, the
polarization is set to the induced polarization value and permittivity is calculated. It can be observed from the equation that the permittivity is maximum at zero field and decreases as the applied field is increased. This behavior is observed experimentally via capacitance-
24 voltage (C-V) measurements. C-V measurements are small signal measurements where a small ac field (e.g. 0.05 V) superimposed with a dc field is applied. The oscillating voltage is used to measure the capacitance and then plotted as a function of the dc field. Generally, permittivity is calculated from capacitance, electric field is calculated using thickness, and the permittivity data are plotted as a function of the applied dc field. Figure 2.7 shows the typical r vs. E curves for a ferroelectric and a paraelectric material.
Figure 2.7 Relative permittivity vs. electric field curves for a ferroelectric and a paraelectric material.
Measurements for ferroelectric materials are usually made with two sweeps, i.e. one
from negative to positive bias and the other from positive to negative to show the hysteresis.
The initial rise in the permittivity with applied field is due to the increased domain wall
25 movement which is locked-in by defects at zero bias and partial switching of the domains
[26]. The maximum permittivity is observed when most of the domains are in the process of
switching and the domain wall movement contribution to the polarization is maximum. At
higher fields, the permittivity decreases due to two reasons. First, the number of domains and
hence the domain walls decrease as they align with the dc field. Second, the oscillation of
any residual domain walls is inhibited by the large dc bias. The only contributions to the
permittivity at high fields are the intrinsic polarization mechanisms (e.g. ionic and electronic
polarization).
In the paraelectric state the material does not exhibit any hysteresis, therefore the
measurements can be made with a single sweep. A high permittivity is observed (at low
fields), even though there are no domains or domain wall contributions. At temperatures not much higher than the transition temperature, the frequency of the lattice vibration mode TO
(Eq. 2.19) is very low. At this point the restoring forces opposing the poling of the crystal are
still weak, so the transient dipoles can interact with the applied ac field resulting in a high
permittivity.
The change in permittivity with the applied field makes these materials attractive for
high frequency voltage-tunable devices such as resonators, phase-shifters and microwave
filters [25, 27-29]. The dependence of permittivity on the applied dc field is called the
tunability. The tunability is defined as,
n = max Eq. (2.24) min
26 where max is the permittivity at zero field and min is the permittivity at saturation fields.
Another way of defining tunability is the relative tunability which is given by,
max min nr (%) = •100 Eq. (2.25) max
In general, the higher the permittivity the higher the tunability [25]. Tunability can be used as a means to compare the extrinsic response to the intrinsic response. For instance, for materials with the same composition, since the intrinsic (lattice) response would be similar, tunability might enable a comparison of extrinsic properties such as phase purity, homogeneity, microstructural properties (e.g. grain size), and crystal quality. This comparison will be used routinely in this thesis to evaluate material quality.
2.3.3.3 Dielectric Loss
Dielectric loss is a critical parameter in microwave applications since a figure of merit is defined based on dielectric loss and tunability for these devices, whereas in high capacitance density applications permittivity is of high importance [25, 29-31]. The dielectric losses in ferroelectric materials can be categorized as extrinsic and intrinsic contributions.
The main extrinsic contribution to the ferroelectric loss is the domain wall movement
[23, 32]. Domain wall motion includes interactions with the surroundings, which cause
27 internal friction. Real materials contain charged defects, local polar regions, impurities and
the interaction of these with the ac field also contributes to dielectric losses. Presence of defects can increase the conductivity of the material resulting in dielectric losses.
Additionally, domain wall movement can also be clamped or pinned by these defects. These defects include oxygen vacancies and electrons trapped in the domain wall area, making the domain switching more difficult and hindering the domain wall motion [33].
In the paraelectric state there are no domains, so the dielectric loss is in principle much lower. For that reason, the non-polar paraelectric phase is used for high frequency applications where low loss tangent is crucial. The other extrinsic mechanisms play a similar role in the paraelectric state. The second group of phenomena that contribute to the dielectric loss is the intrinsic mechanisms. The following is a very brief summary of the models that were derived to explain their origins [25, 34, 35].
For the intrinsic loss, typically the higher the permittivity and the measurement frequency, the higher the loss [25]. The origin of the intrinsic loss is the interaction between the applied ac field and the lattice vibrations in the material. The loss is due to the absorption of energy quantum of the electromagnetic field by the thermal phonons during collisions.
Phonons have much higher energies and this results in three possible schemes of collisions; three-quantum, four-quantum, and quasi-Debye mechanisms [25]. The three-quantum process involves an energy quantum and two phonons. This interaction can only occur if the frequency (or energy) difference between the phonons is small, i.e. on the order of the ac field frequency. This is possible between two degenerate vibrational modes. Since degeneracy arises from the symmetry of the crystal, the temperature and the frequency
28 dependence of the three quantum mechanism are sensitive to the crystal symmetry. In the
four-quantum mechanism where three phonons are involved, the energy restrictions are not
that strict. In the two-phonon process, the momentum conservation allows only vertical
transitions, whereas three-phonon processes can occur in a greater variety without violating
the momentum conservation [36]. For that reason, phonons with different energies can take
place in this process. Therefore, the temperature and the frequency dependence of the four
quantum mechanism are insensitive to the crystal symmetry. The quasi-Debye mechanism is
only active in non-centrosymmetric crystals and in the local polar regions of the
centrosymmetric crystals. In this mechanism, the interaction between the electromagnetic
field and the phonon changes the phonon frequency which results in dielectric relaxation
with a corresponding loss. The contribution of the quasi-Debye mechanism is higher than the
three-quantum and four-quantum mechanisms in the frequency range of interest ( << TO).
Figure 2.8 shows the comparison of the loss tangents for the above mechanisms as a function of frequency.
29 Figure 2.8 Schematic representation of frequency dependencies of (1) three-quantum, (2) four quantum, and (3) quasi-Debye mechanisms. o and o are the soft-mode frequency and damping (average frequency of inter-phonon collisions), respectively (taken from Tagantsev et al. [25]).
2.3.3.4 Dielectric Properties of Ferroelectric Thin Films
The dielectric properties of ferroelectric thin films are usually different than that of their bulk counterparts. Typically, thin films exhibit lower dielectric permittivity and higher loss tangent than the bulk ceramics with the same composition. The origins of these differences in the properties can be categorized under three main groups: (i) difference in processing conditions (e.g. processing temperature), (ii) presence of stress (or strain) in thin films due to substrate constraints, and (iii) scaling effects. Actually, when parameterizing the dielectric properties usually it is observed that all these factors have a cause-and-effect
30 relationship. For instance, typically, the processing window available to thin films are
dependent on the thermal expansion mismatch, chemical reactivities, and difference in other physical properties (e.g. melting point) between the film and the substrate. It affects the dielectric response through properties such as crystallinity, grain size, chemical composition, defect equilibrium, and residual stress. Finally, very thin films can degrade the dielectric properties through low permittivity passive layers with thicknesses comparable to the film.
All of these thin film effects will be discussed in detail in the following sections, specifically for barium titanate & barium strontium titanate thin films.
2.4 Perovskite Structure and The Archetypical Ferroelectric BaTiO3
2.4.1 Crystal Structure and Phase Transitions
The perovskite structure, which takes its name from the mineral perovskite (CaTiO3),
is a versatile structure with a very wide range of properties and functions [37]. The generic
structure has the chemical formula ABO3 with a simple cubic unit cell. This can be visualized
as the A-site cation on the corners, B-site cation in the body center, and oxygens in the
centers of the faces. The resulting structure is a BO6 octahedral network with the smaller
cation filling the octahedral holes (6-coordination) and the large cation filling the
dodecahedral holes (12-coordination). Figure 2.9 shows the cubic perovskite unit cell with
the oxygen octahedron.
31 Figure 2.9 Perovskite unit cell shown with the BO6 octahedron.
Goldschmidt studied a large number of perovskites by substituting a variety of cations including BaTiO3 before the discovery of its high dielectric constant and the structural relationship to ferroelectricity [38]. The geometric relationship that gives the size range of ions that can be substituted in the perovskite structure is given by,
R + R t = A O Eq. (2.26) 2(RB + RO )
where t is the Goldschmidt tolerance factor, RA, RB, and RO are the ionic radii of large cation, small cation, and anion respectively. Typically, structures with a t ~0.95-1.0 are cubic, those with lower tolerance factor values are slightly distorted (often via octahedral rotations) but not ferroelectric, and those with higher values are ferroelectric [11]. In addition to this structural requirement, the presence of a degree of covalency in the B-O bond (small cation-
32 anion) is necessary for the lattice distortion and ferroelectricity [39-41]. Since the ionic
forces are central forces and ionic bonding is not directional, the anions in the octahedron would be expected to hold the B-cation in the center, i.e. equidistant from all neighbors.
However, for ferroelectricity to occur the cation must be closer to one of the anions which requires bond directionality. Megaw showed that the presence of abnormal volume conditions could result in the off-center position of the B-cation. In BaTiO3, this condition is
accommodated by the large Ba ion, which moves apart the oxygen network, so that the
average Ti-O distance is larger than the sum of their ionic radii [39, 40]. Through local
density approximations (LDA) Cohen demonstrated that the covalency results in
hybridization between the titanium 3d states and the oxygen 2p states, which is essential for
ferroelectricity [42].
Barium titanate, the first ceramic in which the ferroelectricity was observed, exhibits
the prototypical perovskite cubic structure (m3m, a=4.009 Å) above its Curie temperature.
o 4+ Below Tc (~125 C), the structure slightly distorts due to the displacement of the Ti (11 pm)
and Ba2+ (6 pm) cations opposite to the oxygen sublattice (3 pm) and becomes tetragonal
(4mm, a=3.992 Å, c=4.035 Å) as shown in Figure 2.10. Since there are six equivalent <100>
directions in the unit cell, the polar axis can be parallel to any of these directions. Upon
further cooling, two more phase transitions occur. First, the unit cell elongates along a face
diagonal and the structure changes from tetragonal to orthorhombic at 0 oC. Second, the unit
cell elongates along a body diagonal and an orthorhombic to rhombohedral at transition
occurs at –90 oC.
33 Figure 2.10 Cubic and tetragonal unit cells of BaTiO3.
The displacement of the Ti4+ cation along the c-axis can be visualized in terms of potential wells. In the tetragonal phase, the cation occupies one of the two equilibrium positions which are shifted from the center of the unit cell as shown in Figure 2.11. It can jump from one equilibrium position to the other, if enough energy is provided to overcome the potential barrier. If an electric field (larger than coercive field) is applied opposite to the polarization direction, then Ti4+ cation can jump to the adjacent site and reverse the polarity
in that unit cell. This will reduce the energy barrier for the neighboring ions and the region
affected by the electric field will eventually switch polarization [7]. The switching can also
occur by 90o, however there is an associated dimensional change since the lengths of the c
and a-axes are different. In addition to an electric field, 90o switching can also be induced by
applying mechanical stress.
34 Figure 2.11 Schematic potential wells.
2.4.2 Dielectric Properties
When discussing the dielectric properties of BaTiO3 it is important to note that there
are no absolute values for the permittivity and the loss tangent. Even the slightest chemical or
physical change has a dramatic effect on the dielectric properties. The Curie point also shifts
with these changes. For that reason, in the following discussion, the general trends will be
pointed out and the effects of deviations from ideality on the dielectric properties will be
discussed in the extrinsic effects (i.e. stress-strain, scaling effects) section.
Above the Curie point, BaTiO3 is in the paraelectric state and the dielectric constant
obeys Curie-Weiss law, = C /T To, showing a peak at the transition temperature. Below the transition temperature the permittivity decreases with decreasing temperature yet it is still high due to the domain wall contribution. The temperature dependence of the permittivity for
35 single crystal BaTiO3 is shown in Figure 2.12 [43]. Since the single crystal is strongly anisotropic, the permittivites measured along c and a-axes are different. At room temperature, the permittivity along the a-axis is ~4000, and along the c-axis is ~160. The reason for the difference is that the displaced Ti4+ is tightly bound by the ferroelectric displacement along the polar c-axis, while it can still vibrate freely in the non-polar a-axis giving higher permittivity. A polycrystalline ceramic would have a permittivity value in between those single crystal values due to the random orientation of the grains.
Figure 2.12 Dielectric constants Ka and Kc for single crystal BaTiO3 (taken from Merz [43]).
36 When BaTiO3 cools through the transition temperature, spontaneous polarization
results in surface charges and an accompanying depolarizing field. The crystal responds to
this by twinning (domain formation), in which the crystal splits into regions of oppositely
signed polarization minimizing the electrostatic energy. The other ways to minimize the
electrostatic energy are compensating the surface charge by conduction through the crystal or
external conduction by a surrounding material [23]. The effects of mechanical stress during
the paraelectric/ferroelectric transition result in the formation of 90o domains to minimize the
strain energy at the expense of domain wall energy so that their sum becomes a minimum
[44]. The 90o domains follow a head-to-tail arrangement to minimize the charge.
Figure 2.13 Relaxation of ferroelectric BaTiO3 (taken from von Hippel [45]).
37 In the tetragonal phase, the permittivity of BaTiO3 shows a frequency dependence
with a drop at around 10 GHz, as shown in Figure 2.13 [45]. This frequency corresponds to
the piezoelectric resonance which is also accompanied by a high dielectric loss. In the cubic phase, piezoelectric resonance cannot occur, since the structure is centrosymmetric. For that reason, the paraelectric phase is used for high frequency applications with its comparatively low loss tangent values.
2.4.3 Compositional Modification with SrTiO3
The dielectric properties of BaTiO3 can be modified via cation substitutions with high
solubility limits. The effects of these substitutions include shifting the Curie point, restricting
domain wall motion, introducing compositional gradient, controlling grain size, and
controlling the oxygen vacancies [7]. The Curie point of BaTiO3 is usually shifted due for two application-based reasons. First, if the transition temperature is shifted down, higher permittivities can be achieved at room temperature. Second, if the paraelectric phase is required, for example for high frequency applications, it can be obtained by shifting the Curie point to a temperature below room temperature.
Solid solutions of BaTiO3-SrTiO3 (BST) are used for this purpose. SrTiO3 is an
incipient ferroelectric material, which forms a complete solid solution with BaTiO3 [46, 47].
For the substitution of Sr2+ for Ba2+ a linear drop of ~3.5 oC per mol% in transition
temperature is observed [11]. The substitution of the small cation for the large one reduces
the cell volume and results in a linear decrease in Tc similar to the effect of application of
38 hydrostatic pressure [48]. Depending on the solid solution composition the material exhibits permittivity maximum in the temperature range –230 oC - 130 oC. Temperature dependence of the dielectric constant with changing composition is given in Figure 2.14 [25, 49]. It is interesting to note that BST solid solutions have higher permittivity peak values than that of pure BaTiO3 and the highest permittivity is observed around the 50/50 composition.
Figure 2.14 Curie temperature dependence of BaxSr1-xTiO3 on Ba concentration (taken from Tagantsev et al. [25], modified version of Smolenskii’s data [49]).
39 2.4.4 Stress-Strain Effects
Application of a mechanical stress has substantial effects on the dielectric properties
of barium titanate. The effects of stress on the Curie point and the permittivity of ceramic and
single crystal BaTiO3 have been studied by various authors [48, 50-53]. Merz showed that
the Curie point of single crystal BaTiO3 decreases linearly with increasing hydrostatic
pressure [48]. This was also confirmed in polycrystalline ceramic samples by others [50, 53].
The reason for the decrease in the transition temperature is that the hydrostatic compression
will favor the smaller volume phase. The cubic paraelectric phase has a smaller volume, so it
is stable down to lower temperatures under hydrostatic stress. On the other hand, when a
two-dimensional stress is applied the Curie point shifts to higher temperatures [50-52]. This
can be explained as the stabilization of polarization in certain direction by the applied biaxial
stress. If the stress is compressive, it compels tetragonality normal to the compression by
contracting the axes in the direction of the stress and expanding the third, so stabilizing
polarization normal to the stress plane. If the stress is tensile, it stabilizes the polarization parallel to the stress plane. Mechanical stress effects on the permittivity of bulk samples have
also been studied [50]. However, since in a polycrystalline ceramic sample the stress systems
acting on each crystallite are complex, it is more difficult to explain the trends in those
systems. Especially, if the material is in the ferroelectric state, the piezoelectric effects, the
changes in domain orientations, and domain wall motions complicate the situation. Shirane
and Sato studied the effects of hydrostatic and two-dimensional pressure on the permittivity
of polycrystalline BST samples [50]. They observed a decrease in the permittivity in the
cubic phase with hydrostatic pressure. Since, the material obeys Curie-Weiss law in the
40 paraelectric state, a shift in the transition temperature will increase T, hence the permittivity
will decrease. Samara made the same observation in single crystal samples, however the
permittivity measured along c-axis in single crystal samples showed an increase [53]. This
was attributed to the switching of some c-domains into a-domains leading to higher
permittivity along c-axis.
The two-dimensional stress is especially important for thin films, since the films are
biaxially constrained on the substrate. The interaction between the film and the substrate can
result in significant mechanical stresses in the film. The origins of the stress in thin films can be classified into intrinsic, extrinsic and thermal stresses [54]. The intrinsic stress is generated by the atoms or ions which are not in their lowest energy state and it depends on the growth parameters such as temperature, pressure, reactant concentration, and impurities.
Extrinsic stresses are caused by dimensional changes. For example, densification during structural evolution or crystallization from an amorphous phase can produce tensile stresses in thin films. For epitaxial thin films, the lattice mismatch between the film and the substrate
can cause tensile or compressive stresses depending on the relative lattice parameters. The
third and generally the most important one is the thermal stress that arises due to the thermal
expansion coefficient difference between the film and the substrate. These stresses occur
during cooling down from a high temperature deposition or firing and their magnitude is
given by,
E f th = ( f s )T Eq. (2.27) 1 f
41 where Ef is the elastic modulus, f is the Poisson’s ratio of the film, T is the temperature change, and f and s are the thermal expansion coefficients of the film and the substrate, respectively. Depending on the sign of the difference ( f s) the stress can be compressive or tensile. It is believed that this stress in the plane of the film causes a change in the dielectric permittivity through a converse electrostrictive effect, i.e. presence of strain results in a quadratic change in dielectric displacement, which is given by [55],
1 1 = 4Q12 Eq. (2.28) f u
where f is the permittivity of the stressed film, u is the permittivity of the unstressed film, and Q12 (<0) is the electrostrictive coefficient. It is important to note that this formula is valid when the film is in the paraelectric state. This is again due to the complexity introduced by piezoelectric and domain wall contributions in the ferroelectric state.
The effects of biaxial stress on the dielectric properties of thin films have been studied both experimentally [54-58] and theoretically [59-60]. Shaw et al. measured that their
BST films on Si had tensile stress ~600 MPa which resulted in a 25% decrease in the permittivity [55]. Taylor et al. sputter deposited BST on five different substrates to observe the effects of a systematic change in thermal strain [57]. They observed that the permittivity of the samples, which had tensile stress, decreased with increasing amount of stress.
42 Pertsev et al. made a thermodynamic model of epitaxial mismatch strain suggesting that presence of biaxial stress, compressive or tensile, would shift the Curie point to higher temperatures [59]. Desu et al. reached similar results using a different free energy expression
[60]. Experimental work of Choi et al. demonstrated that the transition temperature of epitaxial barium titanate films can be boosted to very high temperatures by biaxial compressive strain. The authors achieved a transition temperature of 680 °C with a coherently strained BaTiO3 on DyScO3 [61]. These are also in agreement with the observations in bulk ceramics [50-52]. Contrary to these results, Maria et al. and Streiffer et al. observed a decrease in the transition temperature with thermal stress [56, 58]. Both studies attributed this to the presence of a polarization normal to the plane of the film which is unable to switch. In Pertsev’s model, polarization can switch freely to minimize its energy.
Therefore, in the presence of an in-plane stress, polarization is forced to have an in-plane component to minimize its energy. This in-plane component stabilizes the ferroelectric phase to up to higher temperatures. However, when there is a fixed polarization axis normal to the film, presence of tensile stress counteracts this spontaneous polarization and shifts the transition to lower temperatures.
2.5 Scaling Effects in BaTiO3
The ever-increasing miniaturization in electronic devices brings in the need for working at smaller scales. A decrease in size generally changes the parameters including grain size, composition, defect concentration and stress altering the properties of the
43 ferroelectric material. Therefore, a fundamental understanding of scaling effects on
properties is needed to make high quality materials. The scaling effects on the ferroelectric
properties of barium titanate have been studied for bulk [62-70] , particles [71-73], and thin
films [74-77]. Even though, the bulk effects seem to be well understood, the trends in thin
film properties are much more difficult to explain due to the complicated electrical (e.g.
electrodes and depolarization effects) and the mechanical (stress-strain due to being clamped)
boundary conditions.
2.5.1 Scaling Effects in Bulk BaTiO3
The grain size effects on the dielectric properties can be divided into three size
regions [78]. In the first region the grain size (or particle size) is large (<1 μm) and the
structure is in a multi-domain state with 180° and 90° domain walls. As the grain size
decreases the density of the 90° domain walls decreases and at a critical size (~0.5 μm) the
material becomes single domain. With further decrease in grain size, at around few tens of
nanometers, true size effects come into play and surface energy and depolarization energy
suppress the ferroelectricity [79]. However, it is important to note here that there is no clear
experimental proof of this argument in the literature. Looking at the r-T characteristics, typically, scaling effects result in the following: (1) a shift in the transition to lower temperatures, (2) decrease in the permittivity values in the ferroelectric state, and (3) broadening of the dielectric anomalies.
44 Buessem et al. reported that the permittivity of the fine-grained BaTiO3 (1 μm) is
higher than that of the large-grained (10 μm) ceramics [62, 63]. To explain the authors referenced Little’s work, who measured the thickness of a 90° domain wall as about 0.4 μm
[80]. This means that it is physically impossible to have domain walls in a 1 μm grain.
Therefore, it was suggested that the fine-grained samples were single domain, i.e. there were
no 90° domain walls to relieve the stress. The high permittivity was attributed to the presence
of internal stress which forces the structure back to the cubic state. Their thermodynamic
model showed that with a reasonable amount of stress, the transition can be shifted to obtain
a permittivity close to 6000. Kinoshita et al. measured a series of samples with grain sizes ranging from 1-50 μm observing the same trend, i.e. increase in the permittivity with
decreasing grain size in the ferroelectric state [64]. The permittivity of the paraelectric phase did not show a dependence on the grain size. They also attributed the high permittivity to internal stresses. However, none of these studies investigated the lattice and the domain structure until the comprehensive work of Arlt et al. [65]. By preparing a systematic sample set with grain sizes of 0.3-100 μm and doing electron microscope investigations, Arlt et al.
were able to study both sides of the critical grain size at which the permittivity was
maximum. The highest permittivity was again obtained around 0.7-1 μm as shown in Figure
2.15. TEM and SEM studies revealed two important points. Domain width is grain size
dependent and 90 ° domain walls persist to much lower grain sizes than previously expected.
45 Figure 2.15 Dielectric constant of BaTiO3 as a function of grain size (taken from Arlt et al. [65]).
It was shown that for decreasing grain size the total 90° domain area increases. The increasing permittivity with decreasing grain size down to 1 μm was explained by this increased domain wall density contributing to the permittivity. Below 0.7 μm, the micrographs revealed a decrease in the number of 90° domains decrease accompanied by a structural change observed in the X-Ray patterns. The room temperature structure changed from tetragonal to a pseudocubic structure with peaks ascribed to the orthorhombic phase.
The decrease in tetragonality and the shift of orthorhombic-tetragonal transition to higher temperatures was also observed by other authors [64, 67, 71]. In addition to the global structure study by XRD, local symmetry probed by Raman-scattering displayed peaks that
46 are attributable to the orthorhombic phase supporting the idea that grain-size reduction
enhances the stability of that phase [67].
Arlt et al. also observed a shift in the Curie point to lower temperatures with
decreasing grain size. However, at this point it is important to note that different preparation methods were used for the specific size ranges for this study due to the difficulty in preparing dense nanocrystalline ceramics. Using metalloorganic decomposition Frey et al. was able to make fine-sized powders and then ceramics which were nearly identical in composition and density, so the grain size was the only varying parameter [68]. The sample set had a grain size ranging between 0.07-1.7 μm. The temperature dependence of the permittivity with changing grain size in this study is shown in Figure 2.16.
Figure 2.16 Temperature dependence of permittivity of BaTiO3 with changing thickness (taken from Frey et al. [18]).
47 A number of observations can be made from the plot: (i) the maximum permittivity
(at the transition temperature) decreases with grain size, (ii) there is a dielectric anomaly
even for the smallest grain size (0.07 μm) material, and (iii) the transition temperature does not shift appreciably even down to a 0.07 μm grain size. The second and third observations are contrary to Uchino et al.’s report in which the room temperature crystal structure of
BaTiO3 particles were observed to decrease in tetragonality with decreasing grain size and
became cubic and non-ferroelectric below 0.01 μm [71]. However, Uchino’s results were on
particles which have different boundary conditions than the ceramics. The first observation
was explained in terms of a dilution effect on the permittivity from the grain boundaries. It
was shown that the data can be modeled for a diphasic structure with high permittivity grains
isolated by low permittivity grain boundaries. This “brick-wall” model in which the grains
are connected to the grain boundaries in series explains the decrease in permittivity with a
grain boundary thickness of 8 Å and a permittivity of 130. Therefore, even at very fine grain
sizes, the grain interiors can undergo a ferroelectric transition in the presence of defective
grain boundaries. The brick-wall model had previously been used by Shaikh et al. who
applied a combined series and parallel mixing of grains and grain boundaries. However, the
parallel and series mixing model resulted in high grain boundary thicknesses in an ultra fine-
grained material [66]. It was suggested by Frey et al. that in a situation where the permittivity of the grain is much larger than the permittivity of the grain boundary, electric flux moves away from the grain boundaries which are in parallel resulting in a series dielectric mixing
[68].
48 McCauley et al. further refined the size effect study by preparing fine-grained BaTiO3
ceramics (20-80 nm) in a glass matrix [69]. This changed the electrical boundary condition
for the grain surfaces which were covered with an insulating (glass) matrix. By this way, the
charge compensation at the grain surfaces could be limited which would otherwise
compensate for the depolarization fields. The authors observed a shift in the transition
temperature with decreasing grain size which was attributed to the presence of depolarization fields. In the absence of surface charge to compensate for the depolarization fields, the material creates a polarization gradient in the regions close to the surfaces. According to the
Binder model for scaling effects, these gradients result in a shift and broadening of the phase
transition [70].
2.5.2 Scaling Effects in Thin Film BaTiO3
The dielectric properties of thin films are generally inferior to their bulk counterparts
due to the limitations in processing conditions and the difference in the applied electrical and
mechanical boundary conditions. For instance, due to a substrate constraint the thermal
budgets for the material synthesis could be limited resulting in poor crystalline quality and/or
small grain size. The thickness of the film is also very important since the electrical boundary
conditions could affect the dielectric properties substantially in very thin films. The effects of
microstructure and thickness have been studied widely in the literature.
The microstructural effects that result in lower permittivities for thin films are mainly
due to two reasons, (i) the grain size being much smaller than the 0.7 μm maxima observed
49 in the bulk [65, 68] and (ii) the relatively poor crystal quality of the thin films. The low
thermal budgets compared to bulk processing is the main reason for these effects, especially
for films deposited on silicon substrates with processing temperatures less than 750 °C [74,
75, 81-85]. Above this temperature metal electrode hillocking and delamination problems
arise because of the metal electrode-substrate thermal expansion mismatch [86, 87]. Low
processing temperatures result in small grain sizes and the permittivities of these films are
typically less than 800. The grain structure (columnar vs. equiaxed) was also shown to affect
the permittivity. Hoffmann et al. demonstrated that by tailoring a columnar solution
deposited BaTiO3 structure on silicon wafers, the room temperature can be increased from
500 to 900 [75]. This is, in fact, expected from the brick-wall model, since the dilution from the grain boundaries connected in series with the grains is minimized by through-the- thickness grains.
The thermal expansion mismatch problem can be overcome by using metal foils as substrates [76, 88, 89]. Contrary to thick and rigid substrates such as silicon and sapphire, the thin and compliant foils enable temperatures close to the bulk processing of barium titanate.
Permittivities higher than 1500 can be achieved by firing the thin film samples at temperatures in excess of 900 °C. Typically, due to the refractory nature of the barium titanate system, extensive grain growth cannot be achieved up to temperatures above 1200
°C. Recently, Ihlefeld et al. showed that, applying the bulk processing strategies to thin film synthesis it is possible to enhance the grain size, the density, and the crystal quality of the chemical solution deposited thin films [77]. The authors used barium borate glass flux to make use of the liquid phase sintering to enhance densification and grain growth. By
50 limiting the amount of this second phase to avoid the detrimental effects of a glass phase on
the dielectric properties, they were able obtain permittivities in excess of 3000 at room
temperature.
In addition to the grain size, the crystal quality of the material is also very important.
The crystal perfection of a polycrystalline thin film can be quantified by measuring the
coherent scattering size. Coherent scattering regions are tiny blocks in a grain which are
slightly disoriented one from another [90]. Because of this mosaic structure, the lattice
vibrations in neighboring blocks become incoherent. Since ferroelectricity is due to the long-
range interactions of dipoles in neighboring unit cells, an interruption to these interactions
affects the dielectric properties [91, 92]. A small coherent size means an effectively high
defect concentration within each grain, limiting the coherent scattering size reaching the
actual grain dimensions which degrades the dielectric properties. Higher processing
temperatures anneal out the defects, enhancing the crystal quality and the permittivity of the
thin films [93, 94]. This is important especially for sputtered films where the high energy bombardment of the particles may damage the lattice resulting in high defect concentrations.
The crystallinity of sputtered BaTiO3 thin films was characterized by Surowiak et al. by measuring the crystallite dimension and the lattice strain in the crystallites [95]. The authors found that the films which were sputtered via a high energy bombardment exhibited low permittivity and polarization values. They were able to obtain higher crystallite and lower
strain values when the conditions were not as rigorous which resulted in better dielectric
properties.
51 In a ferroelectric material, the surface requires termination of the spontaneous polarization. However, for phase stability in the ferroelectric the dielectric displacement must be continuous across an interface. The continuity can be maintained by the accumulation of free charge in the presence of an electrode or creating a polarization gradient towards the surface [96, 97]. In a thin film capacitor, a depolarization field forms when the polarization cannot be compensated for by free charges. The depolarization field is strongly film thickness dependent and can have dramatic effects on the phase stability and the dielectric properties [98].
The other phenomenon that is related to thickness dependent scaling effects is the formation of “dead layers” at the electrode-ferroelectric thin film interfaces. These layers act as parasitic capacitors connected in series with the ferroelectric, decreasing the capacitance especially for very thin films, typically below 100 nm. The most common explanations for these layers are (i) Schottky barrier formation between the electrode and the film [99, 100],
(ii) variation of the polarization at the electrode-ferroelectric interface [101-104], and (iii) size-related soft-mode hardening [105]. The effect of the dead layer capacitance on the film response is typically modeled by the following equation,
A t 2t 2t = s + s Eq. (2.29) C ob os
where A is the capacitor area, C is capacitance, t and ts are the thicknesses of the film and the dead layer, and o, b, and s are the permittivity of vacuum, the film, and the dead layer
52 respectively. A plot of inverse capacitance as a function of the film thickness is used to
quantify the thickness and the permittivity of the dead layer. The y-intercept of the line gives
the dead layer capacitance.
When a semiconductor is brought into contact with a metal, due to the difference in
the work functions, a Schottky contact might form. The charge carriers near the surface of
the semiconductor move into the metal, leaving behind a charge carrier depleted region. This
results in the separation of charges which acts similar to a parallel plate capacitor. The capacitance of this layer is much lower than that of the ferroelectric film and can have a dramatic effect on the overall capacitance when the film thickness is very small [99, 100].
The other explanation for the observed thickness dependence of permittivity is the intrinsic dead layer effect. This model considers the effect of a surface termination on the dipole-dipole interactions. According to Zhou and Newns’s description, the dipoles located near the surface environment contain fewer neighboring dipoles. The absence of the enforcing field from the surrounding results in the hardening of the surface dipole. This reduces the polarization and the permittivity of the surface region forming a dead layer [101].
Again, when the thickness is small enough, this dead layer with very low capacitance becomes very important. To understand the fundamentals of this intrinsic effect, Sirenko et al. studied the lattice dynamics of strontium titanate thin films via infrared ellipsometry
[105]. They measured the soft mode frequency and the permittivity as a function of temperature. The results revealed that the lattice goes under soft-mode hardening as the film thickness is reduced which degrades the permittivity. The authors suggested that the soft- mode hardening involves the whole lattice not just an interfacial layer and they pointed the
53 role of strain and defects in this thickness dependent phenomenon. Other groups also suggested the possibility of a through-film effect [106, 107]. The work of Basceri et al. pointed out that the thickness dependence of the permittivity could be due to a true size effect and the dielectric response, which is a cooperative phenomenon, might be affected by the reduced thickness [106]. Sinnamon et al. fit their thickness series data for their BST films with (7.5-950 nm) using the series capacitor model (Eq. 2.29) [107]. The authors hypothesized that if there is a dead layer, an anomaly should appear in the data when the dead layer thickness exceeds the thin film thickness. However, they did not observe such an anomaly down to 7.5 nm suggesting that either that number is the upper limit for the dead layer thickness or such a distinct dead layer does not exist an the drop in permittivity is due to a through-the-thickness effect. A later paper by the same group demonstrated that it is possible the model the thickness dependent permittivity of the films using a grain boundary dead layer model [108]. It was shown that low permittivity grain boundary layers perpendicular or parallel to the high permittivity grains can be used to model the thickness dependence with the same effectiveness as the interfacial dead layer model.
A comprehensive experimental study investigating the thickness effect on the permittivity, the transition temperature, and the broadness of the transition was conducted by
Parker et al. which also questions the validity of the dead layer model [109]. The authors prepared BST films on Pt-coated silicon wafers by liquid-source chemical vapor deposition with thicknesses ranging from 15-580 nm. The temperature dependence of permittivity with changing film thickness is shown in Figure 2.17. It is clear from the plot that the permittivity values decrease with decreasing thickness, the temperature at which the permittivity
54 Figure 2.17 Temperature dependence of permittivity of BST films with changing thickness (taken from Parker et al. [109]).
maximum occurs shifts down to lower temperatures, and the transition broadens with reduced thickness. It was stated that the series model cannot be used to explain this data, since that model assumes that the film and the dead layer permittivities are thickness independent. However, the thickness dependency of Tmax (the transition temperature) shows
that this assumption cannot be made. If they were indeed thickness independent, then the
differences in the -T curves would be due to the changes in the relative volume fractions of
the film and the dead layer without a change in the transition temperature. Therefore, the data
55 can be explained by a model which considers the thickness, transition temperature, and diffuseness. The authors suggested an explanation based on the Binder model [70]. This model accounts for the thickness dependencies of Tmax, max, and the broadness of the transition by assuming a polarization gradient at each surface through the material. Lookman et al. suggested that Parker’s data could be modeled using the series capacitor model with a temperature independent interfacial capacitance [110]. They claimed that instead of using the overall permittivity, by using the film permittivity (b) in Eq. 2.29 and making “corrected”
Curie-Weiss plots the transition temperature for the film comes out to be temperature independent. However, this result arises suspicion in that the transition temperature of the film is thickness independent and the interfacial layer is completely temperature independent
yet their overall response results in a thickness dependent transition temperature.
While the debates on the origin of the thickness dependency were continuing, Saad et al. showed that bulk-like permittivity values and phase transition behavior can be obtained in thin free standing barium titanate single crystals [111]. The thin films were obtained by cutting thin slabs from a single crystal with a thickness range of 75-450 nm. After evaporating gold electrodes and annealing out the defects caused by the ion-milling process, the authors measured permittivities on the order of 25,000 for the 75 nm films. The same films showed very sharp transition peaks at ~125 °C, which is very close to the bulk value, and they noted the absence of any shift in the phase transition temperature or a change in the broadness with a change in thickness. The importance of this work lies in suggesting that the observed scaling effects in thin films are possibly not due to intrinsic effects and they
strongly depend on the electrical and mechanical boundary conditions applied on the film.
56 Therefore, by minimizing the detrimental extrinsic effects it could be possible to obtain bulk-
like properties in ferroelectric thin films. It must be noted for the sake of completion that
there is some suspicion regarding the thinned single crystal data. There remains a question
regarding the electroding geometry of this thinned crystal experiment – specifically, the
experimental procedure allowed for a finite amount of the thicker crystal to be sampled by
the probing field and the extent to which this component contributed to the measured properties remains unclear.
2.6 Processing of BaTiO3 – (Ba,Sr)TiO3 Thin Films
The thin films of BaTiO3 – (Ba,Sr)TiO3 have been synthesized by various deposition
techniques including metalorganic chemical vapor deposition (MOCVD) [106, 109], pulsed
laser deposition (PLD) [107, 110, 112], radio frequency (RF) magnetron sputtering [28, 74,
89, 113-116], and chemical solution deposition (CSD) [75, 76, 88, 117, 118]. Each technique
has its advantages and drawbacks, therefore each could be the choice of deposition method
depending on the selection criteria. For instance, for capacitor applications cost is very
important, since these capacitors should be one of the least expensive components in an
electronic device. In this case, CSD techniques can be used since they offer a low cost, large-
scale production with very high compositional uniformity. RF magnetron sputtering can also
be used with its relatively low cost, ease of composition control, and repeatability. On the
other hand, for high performance applications such as tunable microwave devices MOCVD
techniques can be used to obtain very high quality epitaxial thin films [29]. Regardless of the
57 deposition method used, the goal is to obtain thin films with controlled stoichiometry, high
purity and density, good thickness uniformity, and high crystal quality. By fulfilling these
requirements, high permittivity (and tunability) and low dielectric loss values can be
achieved. Magnetron sputtering and chemical solution deposition will be discussed in detail,
since these two are the deposition methods used in this thesis.
2.6.1 Magnetron Sputtering
2.6.1.1 Basics of Sputtering
Sputtering is a physical vapor deposition (PVD) process, where atoms from a target
(Pt, Cu, etc.) are ejected by high energy ion bombardments and deposited onto a substrate
(Figure 2.18). After the vacuum chamber is evacuated a sputtering gas, typically argon, is
introduced into the chamber. Several kilovolts of dc bias is applied to the negative terminal
of the magnetron gun, which accelerates the electrons towards the anode. The electrons
follow a cycloidal path on the cathode with the applied magnetic field and collide with argon
atoms. An electron with high enough energy can knockout an electron from argon converting it into a positively charged ion (Ar+). Then, the positive Ar+ ions are driven to the cathode
where they collide with the target atoms and eject (sputter) them through momentum transfer.
The plasma is initiated by the multiplication of these collisions. The chamber pressure is
usually kept at between 5-50 millitorrs during sputtering. After a visible plasma is obtained it
is observed that a current flows and the target material is deposited onto the surfaces with
58 potential higher than that of the cathode (i.e. substrate, chamber walls). This dc discharge is
sustained due to the generation of ion-induced secondary electrons at the cathode.
Figure 2.18 Schematic depiction of magnetron sputtering.
If an insulating material is used as the target material, a practically impossible amount
of dc voltage (~1012 V) is needed to achieve the same current density as in a conducting
target [119]. This barrier can be overcome by applying an ac signal at high frequencies. At
low frequencies (e.g. 60 Hz) dc sputtering conditions occur and the cathode and the anode alternate at each half of the cycle. The frequency factor becomes effective above ~1 MHz
[120]. In this range, the electrons oscillating back and forth by the electric field gain sufficient energy to ionize argon atoms. This is in addition to the acceleration away from the target. Since these field-driven electrons generate ions directly, sustaining the plasma does not rely on the secondary electrons emitted from the target. Even though the process seems symmetric considering the cycles, it is asymmetric due to the system geometry. The target
59 area is much smaller than the other electrode (substrate, chamber walls), hence resulting in higher energy bombardment of the target [121]. At radio frequencies, voltage can be coupled through any impedance, therefore the electrode resistivity does not matter. Due to the lower discharges at the target the rf sputtering yields deposition rates a factor of ~2 lower than dc sputtering.
2.6.1.2 Sputtered (Ba,Sr)TiO3 Thin Films
The structure and the properties of sputtered BST thin films depend on the deposition parameters including rf power, working pressure, argon to oxygen gas ratio, target to substrate distance, substrate material, substrate temperature as well as the post-anneal conditions. Therefore, these parameters need to be optimized to achieve the best dielectric properties. The effects of these sputtering conditions on the structure and the dielectric properties have been studied by many researchers.
Group of York at University of California Santa Barbara studied the effects of Ar/O2 ratio on the dielectric properties of (Ba0.5Sr0.5)TiO3 films sputtered on platinized silicon at
550 °C [113]. The authors observed an increase in (100) texturing with decreasing oxygen content. The permittivity also increased with decreasing oxygen. It was suggested that the
(100) texturing resulted in the in-plane enhancement of the polar axis (c-axis) making the a- axis normal to the films surface. Since in tetragonal barium titanate the a-axis permittivity is much larger, the increase could be explained this way. In a later paper, the same group showed that the oxygen also has an effect on the Ti nonstoichiometry and A/B site ratio
60 [114]. By systematically changing the Ar/O2 ratio from 90/10 to 60/40 it was observed that
the permittivity and the loss tangent could be altered substantially. While low oxygen
resulted in high permittivity and tunability films with moderate loss, increased oxygen pressure resulted in low permittivity and very low loss. With increasing oxygen the A/B site
ratio ((Ba+Sr)/Ti) was measured to decrease from 1.00 to 0.82. The authors suggested that
this excess Ti segregated at grain boundaries making them more insulating, thus giving a
lower loss tangent. The A-to-B site ratio was also shown to depend on the total pressure
[115]. It was demonstrated that by increasing the total pressure from 20 to 60 mTorr, the ratio
could be changed from 0.73 to 1.00. Again, the more Ti-excess films gave lower permittivity
values with lower loss tangents.
Tsai et al. studied the effects of Ar/O2 ratio on (Ba0.5Sr0.5)TiO3 films sputtered on
platinized silicon at various temperatures [122]. Contrary to York group, the authors did not
observe any change in the A-to-B site ratio in an Ar/O2 range of 100/0 to 40/60. Furthermore,
the dielectric constant increased with increasing oxygen content reaching a maximum at a
ratio of 50/50. Crystallinity of the films was also increased with increasing oxygen content.
The effects of gas ratio was also studied by Lee et al. and Chen at al. [123, 124]. Both groups
observed an increase in the permittivity with increasing oxygen content. All these results
suggest that in addition to sputtering conditions, the stoichiometry and the structure of the
films depend on many additional parameters such as system geometry, target composition
and purity, and gas purity.
Baniecki et al. investigated the crystallization and the effects of deposition
temperature on the dielectric properties of BST films [81]. The authors sputtered
61 (Ba0.7Sr0.3)TiO3 thin films on platinized silicon in a deposition temperature range from 100 to
650 °C. The X-Ray data showed the onset of crystallization at 250 °C. Transmission electron
microscopy (TEM) study confirmed this data revealing a mixture of crystalline layer on top
and a less crystalline phase on the bottom. It was noted that above 350 °C there was no
distinct less-crystalline layer. Below 500 °C the films were mainly (110) textured and above this temperature the films became (100) textured. The change in texturing was also observed by other authors, above 600 °C [74, 123]. The permittivity increased with increasing deposition temperature due to the enhanced crystallinity and grain size reaching a value of
600 with a deposition temperature of 650 °C.
In addition to silicon, number of other substrates have been used for the sputtering of
BST thin film microwave devices, including LaAlO3, MgO, sapphire, and polycrystalline
Al2O3 [116, 125, 126]. Since these devices use interdigitated electrodes instead of the metal-
insulator-metal configuration, i.e. do not require bottom electrodes, the hillocking and delamination problems caused by the bottom electrodes are eliminated in these structures.
Therefore, depending on the lattice mismatch these can be fired at temperatures higher than
750 °C which is silicon’s limit. It was also shown that base metal foils could be used to take
advantage of high annealing temperatures to obtain high permittivity values with low
dielectric loss. Laughlin et al. sputtered (Ba0.6Sr0.4)TiO3 films directly on copper foils at 100
°C [89]. The authors demonstrated that by doing low pO2 anneals at 900 °C it was possible to
crystallize the films without oxidizing the copper which was confirmed by XRD and
transmission electron microscopy (TEM) results. A permittivity of 600 and a 3.5:1 tunability
with a loss tangent of 0.018 were obtained in these metal-insulator-metal devices. It will be
62 shown in this thesis that, this method could be extended to nickel foils to take advantage of even higher processing temperatures to get higher permittivity and tunability values.
2.6.2 Chemical Solution Deposition
Chemical solution deposition (CSD) is a widely used technique to synthesize ferroelectric thin films with its low capital cost and compatibility with other semiconductor fabrication techniques [127]. This method offers many other advantages including high purity, high compositional homogeneity due to the mixing of the species at the molecular level, ability to control structural evolution, fabrication over large areas, and easy variation of stoichiometry. Nevertheless, this easy variation in the composition is also this method’s major drawback because it makes repeatability of the process much more difficult. The other disadvantages include poor step coverage and difficulty in depositing epitaxial films.
In thin film processing, the term sol-gel is often used interchangeably with chemical solution deposition (even though it is only a CSD approach), since all the CSD routes involve preparation of a solution and then gelation of this solution. A sol is defined as a suspension of nanoscale solid particles in a liquid. This forms a gel through solvent evaporation and polymerization of the molecules or through forming a network via attractive dispersion forces. Therefore, a gel can be defined as a solid network of molecules or particles enclosing a continuous liquid phase [128]. With the application of heat, the gel can be dried into an amorphous phase and then densified and crystallized into a ceramic. Thus, the steps of thin film chemical solution deposition are (i) solution preparation, (ii) solution deposition, and
63 (iii) thermal treatments for structural evolution. Structural changes observed during the heat
treatments can be divided into three regions [128]. Region I, which is typically between 25-
150 °C, involves gelation and the evaporation of water and the solvent. Region II, which is typically between 150-500 °C, involves condensation reactions, removal of organics, and
structural relaxation. Finally, region III involves sintering and crystallization of the material.
All these steps will be discussed in detail in the following sections.
2.6.2.1 Solution Preparation
Chemical solution deposition is generally categorized into three groups depending on
the solution chemistry and the chemical reactions that occur. These are classical sol-gel
processes which use alkoxide precursors and alcohols as solvents, metalorganic
decomposition routes which use carboxylate precursors and non-polar solvents, typically
xylene, and the hybrid processes which combine the first two utilizing both carboxylate and
alkoxide precursors [129, 130].
In sol-gel processing of perovskite thin films, typically metal alkoxide precursors are
dissolved in 2-methoxyethanol and they go under hydrolysis and condensation reactions to
form metal-oxygen-metal (M-O-M) bonds:
M(OR) x + H2O M(OR) x1(OH) + ROH hydrolysis
2M (OR) x1 (OH ) M 2O(OR) 2x3 (OH ) + ROH condensation (alcohol elimination)
2M (OR) x1 (OH ) M 2O(OR) 2x2 + H 2O condensation (water elimination)
64 Since alkoxide precursors are highly reactive, they easily undergo hydrolysis and
condensation. To avoid premature hydrolysis and condensation, there is another key reaction
which decreases the sensitivity of the precursor to water. This reaction is the alkoxy
exchange in which 2-methoxyethanol forms a methoxyethoxide which is less reactive:
M (OR) x + xROH M (OR) x + xROH alkoxy exchange
Condensation reactions of monomers form intermediate size molecules called
oligomers. This polymerization can continue to build larger and larger molecules which
results in the formation of a solid network in a continuous liquid phase forming a gel. The
extent and the rates of these reactions can be controlled by controlling the temperature, pH,
refluxing, distillation, and the water content to tailor the solution and the final material
properties. However, these procedures require extensive knowledge of chemistry and for a
non-chemist they can be quite complex. Furthermore, the solvent 2-methoxyethanol is known
to cause birth defects inhibiting the industrial use [130].
Metalorganic decomposition routes use carboxylates and -diketonates (acac-type compounds) which are much less sensitive to water than the alkoxides. The large carboxylate compounds are usually dissolved in xylene and combined to achieve the desired stoichiometry. Since the species are not very reactive, the synthesis is rather simple and the final precursor strongly resembles the starting compounds. However, this simplicity also limits the ability to engineer the solution and hence the material properties. Another disadvantage of this process is that the large organic molecules result in excessive weight loss and shrinkage during heat treatment steps causing cracking of the films [129].
65 The third group is the hybrid processes which are commonly used for the perovskite film synthesis. Generally, the A-site carboxylate precursor (e.g. Ba-acetate) is dissolved in a carboxylic acid (e.g. acetic acid). The more reactive B-site alkoxide precursor (e.g. Ti- isopropoxide) is first chelated, i.e. modified to decrease its reactivity against water, and then added to the A-site solution. The chelating reaction is the key in the hybrid route which enables the handling of the alkoxide in ambient air. This route is very attractive for the non- chemist due to the relative simplicity of the solution preparation, even though the chemistry is quite complex due to the number of reactions that occur [130]. A disadvantage of the hybrid-chelate processes is that the solutions remain reactive after the synthesis degrading the solution properties and eventually causing precipitation.
2.6.2.2 Solution Deposition
Once the solutions are prepared thin film deposition is usually accomplished by using spray coating, dip coating, or spin coating. In spray coating a wet mist or aerosol is delivered onto the substrate by using a nebulizer. An inert carrier gas is usually used and the settling is achieved by the gravitational or electrostatic forces [130]. The advantage of this method over the others is the conformal step-coverage. By using a high frequency nozzle with small droplet size, conformal deposition over the non-planar structures such as steps and trenches are possible [131].
In dip coating the substrate is immersed into the coating solution and then removed during which the deposition occurs. The process could be batch or continuous. The batch
66 process involves five steps; immersion, where the substrate is completely dipped into the
coating solution, start-up, where pulling the substrate out of the solution begins, deposition,
drainage, and solvent evaporation [128]. The thickness of the film is a result of the
competition between various forces including gravity, viscous drag forces, and the surface
tension in the concavely curved meniscus.
In spin coating the substrate is held on a spinner by a vacuum chuck and then is
flooded with excess solution. Then it is rotated at a speed of 1000-8000 rpm to achieve
uniform coverage. The spin coating can be divided into four stages which are deposition,
spin-up, spin-down, and evaporation [132]. During the spin-up stage the solution flows
radially outward to the perimeter due to the centrifugal forces. During the spin-down stage, the extra fluid flows off the substrate edges. The thickness in these stages is determined by the competition between the centrifugal and viscous drag forces, i.e. spin speed vs. viscosity.
As the film gets thinner, the viscosity increases due to the increased concentration of non- volatile components, and the resistance to flow decreases. After that, evaporation becomes the major mechanism for further thinning. For Newtonian liquids, in which the viscosity is not shear rate dependent, once the liquid film reaches a uniform thickness it stabilizes [128].
Therefore, the thickness can be controlled by solution viscosity, spin speed, and spin time.
2.6.2.3 Gelation and Drying
In thin films, due to the high surface to volume ratio gelation and drying occur simultaneously. Gelation can be divided into two groups as physical and chemical [130].
67 Physical gels are formed from particulate sols which are held together by van der Waals forces. These can be reverted to their sol state by dissolving in their parent solvent. Physical gels usually become chemical gels in time or with the application of heat. Chemical gelation involves the formation of a metal-oxygen-metal network through hydrolysis and condensation reactions. These reactions result in the formation of clusters, as the clusters grow they collide and form bonds with each other. At the gel point, they produce one giant cluster which extends throughout the liquid. This point is the onset of elasticity, since there is a continuous solid network [128]. In time, other clusters continue to attach to the spanning cluster increasing its stiffness. This further condensation, in fact, is not desired, because it results in a porous structure. Formation of a cross-linked stiff network does not allow structural rearrangements which results in a low density. Generally, it was observed that by using lower reactivity precursors, and volatile solvents films with higher density were obtained [133, 134].
Drying involves evaporation of the solvent and an accompanied shrinkage due to the capillary pressure. The dried gel, which is called a xerogel, can be reduced in volume up to an order of magnitude. When the liquid evaporates, it leaves behind solid-vapor interfaces with higher energy than solid-liquid interfaces. Therefore, to minimize the interfacial energy the liquid tends to cover the exposed solid surfaces. Assuming a cylindrical pore with radius r and length l, the change in the energy can be written as,
E = 2rl( SV SL ) Eq. (2.30)
68 where SV and SL are the surface tensions of the solid-vapor and the solid-liquid interfaces,
respectively. By rising in the pore the liquid does work against gravity which is equal to
2 PcV, where Pc is the capillary pressure and the volume of the liquid moved is V=r l. By equating this to the energy change and using Young’s equation for the balance of surface tensions ( = + cos ) the capillary pressure can be written as, SV SL LV
2( SV SL) 2 cos P = = LV Eq. (2.31) c r r
where is the contact angle. The negative sign means that the liquid is in tension (the sign
convention for pressure is opposite to that for stress). This tension is balanced by
compression in the solid which results in the shrinkage of the gel [135]. The displacement of
the liquid also creates a pressure gradient driving the flow from the interior.
At the drying stage, shrinkage mainly depends on the competition between
evaporation (drives network contraction) and the condensation reactions (drives network
stiffening). While the network is still compliant, capillary pressure can contract the solid
network, however once the network gets stiff enough (through condensation reactions) that
the capillary forces cannot overcome the modulus of the network, the shrinkage is
significantly reduced and further evaporation results in porosity. Thin films are generally
much denser than bulk gels, because the rapid evaporation causes films to remain compliant,
so that the pores are collapsed by the capillary pressure during drying.
69 The pressure gradient caused by the low permeability of the solid network causes a difference in the shrinkage rates between the interior and the exterior regions resulting in a drying stress. The differential shrinkage would result in a tensile stress in the solid reaching up to ~100 MPa. Above a critical thickness these stresses can cause cracking. This thickness dependence is related to the minimization of energy. The presence of stresses increases the elastic energy. The system forms cracks and creates new surfaces to reduce this elastic energy at the expense of increase in the surface energy. At a critical thickness, the reduction in the elastic energy cannot compensate for the increase in the surface energy, and hence the crack cannot propagate. Typically, thin films with thicknesses <0.5 μm do not crack regardless of the drying rate, whereas films thicker than 1 μm almost always crack [128]. The critical thickness can be increased by decreasing the elastic modulus of the solid through precursor chemistry and by controlling the evaporation/condensation rates.
2.6.2.4 Structural Evolution during Thermal Treatments
After the gel is dried, the obtained xerogel is further heat treated at elevated temperatures to synthesize the ceramic with desired properties. In the xerogel state, the material can be considered as a high surface area (500-900 m2) network of M-O species with adsorbed carboxylate and hydroxyl groups. As the temperature is increased, in the temperature range 25-150 °C, desorption of water and residual solvent occurs with an accompanied weight loss and a small amount of shrinkage due to the capillary pressure. With further increase in temperature, in the 150-500 °C range there are three processes that
70 contribute to shrinkage. These are the organic removal reactions, condensation reactions, and
structural relaxation [128].
Organic removal involves thermolysis (without oxygen) or pyrolysis (with oxygen)
and oxidation reactions. In thermolysis and pyrolysis organic species are removed by
breaking M-O-C and M-O-H bonds. In barium titanate systems, oxidation reactions occur
that form refractory carbonate (M-O-CO2) phases. Removal of organics results in significant
weight loss with a small amount of shrinkage. In thin film deposition, generally, the heat
treatments are conducted in two steps. Before the high temperature treatment there is a first
step that involves a hot plate dry (200-400 °C) after the deposition of each layer to avoid
cracking. The condensation and pyrolysis that occur during the heating of a xerogel give off
large volumes of gas. This can generate high pressures due to the low permeability of the
structure resulting in the crack formation in large thicknesses. By the two-step process the
organic constituents can be removed completely before the densification and the
crystallization of the film.
The second mechanism for shrinkage in the 150-500 °C range is condensation
reactions. In these reactions hydroxyl groups are eliminated as water leaving behind M-O-M bonds. These reactions result in both shrinkage and weight loss. Finally, structural relaxation also contributes to shrinkage. In this process, to decrease the free energy, the excess free volume is removed through bond restructuring or rearrangements without any weight loss.
The process occurs by diffusive motions of the network [128]. In general, there are no
thermodynamic barriers to condensation and structural relaxation. They depend on material
transport and so are kinetically limited.
71 At elevated temperatures the densification is accomplished by sintering mechanisms.
Sintering is the reduction in the area of a consolidated particle mass, driven by gradients in curvature. Material is transported by viscous flow (in amorphous materials) or diffusion (in crystalline materials) to eliminate the porosity and decrease the solid-vapor interfacial area.
In bulk materials, the transport of material via viscous flow and diffusion from the grain boundary area to the neck area between two particles results in densification. By these mechanisms the centers of the two particles move closer to each other reducing the surface area. However, evaporation-condensation and diffusion from the surface to the neck area do not move the centers toward each other, hence they only result in coarsening. In thin films, where the thickness of the films is comparable to the grain size, these two mechanisms can also cause densification if they transport vacancies all the way to the surface of the film
[136].
The densification by viscous sintering is faster than densification by solid state sintering which relies on diffusion. This is because, in viscous sintering there is a volume flow of material through a relatively low viscosity matrix, whereas in diffusion the material moves due to local concentration gradients through impinging crystals with high viscosity
[137, 138]. This enhanced material transport and particle rearrangement results in higher densification. The densification rate for viscous sintering is approximately given by [136],
1 d n 3 SV SV Eq. (2.32) dt r
72 where is the viscosity, n is the number of pores per unit volume of solid, and r is the
particle size. According to this equation the densification rate depends on viscosity, surface tension, and the pore size. Hence, precursor chemistry, deposition conditions, and the heat treatment schedule can be used to control the densification behavior.
Crystallization in amorphous pyrolyzed films occurs by nucleation and growth processes. Nucleation of a new phase requires energy to create a new interface and undercooling provides the driving force for this process as shown in Figure 2.19. It is observed from the figure that the free energy of the amorphous gel phase is larger than the supercooled liquid. This is due to the large surface area, residual hydroxyl, and excess free volume [130]. At low temperatures, even though the gel is unstable and the degree of undercooling is large, crystallization is inhibited by low atomic mobility [128].
Figure 2.19 Schematic plot of an amorphous CSD film, the supercooled liquid, and the crystalline perovskite phase (taken from Schwartz [130]).
73 From the classical nucleation theory, the thermodynamic barriers for homogeneous and heterogeneous nucleation are given by,
16 3 * Eq. (2.33) Ghomo = 2 3(GV )
16 3 * Eq. (2.34) Ghetero = 2 f () 3(GV )
2 3cos + cos3 f () = Eq. (2.35) 4
where is the surface tension, GV is the driving force for nucleation, and is the dihedral
angle between the nucleus and the heterogeneous site. These equations implicate that the
difference in the thermodynamic barriers depend on the driving force and the dihedral angle.
Therefore, the values of these terms have important consequences in the transformation and
the microstructure. For example, at low temperatures the driving force is very large (Figure
2.19) and the GV term dominates in the equations, making both homogeneous and
heterogeneous nucleation possible. On the other hand if crystallization starts at higher
temperatures, then the driving force will be small and the difference in the barriers will be
determined by the f() term favoring heterogeneous nucleation. The crystallization
temperatures can be shifted due to the changes in transformation pathways, precursor
74 chemistry and heating rates [130]. Typically, barium titanate thin films form the perovskite phase via an oxycarbonate phase and lead zirconate titanate (PZT) films form the perovskite via the pyrochlore phase which delay the perovskite crystallization temperature. While PZT
mostly forms a columnar microstructure, barium titanate results in equiaxed grains. The
pyrochlore phase in PZT does not act as nucleation sites for the perovskite formation, hence
heterogeneous nucleation takes place at the substrate interface resulting in a columnar
microstructure [139]. However, in barium titanate it was suggested that the perovskite phase
crystallizes from the oxycarbonate which nucleates at low temperatures where the driving force is large resulting in an equiaxed grain structure [75, 130]. The altering of precursor chemistry through utilizing various alkyl chain lengths and using chelating agents was also shown to change the transformation pathways and the microstructure [117].
Once the material crystallizes densification occurs by solid state sintering which is much slower than the viscous sintering [128, 130, 136]. Thus, it would be beneficial to delay the crystallization to higher temperatures until a high density is achieved or the densification is completed. This is in fact possible, because the driving forces for the two processes are different. While crystallization is driven by the amount of undercooling, i.e. temperature dependent, it weakly depends on the surface energy, which is the driving force for sintering.
Therefore, by controlling the thermal treatment it is possible to favor one process over the other. This can be analyzed by using time-temperature transformation (TTT) diagrams which show the effect of thermal history on phase transformation. Volume fraction of the crystallized material is given by the Avrami’s equation,
75 V =1 exp( I u3t 4 ) Eq. (2.36) c 3 v
where Iv is the nucleation rate, u is the growth rate, and t is time. Using these to construct the
TTT diagram and superimposing the densification curves it is possible to analyze the
competition between sintering and crystallization as shown in Figure 2.20. As seen from the
figure, slow heating rates will result in incomplete densification. However, if the heating rate
is fast enough, then it is possible to completely densify the material before the crystallization starts.
Figure 2.20 TTT and sintering curves for an amorphous material (adapted from Uhlmann et al. [128]).
76 The effect of heating rate can also be visualized by considering the nucleation and the growth rates separately. The growth rate (u) increases with undercooling below the melting point as the free energy difference between the crystal and the amorphous gel, reaches a maximum and begins to decrease due to the rising viscosity (or low mobility). The nucleation rate (Iv) rises at a relatively large undercooling, because of the thermodynamic barrier to form a nucleus and then decreases at lower temperatures due to the increasing viscosity. By using faster heating rates to pass quickly the temperature range where the nucleation rate is high, so that there is not enough time for many nuclei to form, it is possible to densify the material before an appreciable amount of crystallization occurs (Figure 2.21).
Figure 2.21 Nucleation (Iv) and growth (u) rate data for anorthite-CaO•Al2O3•2SiO2 (taken from Scherer [136]).
77 Another way to decouple the rates of crystallization and sintering is controlling the
microstructure. While the crystallization rate does not depend on microstructure, the sintering
rate strongly depends on the pore size. Therefore, by controlling the microstructure and the
pore size through precursor chemistry, it is possible to obtain small pore size to increase the
surface energy and the densification rate.
2.6.2.5 Solution Processing of BaTiO3 and (Ba,Sr)TiO3
Conventional processing of barium titanate involves the solid state reactions between
the raw materials BaCO3 and TiO2 which requires temperatures in excess of 1200 °C to
decompose the carbonate and accelerate the diffusion between the species to complete the
reaction. However, this process results in coarse inhomogeneous particles with impurities
and secondary phases [140]. To overcome these problems solution routes were utilized to
obtain powders with small particle size, high purity, and homogeneity with reduced
processing temperatures. Then, the benefits of sol-gel processing in thin films were realized
as the thin films were integrated into microelectronic devices.
The first cited report on the sol-gel processing of barium titanate was from
Yanovskaya et al. [141]. The authors deposited alcoholic solutions of barium and titanium
ethylate on platinum and quartz substrates, which were then fired at temperatures between
700-1250 °C. Even though the samples had secondary phases from the BaO-TiO2 system, they were able to measure the temperature dependence of the dielectric constant with a distinct transition at ~120 °C. Tuchiya et al. was able to synthesize dense and single phase
78 barium titanate films on platinum substrates via hybrid routes [142]. The authors
demonstrated the enhancement in the dielectric properties with increased firing temperatures.
The room temperature permittivity data showed almost an order magnitude increase as the
processing temperature was increased from 700 to 1000 °C. A room temperature permittivity
of 1000 with a loss tangent of 0.035 was obtained with a sharp ferroelectric/paraelectric
transition in the r-T curve. This report clearly shows the advantage of the film-on-foil
process where high processing temperatures can be used to enhance the dielectric properties
without facing cracking or delamination problems that are commonly observed in rigid
substrates. Hayashi et al. deposited barium titanate films via metal alkoxides [143]. They
demonstrated that sol-gel films that show ferroelectric behavior could be deposited on
various substrates including platinized silicon, MgO, and sapphire.
By controlling the precursor chemistry and the deposition parameters Hoffmann et al.
were able to tailor the film morphology [75]. The authors deposited BST films on platinized
silicon using hybrid routes. Diluting the short chain Ba-carboxylate solutions from 0.3 M to
0.1 M changed the microstructure from equiaxed to columnar. This was attributed to the high crystallization temperature which decreased the driving force for nucleation resulting in heterogeneous nucleation. Later, Schwartz et al. demonstrated that crystallization of a dilute
seed layer is sufficient to achieve columnar microstructure [118].
Chemical solution deposition of thin films directly on base metal substrates (Ni and
Cu) were demonstrated by Dawley et al. and Ihlefeld et al. in an attempt to fabricate
inexpensive base metal electrode capacitors [76, 88]. Both groups were able to achieve
79 permittivities larger than 1500 by crystallizing their films in a reduced atmosphere to avoid base metal oxidation.
Phase evolution in solution processed barium titanate differs from conventionally processed bulk ceramics. Generally, decomposition of the precursors results in the formation of an intermediate oxycarbonate phase in all of the sol-gel, metalorganic, and hybrid routes
[75, 117, 144-146]. Hasenkox et al. studied the effects of precursor chemistry on the phase
formation of barium titanate thin films. For the hybrid routes, which involve the reaction of
Ba-carboxylate and Ti-alkoxide, the authors made the following observations. The titanium
precursor decomposes before the barium precursor around 300-350 °C [117]. At that point
the structure is a Ti-O gel network with adsorbed Ba-carboxylate species [130]. The barium
precursor decomposition occurs in the range 400-500 °C depending on the chain length.
Transformation pathway is also determined by the Ba-carboxylate chain length. For a long
chain length precursor (2-ethylhexanoate) decomposition occurs at lower temperatures and
BaTiO3 forms via,
BaCO3 + TiO2 BaTiO3 + CO2
On the other hand, if the precursor is an acetate or a propionate it decomposes at higher
temperatures and forms the oxycarbonate phase through reacting with titania. Then the
BaTiO3 formation occurs via,
Ba2Ti2O5CO3 2BaTiO3 + CO2
Hence, the transformation pathway depends only on the barium precursor. Oxycarbonate
phase formation shifts the crystallization temperatures resulting in higher densities [117].
80 2.6.3 Firing of Thin Films on Base Metal Substrates
Multilayer ceramic capacitors (MLCC) based on BaTiO3 have been manufactured using palladium or silver palladium alloys as the electrode material until the Pd price increased dramatically [147]. This necessitated finding less expensive electrode materials which can be co-fired with the ceramic. In 1963, Herbert suggested that any metal with a sufficiently high melting point (>1300 °C) could be used unless its oxygen affinity causes the reduction of barium titanate (e.g. Ti and Zr) [148]. By using nickel electrodes, cost savings of a factor of five compared to the noble electrodes were achieved [147]. However, these capacitors need to be fired in reducing atmospheres (N2/H2 or CO/CO2) to avoid metal electrode oxidation which also reduces the barium titanate creating oxygen vacancies. For the forming gas atmosphere the reaction can be written as [147]
BaTiO3 + xH2 BaTiO3x []Vo x + xH2O
The reduction creates free electrons which decrease the insulation resistance of the material.
This reaction for barium titanate can be written using the Kröger-Vink notation as [149],
1 •• Oo 2O2 + Vo + 2e
Herbert also suggested the use of metal cations which can substitute for Ti4+ with lower valence (i.e. acceptors) such as Mn, Co, Cr, and Fe. These could compensate for the free electrons and increase the insulation resistance [148]. Burn and Maher demonstrated this by doping the barium titanate based thick films with Mn, Co, and Mg [150]. The authors measured a three orders of magnitude increase in the resistivity, from 109 to 1012 .cm, with the addition of these dopants. As a result of acceptor doping the free electrons are annihilated
81 by the acceptor states or by positively charged carriers, i.e. holes [149]. Nevertheless, the insulation resistances of the doped-materials were observed to degrade when they were under electrical field for long periods of time due to the electromigration of charged oxygen vacancies [151]. This could be overcome by using donor-acceptor complexes or amphoteric rare-earth ions such as Y3+, Dy3+, and Ho3+ [152-155]. The amphoteric dopants can occupy both A and B sites in barium titanate limiting second phase formation and also segregate to grain boundaries limiting the ionic transport of oxygen vacancies [156].
Furthermore, the insulation resistance of base metal electrode capacitors can be also improved by a reoxidation treatment. This typically involves annealing the capacitor at 900-
1100 °C in an N2 atmosphere containing 50-100 ppm O2. The aim here is to decrease the
oxygen vacancy concentration in the material while kinetically limiting the base metal
oxidation. Especially in the presence of multivalent acceptor ions such as Mn and Fe, the
reoxidation changes the cation valency (e.g. Mn2+ to Mn3+, Mn4+) which further decreases the number of oxygen vacancies [147].
Thermodynamics of processing oxide ceramics without oxidizing the base metal electrodes can be understood by analyzing the free energies of the oxidation-reduction reactions of the constituent materials. Considering a simple oxidation reaction for a metal M,
2M(s) + O2(g) = 2MO(s)
The standard Gibbs free energy change for the reaction is given by,
a 2 o and MO Eq. (2.37) G = RT ln K K = 2 aM pO2
82 Figure 2.22 pO2 versus temperature diagram for the oxidation of metals.
where R is the gas constant, T is temperature, K is the equilibrium constant, and a is the activity. Assuming the activities of pure solids to be unity, the free energy change can be written as,
1 Go = RT ln Eq. (2.38) pO2
The variation of G°or pO2 with temperature can be plotted using the
thermodynamical data in the literature for the oxidation of metals [157]. Hence, by plotting
83 the oxidation curves it is possible to find the processing window in which the base metal is
thermodynamically stable with the constituent oxides. Figure 2.22 illustrates the curves for
barium, titanium, and the base metals nickel and copper. In this diagram, which is called an
Ellingham diagram, the oxides are stable above the lines and metals are stable below the
lines. The reason for avoiding the metal oxidation is that even though the base metals are
thermodynamically stable with barium titanate, their oxides will react to form second phases
that would degrade the capacitor properties [158].
Adapting the MLCC firing technology Dawley et al. demonstrated the fabrication of
BST thin films capacitors on nickel tapes using chelate chemistry [88, 159]. Chemical
solution deposited BST thin films were annealed at 900 °C in an atmosphere of 3% H2/N2
-18 bubbled through room temperature water which gave a pO2 of ~10 atm. As it can be seen
in Figure 2.22, these conditions are within the processing window of barium titanate on
nickel. The authors were able to obtain a permittivity of 500 for random orinted grains and
1500 for their textured films. The dielectric losses were between 1-3%. Ihlefeld et al.
expanded this work to copper foils using a similar chemistry approach [76, 160]. By
-11 annealing at 900 °C at a pO2 of 10 atm, permittivities in excess of 2500 were achieved with
grain sizes up to 0.3 μm. This large grain size was believed to be the reason for bulk-like permittivities [76]. Furthermore, the r-T curves showed a clear hysteresis and the X-Ray
diffraction patterns confirmed the tetragonal structure which is rarely seen in thin films.
Laughlin et al. synthesized BST thin films on copper by rf magnetron sputtering [89]. By
84 firing at 900 °C in a controlled atmosphere the authors obtained a permittivity of 600 with a
55 nm grain size.
The second part of this thesis builds upon Ihlefeld’s CSD on copper foils approach and investigates the effects of firing parameters and different firing schedules on the phase formation and dielectric properties. In an attempt to optimize the dielectric properties, in-situ experiments that probe the effects of firing parameters on barium titanate phase formation and microstructure development were performed. Stockenhuber et al. have used this approach to study the decomposition of mixed barium titanium oxalates using a residual gas analyzer.
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103 CHAPTER 3. EXPERIMENTAL PROCEDURES
3.1 Barium Strontium Titanate Sputtering on Base Metal Foils
Copper and nickel foils were used as the substrates and the bottom electrodes for the
BST capacitors fabricated in this study. Copper foils were Oak-Mitsui PLSP foils with 18 μm thickness. The nickel foils were obtained from Alfa Aesar (Nickel Thinfoil, 99.95 %) and had a thickness of 10 μm. The root mean square (rms) surface roughnesses of the copper and nickel foils were measured to be 100 and 270 nm respectively on an 8 μm 8 μm area. The atomic force microscopy images are shown in Figure 3.1. It is important to note that these roughness values are between two and three orders of magnitude higher than values for single crystal substrates such as silicon and sapphire.
104 Copper Nickel
Figure 3.1 Atomic force microscopy images of Cu and Ni foils.
(Ba0.6Sr0.4)TiO3 films were sputtered using rf magnetron sputtering from a 4" stoichiometric target (Super Conductor Materials, Inc., NY). The magnetron gun was oriented 30° off-axis to reduce the plasma damage caused by the bombardment of oxygen anions. The substrates were mounted on a heated and rotating manipulator for optimum stoichiometry and uniform thickness. The manipulator consisted of a stage with BN coated graphite heating element and a motor feedthrough for stage rotation. The manipulator was designed so that the stage was able to rotate around the fixed heater. The stage was rotated using a 12V dc motor at a speed of ~5 rpm. An S-type thermocouple was used to monitor
105 substrate temperature. The thermocouple was positioned equidistant to the heating element
and the substrate. The schematic depiction of the system is given in Figure 3.2a. The copper and nickel foils were put on a 3" quartz plate side-by-side and held down by 0.836" diameter copper gaskets as shown in Figure 3.2b. The samples were heated via the radiation of the heater through the quartz plate.
The as-received foils were cut into square peaces of 1" 1" and placed into the chamber. The chamber was pumped down to a base pressure of ~110-5 Torr. Then, UHP
argon (99.999%) was introduced to the system at a flow rate of 20 sccm using an MKS
Instruments (Andover, MA) mass flow controller. The depositions were performed at 3.7
W/cm2 using an Advanced Energy RFX-600 rf power supply and an RF Plasma Products
MN 500-E matching box. The sputter gun was a Kurt J. Lesker Torus 4 magnetron gun with
Figure 3.2 (a) Schematic illustration of the sputtering system and (b) nickel and copper samples on a quartz plate.
106 the flex mount capability. A one-hour deposition at 10 mTorr with an 8 cm target-substrate
distance resulted in a film thickness of 0.8 μm. The thicknesses were measured using a
Sloan-Dektak-2 profilometer. The films were deposited at manipulator temperatures ranging
from 100 to 500 °C.
Before cofiring the samples, to complete the metal-insulator-metal stack Pt top
electrodes were sputtered via dc sputtering using a 2" AJA ST-20 magnetron gun. The target
was a 2" Pt foil (99.9% Alfa Aesar). An Advanced Energy MDX 1.5K power supply was
used to obtain a power of 3.7 W/cm2. Circular electrodes with a 0.5 mm diameter were
defined sputtering through shadow masks. The depositions were performed at 30 mTorr
argon pressure for 3.5 min. which resulted in 0.25 μm thick electrodes. The top electrodes
had a relatively large thickness to minimize the de-wetting effects that result from firing at
elevated temperatures [1].
3.2 Chemical Solution Deposition of Barium Titanate
Chemical solutions were prepared using the methods of Ihlefled et al. developed at
North Carolina State University. The methods are based on the original works of Hoffmann
and Schwartz [2-4]. A glove box was used to provide a low humidity environment during
solution preparation. Before each preparation, the glove box was purged with desiccated
nitrogen to obtain relative humidity levels consistently less than 15%. This enabled handling
of the reactive titanium isopropoxide. To prepare the barium precursor, 6.000 grams of
barium acetate (99% Sigma-Aldrich) was put in a 50 mL screw top Erlenmeyer flask
107 (Kimble Kimax). Then, 51.000 grams of glacial acetic acid (99.99% Sigma-Aldrich) was
added to the powder using syringes and eyedroppers. The masses were measured using a
Mettler-Toledo AT201 5-decimal analytical balance. To prepare the titanium precursor, first,
4.048 grams (0.08 mol) of acetylacetone (99% Sigma-Aldrich) was put in an Erlenmeyer
flask and then 5.685 grams (0.02 mol) of titanium isopropoxide (99.999% Sigma-Aldrich)
was added. The masses of all the chemicals were carefully recorded for the precise
calculation of the barium precursor amount which would be added to the titanium precursor
to yield 1:1 stoichiometric ratio. Both solutions were stirred at room temperature for 2 hours
at 200 rpm using 0.625" Teflon coated magnetic stirring bars. Next, the calculated amount of
barium precursor was added to the titanium precursor, again using syringes and eyedroppers
for high precision. The mass measurements suggested a stoichiometric ratio accuracy within
100 ppm. Finally, 0.536 grams of diethanolamine (99% Sigma-Aldrich) was added to
increase the viscosity. The resulting solution was ca. 0.3 M. This solution was stirred for 12
hours to obtain the barium titanate precursor.
The following steps were applied for solution deposition and drying. The as-received
copper foils were cut into 2" 1" pieces. The copper foil was taped on two edges to a 3" quartz plate. Then, the quartz plate was placed on the vacuum spin chuck. A syringe with a
0.2 μm filter was used to flood the copper substrate with excess barium titanate solution until all the area was covered. The films were spun at 3000 rpm for 30 s. using a Cookson
Electronics P-6000 spin coater. After that, the films were dried on a hot plate at 250 °C for 5 min. This procedure was repeated until the desired film thickness was achieved. Each layer
108 had a thickness of ~0.1 μm. The films were then ready for high temperature firing. The process flow for the film preparation is shown in Figure 3.3.
Figure 3.3 Process flow for barium titanate chemical solution deposition.
3.3 Low pO2 Processing of Thin Films
3.3.1 Firing of Sputtered BST Thin Films
The films need to be fired at elevated temperatures for complete phase formation,
densification and crystallization. Firing barium titanate thin films on base metal substrates requires reducing atmospheres to avoid metal oxidation, as discussed in Section 2.6.3. Firing
-11 at temperatures in excess of 700 °C requires a pO2 less than 10 atm [5]. This cannot be
109 achieved by using for example UHP nitrogen gas which typically gives pO2 values on the
-6 order of 10 atm. To overcome this problem, generally, H2O-H2 gas mixtures are used when
the oxygen partial pressure is required to be fixed at a low value [6]. For example, from
-13 Figure 2.22 it can be seen that at 900 °C a pO2 of ~10 atm is required. It is possible to
obtain this value by establishing the equilibrium
1 H 2(g) + 2O2(g) = H 2O(g)
for which the free energy change of the reaction is given by,
o G = 247,500 + 55.85T Eq. (3.1)
Using Equation 2.37 and 3.1, the equilibrium constant K is calculated to be 1.27108 at 1173
K. The equilibrium constant for the reaction is given by the expression,
PH O K = 2 Eq. (3.2) P P1/2 H 2 O2
-13 so, for a pO2 of 10 atm, the ratio of water vapor pressure to hydrogen partial pressure is
about 40. If we flow forming gas (1% H2 balanced with nitrogen) at a flow rate of 20 sccm and flow UHP nitrogen at a flow rate of 400 sccm, by assuming the partial pressure of nitrogen to be 1 atm we get a hydrogen partial pressure of 0.0005 atm. This would require a
110 water vapor pressure of 0.02 atm. Using the equation for the saturated vapor pressure of
water as a function of temperature [6], viz.
2900 log P = 4.65 logT +19.732 Eq. (3.3) T
for a vapor pressure of 0.02 atm, the temperature is calculated to be 291 K, i.e. 18 °C.
-13 Therefore, a pO2 of 10 atm can be achieved by bubbling the above gas mixture through
liquid water at 18 °C.
A Lindberg-Blue M glowbar tube furnace was used for heat treatments. For
controlled atmosphere processing, a 2" diameter fused silica tube was used with CVD end
caps and Viton® o-ring seals. The furnace had an approximately 10 cm hot zone capable of
reaching 1400 °C. The samples were placed on a quartz plate and held on the plate using copper chunks cut from used copper conflat flange gaskets The above gas mixture, i.e. 400
sccm N2 and 20 sccm forming gas (1% H2 balanced with nitrogen), was passed through a
water bubbler using MKS mass flow controllers. The exhaust was connected to another
bubbler to avoid back streaming and to observe the gas flow. The pO2 was monitored in-situ
by a solid-state oxygen sensor (Australian Oxycontrol Systems DS-Series). The schematic of
the furnace is depicted in Figure 3.4. The sensor was located in the hot zone and also had a
thermocouple, thus the pO2 and the temperature near the sample was monitored with high
accuracy. The samples were fired at 900 °C for 30 min with a ramp rate of 30 °C/min. After
111 the anneals, the samples were furnace cooled to 150 °C, and then removed from the furnace
to avoid copper oxidation.
Figure 3.4 Illustration of the system used for low pO2 firing.
3.3.2 Firing and Probing the Phase Evolution of CSD Barium Titanate Thin Films
The phase formation steps of chemical solution deposited barium titanate thin films
involve decomposition reactions which result in carbon dioxide emission. During the organic
removal step, the gelated barium titanate precursor forms an intermediate oxycarbonate phase
and at elevated temperatures (>600 °C) this intermediate phase crystallizes into barium
titanate [7, 8]. These process steps as a function of time/temperature are summarized with the
pertinent chemical and physical processes in Figure 3.5. These processes are interdependent and participate in determining the phase evolution and the final microstructure. For instance, incomplete organic removal can slow down crystallization or a low crystallization
112 temperature can result in porous films as discussed in the previous sections. Therefore, being
able to monitor the changes during these process steps would be a valuable means to achieve
the optimum microstructure and dielectric properties.
Figure 3.5 Physical and chemical processes that occur during firing of a chemical solution deposited thin film.
A system was constructed for in-situ probing the effects of firing parameters such as pO2 and heat rate on the phase formation and microstructural development of chemical
solution deposited barium titanate thin films. The changes in the partial pressure of gases in
the firing atmosphere, especially carbon dioxide, were monitored using an SRS-200 residual
gas analyzer (RGA). A Thermco Mini-Brute (MB-71) 3-zone furnace with a 2" diameter
fused silica tube was used for firing the samples. The long hot zone (~80 cm) enabled firing
of many samples at a time to enhance the resolution of the RGA data. Similar to the system
used for sputtered films, nitrogen and forming gas were bubbled through liquid water using
113 mass flow controllers. The end of the furnace was connected to the RGA system to monitor the gases. The exhaust gases were leaked into the RGA using a leak valve. The illustration of the experimental system is shown in Figure 3.6.
Figure 3.6 Schematic illustration of the system used for in-situ experiments.
The end of the tube furnace was connected to the RGA via stainless steel tubing which was wrapped by heating tape kept at temperatures >120 °C to avoid condensation. A k-type thermocouple was passed through the end cap and placed in the furnace near the samples for accurate temperature monitoring. An Omega DPi32 temperature reader was connected to the thermocouple. A LabVIEW™ program was written to interface the RGA and the temperature reader with the computer and record the changes in the partial pressures of gases as a function of time and temperature.
A residual gas analyzer is a small size mass spectrometer in which the ionized gas molecules are detected and measured according to their mass-to-charge ratios. The RGA used in the experiments, i.e. SRS-200, consisted of an ionizer, a quadrupole mass filter, and
114 an ion detector. In the basic operation, positive ions are produced by bombarding the gas
molecules with electrons emitted from a heated filament. These ions are then driven to the
quadrupole mass filter which is formed of four cylindrical electrodes. A combination of rf
and dc voltages is used to separate the ions based on their mass-to-charge ratio. The ions are
then directed to the ion detector where the ion currents are measured. The operating pressure
of the SRS-200 was from UHV to 10-4 Torr. The minimum resolution was 510-11 Torr.
For each furnace run, 4 samples with dimensions of 2" 1" were used. For the pO2
-13 experiments, a pO2 of 10 atm was obtained by flowing a mixture of 400 sccm N2 and 20
-11 sccm forming gas (1% H2 balanced with nitrogen), a pO2 of 10 atm was obtained by
-15 flowing a mixture of 400 sccm N2 and 5 sccm forming gas, and a pO2 of 10 atm was
obtained by flowing 100 sccm forming gas through a water bubbler using MKS mass flow
controllers. For the heat rate experiments, the samples were heated up to 900 °C with 1
°C/min, 3°C/min, and 20°C/min. The rapid heat-up experiments were conducted by sliding
the samples into the hot zone at 900 °C via a transfer arm. The dwell times were 30 min. for
all the experiments. Furthermore, the effects of a two-step processing were also investigated.
-13 The samples were baked at 450 °C for 15 min. under a pO2 of 10 atm after each drying step and then fired at 900 °C. The total gas pressure in the RGA was set at 110-5 Torr via the leak valve. The changes in the water, nitrogen, carbondioxide, oxygen, and hydrogen partial pressures were monitored as a function of time and temperature. Specifically, carbon dioxide was important since it is emitted during the decomposition reactions. A rough calculation shows that it is possible to detect the carbon dioxide given off during firing of the thin film samples using the residual gas analyzer. The partial pressure of carbon dioxide in
115 the mixture can be very roughly calculated as follows. Four 2" 1" samples result in an area
of 50 cm2. If we assume a shrinkage of 40% [9], we can calculate the decrease in thickness as
~0.4 μm since we know the final thickness is 0.6 μm. This corresponds to a 210-3 cm3 loss in the solid volume. Assuming a gel density of 2 g/cm3 and assuming most of the emitted gas will be carbondioxide with a density of 210-3 g/cm3, the samples will give off ~2 cm3 of
gas. The volume of the furnace tube is ~2400 cm3. When the total pressure in the RGA
system is 110-5 Torr, carbon dioxide will have a pressure on the order of 10-8 Torr which is
within the sensitivity range of the RGA.
When preparing the samples for dielectric measurements, each sample set for the
ramp rate and pO2 experiments were cut from the same 2" 1" sample to be able to make
sensible comparisons. These were then fired at varying ramp rates or oxygen partial
pressures. Finally, Pt top electrodes were sputtered on the films following the same
procedure explained in Section 3.1.
3.3.3 Reoxidation Anneals
There are several possible mechanisms that control the oxygen vacancy concentration
in barium titanate. The most important ones are the pO2 dependence, presence of acceptor impurities, and the Ba:Ti ratio in the material.
As discussed in Section 2.6.3, the firing under reducing conditions result in the formation of oxygen vacancies in the material via the reaction,
O 1 O V•• 2e o 2 2 + o +
116 for which the mass action expression is given by,
1 H 1 V •• n2 = K pO 2 = K exp n pO 2 Eq. (3.4) []o n 2 n RT 2
where K n is a constant which accounts for the change in the number of occupied sites and
H n ~568 kJ/mol is the enthalpy of reduction [10, 11]. The approximate electroneutrality condition for the reaction is given by,
•• 2[]Vo n + []A Eq. (3.5)
where []A is the concentration of acceptor impurities. Acceptor impurities such as Fe, Mg,
Al are unavoidably present in all barium titanate samples due to their natural abundance compared to the donor impurities as La, Nb, Ta, etc [10]. Depending on the relative concentrations of electrons “n” (introduced by reduction) and the acceptor impurities []A , the oxygen vacancy concentration is controlled by intrinsically or extrinsically. Smyth plotted the defect concentrations as a function of oxygen partial pressure for barium titanate using Equation 3.4 and assuming an acceptor concentration on the order of 100 ppm as shown in Figure 3.7. As seen from the figure, for the firing conditions used in this thesis, 900
-13 -14 °C and pO2 of 10 atm~10 MPa, and assuming similar amounts of acceptor impurities, the pO2 has a comparable effect to the acceptor impurities. Therefore, the low pO2 can result in
117 the decrease of the insulation resistance. This was observed in the dielectric loss measurements with high loss tangents.
Figure 3.7 Defect concentrations in undoped-BaTiO3 as a function of pO2 (taken from Chan et al. [10]).
The insulation resistance of the samples were improved by a low temperature higher pO2 anneal. The aim here was to decrease the number of oxygen vacancies in the barium titanate while kinetically limiting the substrate oxidation. A vacuum furnace was used for this purpose. The furnace was pumped down do a base pressure of ~7.510-7 Torr. Then, it was ramped up to 500 °C and the sample was slid in the furnace via a transfer arm passed through an Ultra-Torr® fitting while maintaining the vacuum. The pressure was increased to
510-5 Torr by leaking UHP oxygen (99.999%) to the chamber using a leak valve. The samples were annealed for 30 min., then moved away from hot zone and cooled down to 150
118 °C without breaking the vacuum. This process is called reoxidation, since it oxidizes the
reduced film decreasing the number of oxygen vacancies created by firing in reduced
atmospheres.
3.3.4 Physical Characterization of the Thin Films
X-Ray diffraction (XRD) was used to confirm phase formation and crystallinity. The measurements were made by a Bruker AXS D-5000 diffractometer equipped with a HighStar area detector. A 0.8 mm collimated Cu-K (=1.54 Å) X-Ray beam was used for measurements. The foils were attached to a glass slide using double sided tape and then mounted on the aluminum stage. An area map of diffraction intensity was collected in which the horizontal axis was the 2 and the vertical axis was the tilt in the sample plane . Then,
the intensity versus 2 plots were obtained by integrating counts over the -circle.
The planar and cross-sectional microstructure characterizations were performed using
scanning electron microscopy (SEM). The electron de-wetting in co-fired BST thin films was
characterized using the backscattered mode of a Hitachi S3200 electron microscope equipped
with a Robinson BSE detector. The electrode area mapping was conducted using the ImageJ
software. The surface characterization of the chemical solution deposited barium titanate
films were made by an Ultra-High Resolution Hitachi S-5500 SEM using the secondary
electron mode. The grain sizes of the samples were calculated from the secondary electron
images using the linear intercept method. The cross-sections were analyzed by a JEOL 6400F
Field emission SEM using the secondary electron mode. The cross-section images were used
119 to identify the grain morphology and to calculate the film thickness. For accurate thickness
measurements and avoiding the curling of the copper foils, the samples were prepared by
sandwiching the foil samples between silicon pieces. Each sample was adhered in between
two silicon pieces using Vishay 600 M-bond. Then, the stack was placed in a small vice and
cured on a hot plate at 200 °C for 45 min. After that, the cross-section was ground using 600-
grit SiC paper and then fine polished via 1 μm and 0.05 μm alumina slurries.
Microstructural characterization of the sputtered films, which had smaller grain size compared to the solution deposited films, was performed using a Nanosurf Easyscan 2 atomic force microscope (AFM) in the contact mode. The root mean square roughness values of the foils and the films were calculated using the AFM software. Again, the grain sizes were calculated using the linear intercept method.
3.3.5 Electrical Characterization of The Thin Films
The thin film dielectric properties, i.e. capacitance and loss tangent as functions of
voltage, frequency, and temperature, were measured using an HP 4192A (Agilent
Technologies, CA) impedance analyzer. The electrical connection between the impedance
analyzer and the thin film capacitors were made using HP 16048A test leads and Signatone
micromanipulators with tungsten probes. One of the probes was pierced through one of the
capacitors to make contact with the bottom Cu electrode and the other one was contacted to the top electrode of each capacitor. Through-the-thickness capacitance measurements such as in a parallel plate capacitor were performed this way. The data were recorded using a
120 LabVIEW™ program. Room temperature capacitance-voltage measurements were made
using an oscillating voltage of 0.05 V at 10 kHz with a superimposed dc bias sweep from –35
to 35 V (in 1 V steps) for the sputtered films and –10 to 10 V (in 0.5 V steps) for the solution
deposited films.
The temperature dependence of capacitance and loss tangent was measured via an
MMR Technologies cryogenic temperature stage. The working principle of the stage relies
on the Joule-Thomson effect, in which the adiabatic expansion of gas results in cooling. The
cooling stage consists of a quartz arm with capillary channels and a resistively heated stage
on the tip. High pressure gas (>1800 psi) is passed through these microchannels and then
allowed to expand in the tip (10 psi) decreasing the temperature. Capacitance and loss
tangents were measured with an oscillating voltage of 0.05 V at 10 kHz using this stage while cooling from 500 to 100 K. The contact to the samples was made using micromanipulators which were connected to the impedance analyzer. Temperature was controlled using a K-20 programmable temperature controller (MMR Technologies, Inc, CA) and the data were recorded using a LabVIEW™ program.
Room temperature leakage current measurements of the sputtered films were performed by using a Keithley 617 programmable electrometer with a sweep from –25 to 25
V with 1 V steps. A prerelaxation and a delay time of 3 s each were used.
121 References
1. Daniels, P., et al., Smart electrodes for ultralarge-area thin film capacitors. Journal
of Materials Research, 2007. 22(7): p. 1763-1766.
2. Schwartz, R.W., et al., Control of thin film processing behavior through precursor
structural modifications. Ceramic Engineering Science Proceedings, 1995. 16: p.
1045.
3. Hoffmann, S. and R. Waser, Control of the morphology of CSD-prepared
(Ba,Sr)TiO3 thin films. Journal of the European Ceramic Society, 1999. 19(6-7): p.
1339-1343.
4. Schwartz, R.W., Chemical solution deposition of perovskite thin films. Chemistry of
Materials, 1997. 9(11): p. 2325-2340.
5. Barin, I., Thermochemical data of pure substances. 1989, Weinheim, Federal
Republic of Germany; New York, NY, USA: VCH. v.
6. Gaskell, D.R. and D.R. Gaskell, Introduction to the thermodynamics of materials. 3rd
ed. 1995, Washington, D.C.: Taylor & Francis. xxi, 568 p.
7. Gopalakrishnamurthy, H.S., M.S. Rao, and T.R.N. Kutty, Thermal-Decomposition of
Titanyl Oxalates.1. Barium Titanyl Oxalate. Journal of Inorganic & Nuclear
Chemistry, 1975. 37(4): p. 891-898.
8. Frey, M.H. and D.a. Payne, Synthesis and Processing of Barium-Titanate Ceramics
from Alkoxide Solutions and Monolithic Gels. Chemistry of Materials, 1995. 7(1): p.
123-129.
122 9. Keddie, J.L. and E.P. Giannelis, Effect of Heating Rate on the Sintering of Titanium-
Dioxide Thin-Films - Competition between Densification and Crystallization. Journal
of the American Ceramic Society, 1991. 74(10): p. 2669-2671.
10. Chan, N.H., R.K. Sharma, and D.M. Smyth, Non-Stoichiometry in Undoped Batio3.
Journal of the American Ceramic Society, 1981. 64(9): p. 556-562.
11. Smyth, D.M., The defect chemistry of metal oxides. 2000, New York: Oxford
University Press. x, 294 p.
123 CHAPTER 4. HOT SPUTTERING OF BARIUM STRONTIUM
TITANATE ON BASE METAL FOILS
4.1 Hot Sputtering of Barium Strontium Titanate on Nickel Foils
Section 4.1 corresponds to a manuscript published in Journal of Applied Physics: Volume
103, 084123, April 2008
Seymen M. Aygün, Patrick Daniels, and Jon-Paul Maria
North Carolina State University, Department of Materials Science and Engineering, Raleigh,
NC 27695
William Borland
DuPont Electronic Technologies, Research Triangle Park, NC 27709
Abstract
The relationships linking temperature and voltage-dependent dielectric response,
grain size, and thermal budget during synthesis are illustrated. In so doing, it was found that
maximizing thermal budgets within experimental bounds leads to electrical properties comparable to the best literature reports irrespective of processing technique or
microstructure. Optimal film properties include a bulk transition temperature, a room
temperature permittivity of 1800, a voltage tuning ratio of 10:1 at 450 kV/cm, and loss
tangent less than 1.5% at 450 kV/cm. The sample set illustrates the well-known relationship
between permittivity and crystal dimension, and the onset of a transition temperature shift at
124 very fine grain sizes. A brick wall model incorporating a high permittivity grain and a low permittivity grain boundary is used to interpret the dielectric data. The data show, however, that high permittivity and tunability values can be achieved at grain sizes or film thicknesses that many reports associate with dramatic reductions in the dielectric response. These differences are discussed in terms of crystal quality and maximum processing temperature.
The results collectively suggest that scaling effects in ferroelectric thin films are in many cases the result of low thermal budgets and the consequently high degree of structural imperfection and are not from the existence of low permittivity phases at the dielectric- electrode interface.
Keywords: ferroelectric thin films, barium strontium titanate, nickel
4.1.1 Introduction
Compositions of the BaTiO3-SrTiO3 binary solid solution system allow a wide range of application possibilities with systematically variable dielectric constants and Curie points.
Through modification of the composition, the Curie temperature can be tuned for the required application temperature and optimal values of permittivity can be obtained [1]. Thin films of the paraelectric phase (Ba,Sr)TiO3 (BST) are particularly attractive for applications in embedded memories, frequency-agile devices, IR detection, and embedded capacitance layers [2, 3]. High quality BST thin films have been deposited via various techniques including chemical vapor deposition, chemical solution deposition and radio frequency (RF) magnetron sputtering [2, 4-6]. Most of the work on BST has employed single crystalline
125 semiconductor or oxide substrates for making BST decoupling capacitors, microwave filters,
and phase shifters.
The use of base metal foils as substrates for ferroelectric thin films provides a viable
solution for integrating embedded passive components in a printed wiring board (PWB).
Base metal foils have several advantages including flexibility, low cost and compatibility
with processing temperatures in excess of 700 oC [7-9]. In addition, the flexible nature of film-on-foil capacitors holds interest for applications where non-planar geometries hold advantage like conformable antennae, electronic textiles, and energy storage. Ni foils are of
interest for these applications, but in addition, Ni foils enable BST synthesis over a wide
firing window under reducing atmospheres which encompasses temperatures in excess of
1300 °C. These temperatures approach the sintering temperatures of bulk BST ceramics thus
provide the means to study the impact of thermal budget on the dielectric response.
As has been shown for the case of Cu and Ni, there is an inconspicuous advantage to
foil substrates - the small thickness and highly compliant mechanical properties (as compared
to Si, SrTiO3, or sapphire crystals) make possible film annealing to temperatures in excess of
1000 °C without the thermomechanical instabilities routinely encountered by thermal
expansion mismatch in rigid substrate-film systems. Consequently, a range of temperatures
that promote film densification, grain growth, and structural refinement are experimentally
viable: this presents the possibility for better exploring the crystal dimension - crystal quality
- electrical property relations that regulate ferroelectricity. The authors utilize this expanded
processing window to study sputtered barium strontium titanate thin films, to better
understand scaling effects, and to improve the ability to engineer the dielectric response.
126 In this work, (Ba,Sr)TiO3 was RF magnetron sputtered directly on Ni foils. The
effects of sputtering temperature on the final film structure and electrical properties were
investigated. We demonstrate that deposition temperature influences grain size, crystal
quality, and extrinsic permittivity. Ultimately through comparisons of literature reports, we
show that dielectric properties are best optimized through high thermal budgets while grain
size (the 10s of nm range) is of secondary importance. This finding ultimately impacts the
manner in which scaling effects are viewed in thin ferroelectric layers.
4.1.2 Experimental Procedure
(Ba0.6Sr0.4)TiO3 thin films were RF magnetron sputtered on 10 m thick nickel foils
(Alfa Aesar, 99.95%) from a 10.16 cm diameter stoichiometric (Ba0.6Sr0.4)TiO3 target (Super
Conductor Materials Inc., NY). The magnetron gun was oriented at 30o off-axis to reduce the
plasma damage caused by the bombardment of oxygen anions. The substrates were mounted
on a heated and rotating manipulator for optimum stoichiometry and uniform thickness. X-
ray fluorescence measurements revealed an A:B ratio of 1 with a ±3% uncertainty.
Depositions were made at 3.7 W/cm2 target power density for 1 h with a target to substrate
separation distance of 8 cm, which resulted in 0.8 μm thick films. Pure argon was used as the sputtering gas with a deposition pressure of 10 mTorr. The films were sputtered at sample manipulator temperatures between 100-450 oC. After BST deposition, 0.25 μm thick Pt top electrodes were DC magnetron sputtered to complete the metal-insulator-metal stack.
Depositions were performed at 3.7 W/cm2 in Ar pressure of 30 mTorr, through a shadow-
127 mask to define 0.5 mm diameter capacitors, which were ready for high temperature
annealing.
The high temperature processing of Ni should be carried out under reducing
atmospheres to avoid oxidation. The required partial pressure of oxygen at an equilibrium temperature can be calculated by plotting pO2 vs. T diagram using reference thermochemical
data [10, 11]. Figure 4.1 shows the equilibrium oxygen partial pressure curves for Ba, Sr, Ti,
Ni and their respective oxides as a function of temperature. These curves clearly identify the
equilibrium conditions for stability between metallic Ni, (Ba,Sr)TiO3, and O2 (g). From the
-12 o figure, pO2 ~10 at 900 C are within this range of stability. The required oxygen partial
pressure was obtained by flowing a mixture of 400 sccm N2 and 20 sccm forming gas (1% H2
o balanced with N2) through a water bubbler at 25 C. The pO2 was monitored in-situ using a
Figure 4.1 pO2 vs. temperature diagram showing the processing window in which the oxides of Ba, Sr, and Ti are stable with metallic Ni.
128 zirconia electrolyte oxygen sensor. The samples were co-fired at 900 oC for 30 min. under atmospheric pressure. To compensate for the oxygen non-stoichiometry established by equilibration with the low pO2 annealing atmosphere, a reoxidation anneal was performed at
500 oC in a high vacuum tube furnace for 30 min. under a background oxygen pressure of 10-
8 atm.
X-Ray diffraction was used to confirm phase formation and crystallinity with a
Bruker AXS D-5000 Diffractometer equipped with a GADDS area detector. The surface and the microstructural characterizations were performed with a Hitachi S3200 scanning electron microscope (SEM) and a Nanosurf easyScan 2 atomic force microscope (AFM) using contact mode. The dielectric measurements were made using a Hewlett-Packard 4192A Impedance
Analyzer and an MMR Technologies Inc. Joule-Thomson cooler. Capacitance-voltage measurements were made under a DC bias sweep (-35 to 35 V) with steps of 1 V and an oscillation voltage of 0.05 V at 10 kHz. Temperature dependence was measured while cooling from 450 to 100 K at zero bias with the same ac signal. Room temperature leakage current measurements were conducted using a Keithley 617 programmable electrometer with a sweep from –25 to 25 V and 1 V steps. A pre-relaxation and a delay time of 3 s each were used.
129 4.1.3 Results and Discussion
The X-Ray diffraction patterns of the as-deposited and fired BST deposition
temperature series are shown in Figures 4.2a and 4.2b respectively. Diffraction patterns show
Figure 4.2 X-Ray diffraction patterns of the samples for (a) as-deposited and (b) fired at 900 oC.
130 the increasing crystallinity with increasing sputtering temperature as evidenced by narrower peaks with higher relative intensities. It is important to note that NiO formation was not observed by XRD in the deposition temperature range between 100 and 400 oC. At 450 oC, the high relative intensity peaks of NiO, (111) and (200), appeared. These peaks were no longer discernable after high temperature annealing indicating that NiO was either reduced back to metallic Ni or dissolved into the BST, or a combination thereof. Analysis of the X-
Ray patterns show that the as-deposited samples are incompletely crystallized thus unable to develop the nonlinear dielectric response and high permittivity associated with ferroelectric oxides. For example, though some peaks attributed to BST are present in the as-deposited case, the {200} reflections can only be seen after the 900 °C anneal. Figure 4.3 shows the capacitance vs. field curves for the as-deposited films, which were sputtered at 100 oC and
Figure 4.3 Capacitance and loss tangent vs. field curves for the as-deposited samples sputtered at 100 oC and 400 oC.
131 400 oC. The capacitance values were very low and the films showed no tunability. Similar dielectric responses for low thermal budget BST films was reported by Baniecki et al [12].
For that reason, the films were fired at 900 oC to increase the crystal quality and to develop
the desired dielectric properties.
Figure 4.4a shows the room temperature capacitance vs. field curves for the entire
sample set measured at 10 kHz. The curves exhibit typical paraelectric C-V behavior with
maxima at zero bias and saturation to a minimum high-field value. The zero bias capacitance
increases with increasing sputtering temperature, while the saturation values remain
relatively constant. This is similar to the trends observed in several literature reports of BST
prepared on platinized silicon [12, 13]. The asymmetry in the curves may be attributed to the
different top and bottom electrode materials. The sputtering temperature dependence of
tunability is illustrated in Figure 4.4b. The tunability is given as the ratio of Cmax (capacitance
at 0 V) to Cmin (capacitance at 35 V). The tunability showed a roughly parabolic increase with
increasing deposition temperature and a tunability of 10:1 was obtained from the sample
sputtered at 400 oC. The fugitive nature of the as-deposited NiO interface layer causes microstructural instability and local delamination of the BST. Consequently, the capacitors
processed at 450 oC showed very high dielectric losses and could withstand very little electric
field.
132 Figure 4.4 (a) Capacitance and loss tangent vs. field curves for the samples sputtered in the range 100-400 oC (b) Tunability vs. sputtering temperature plot.
133 Due to the high surface roughness of Ni foils (30 nm rms on a 1 μm 1 μm area), the
BST layer was co-fired with the top Pt electrode to increase capacitor yield. As reported previously, this co-firing approach persuades Pt top metallization to retreat from regions of high curvature (like crack edges or sharp asperities on the Ni surface) to minimize its interfacial energy, and hence decreasing the possibility of through-the-thickness short circuit pathways [14]. However, a consequence of co-firing is partial local de-wetting of the Pt film, which precludes the use of simple capacitor area calculations using the measured electrode diameter. To calculate the accurate area, fraction mapping of the Pt was conducted using the
SEM images taken at various magnifications. In this manner, the actual contact area, hence capacitor dimensions could be computed with high confidence. The area ratio of Pt to the
BST film was calculated using the secondary electron contrast between the Pt electrode and
BST. Figure 4.5 shows an SEM image of one capacitor used for this study (sputtered at 400
Figure 4.5 SEM surface image of the sample, which was sputtered at 400 oC (de- wetted light colored areas are Pt).
134 oC). The de-wetting of Pt can be easily seen from the image. The Pt area was calculated by
averaging the values from the images taken at multiple magnifications and it was consistently
found to be ~70% of the nominal electrode area. Field dependence of permittivity and
leakage current density was plotted using this value.
Figure 4.6 presents the dielectric properties of this sample, with a maximum permittivity of 1800 and a loss tangent of 0.012 at 10 kHz. This permittivity value with a
10:1 tunability is remarkably high for a sputtered BST thin film [2, 15-17]. The permittivity saturates at a value of ~180 which is typical for Ba-based ferroelectric materials at fields approaching 0.5 MV/cm. The leakage current density was measured and is also shown in
Figure 4.6. The permittivities of all other samples were estimated using this calculation. SEM analysis and constant platinum thickness confirmed that the area fraction was similar in all cases.
Figure 4.6 Field dependency of (a) Dielectric constant and (b) Leakage current density of the sample sputtered at 400 oC.
135 Figure 4.7 shows the AFM images taken using the contact mode of the samples sputtered at temperatures between 100 °C and 400 oC and subsequently fired at 900 °C. The images were taken on 1 μm 1 μm areas. Using linear stereology, the average grain size was
Figure 4.7 Atomic force microscopy images of the samples sputtered at (a) 100 oC, (b) 200 oC, (c) 300 oC, and (d) 400 oC.
136 calculated to be 50 nm for the sample sputtered at 100 oC and it increased to 81 nm when sputtering temperature was elevated to 400 oC. The grain size values and the rms roughnesses are summarized in Table 4.1.
TABLE 4.1 Summary of the atomic force microscopy results.
rms T Grain Size sputtering roughness (oC) (nm) (nm) 100 50 20.8 200 54 9.7 300 62 9.4 400 81 10.1
The dielectric properties of BST thin films strongly depend on microstructure and grain size. There have been numerous investigations of grain size effects on BaTiO3 and a combination of these reports for bulk ceramic and thin film embodiments can be used to interpret the present data and to evaluate existing models for size-induced property dependencies. Frey et al. explained the change in permittivity with grain size in bulk ceramics with a mixing model where grains (with high permittivity) and grain boundaries
(with low permittivity) are connected in series [18]. Therefore, with decreasing grain size, the contribution of the low permittivity grain boundaries increases and the composite permittivity falls. The Frey model is of particular interest as it does not require an intrinsic size effect, but an extrinsic dependency imparted by the existence of grain boundaries and their finite thickness, at least for grain sizes down to 70 nm. The Frey data is an important
137 benchmark as it exhibits the highest permittivities for nano-grained ceramic BaTiO3, and bulk transition temperatures (i.e., TC ~ 130 °C) down to the smallest grain sizes.
The AFM images in Figure 4.7 and the temperature dependent permittivity data in
Figure 4.8 illustrate a similar trend. With higher final processing temperature, the BST grain
size increases with a concomitant increase in permittivity. The dielectric maxima at the phase
transition temperature also become substantially sharper. We note that when comparing
Frey's 40 nm and 70 nm data points the permittivities agree favorably, though the phase
transition in Frey's work are substantially sharper [19]. Note that this comparison uses Frey's
permittivity values at 35 °C above TC. This provides a sensible comparison since the room
temperature values of permittivity for the current BST sample set are approximately 35 °C
above their Tmax value.
Figure 4.8 Temperature dependency of dielectric constant and loss tangent for the samples sputtered at 100-400 oC.
138 There is one exception to the data set, the 400 °C sputtered sample shows the sharpest
phase transition, but the Curie temperature is substantially suppressed. Recall from Figure 2a
however, that the deposition at 450 oC resulted in formation of NiO. Therefore, even though it was not detected by X-Ray diffraction, a small amount of NiO is likely to be present in the sample sputtered at 400 oC. This NiO layer will react and dissolve into BST during
annealing, and the compositional modification would influence the temperature dependent
dielectric properties. Hafid et al. have studied the effects of Ni doping on the electrical
properties of (Ba0.6Sr0.4)TiO3 ceramics [20]. They reported that doping BST with 1.5% Ni
o results in a 25 C decrease in Tmax. The temperature shift that was observed in our sample is likely due to the same effect. The X-Ray area detector used for characterization is sensitive to layers between 5 nm and 10 nm. Thus, a 5 nm NiO interface layer would be invisible to diffraction, but when dissolved into an 800 nm BST film would produce ~1% Ni doping and a temperature depression consistent with experimental observations.
This data set shares a similarity with numerous other papers on size effects: the magnitude of the permittivity scales with crystalline dimension, and that at very low dimensions, in the present case ~ 50 nm, the ferroelectric transition temperature shifts to lower values. The size onset of a TC shift is comparable to the reports of Ihlefeld, Frey, and
McCauley, and the permittivity magnitudes are comparable when grain sizes are similar [18,
21, 22]. The data set, however, is distinctly different from many thin film studies, especially
those produced by PVD. For instance, Parker et al. studied crystal dimension dependency of
permittivity and transition temperature for BST 70/30 thin films prepared by MOCVD [5].
Bulk values of transition temperature were achieved in films with 600 nm columnar grains,
139 and at this thickness, permittivity saturated at about 700. Similarly, Sinnamon et al. reported size dependent dielectric properties for BST 50/50 thin films [23]. In their work, permittivity values saturated at about 500 for films with columnar grains 1500 nm tall and greater than
100 nm in average diameter. Shaw et al. reviewed the size-dependent properties of ferroelectric crystals which included the efforts of IBM to prepare thin film BST in the late
1990s [24]. Again, permittivity values for BST 70/30 films saturated as a function of thickness at around 600 for films 150 nm thick with columnar grains. Finally, Hwang et al, and Chen et al., reported nearly identical findings, permittivities saturating near 600, for sputtered BST 60/40 films [25, 26].
Though the rate of permittivity decrease with thickness, and the value of film thickness or grain diameter may change between these authors, one commonality links all reports: regardless of deposition method or electrode composition, permittivity saturates at values near 600. In the present case, films with comparatively small grain sizes, ~ 80 nm, show room temperature permittivities of 1800. In Sinnamon's and Parker's work, a comparable sample exhibited permittivities of ~ 150 and 200 respectively [5, 23]. There is an additional commonality between these reports, in all cases, the maximum processing temperature lies between 600 °C and 700 °C.
In this work, films are prepared at sputtering temperatures that are low compared to traditional oxide film processing. The ~ 400 °C limit stems from the need to avoid metal foil oxidation. As such, the grain size is largely fixed at the time of deposition. The high nucleation rate for low temperature sputtering of polycrystalline films results in the fine nodular microstructure, and since the BST system is highly refractory with scant solubility,
140 extensive grain growth beyond the as-deposited microstructure does not occur unless temperatures above 1200 °C are used. However, after deposition, all films are exposed to a
900 °C anneal. The aforementioned references and a collection of additional reports of BST thin film processing are plotted in Fig. 4.9 [2, 4, 5, 21, 23, 25-35]. In this graph, permittivity is plotted against grain size for a number of BST films in the technologically interesting 50 nm to 200 nm thickness range. Two populations become evident: a population with permittivity values greater than 1000, and a population with permittivity values less than 700.
For both populations, grain sizes span the same range, the critical difference lies in the thermal budgets used during synthesis. Without exception, thermal budgets which incorporate temperatures in excess of 900 °C are associated with high permittivity.
Figure 4.9 Comparison of dielectric constant values as a function of crystal dimension taken from several reports (data points are numbered according to their reference numbers).
141 We hypothesize that this comparatively high temperature heat treatment produces large permittivity in grain sizes which are typically associated with strong suppression of the dielectric response. Though the reason for this increase is not perfectly understood, we propose that a 900 °C anneal improves the crystallinity within each grain, reducing structural defects and effectively thinning the grain boundaries. Ihlefeld et al. has demonstrated this effect using synchrotron x-ray scattering and we believe the same processes are occurring in these films [21].
As a consequence of this work, the ability to observe large permittivity in fine grain ceramic films brings into question the use of interfacial capacitance models to describe dimensionally dependent dielectric properties. Sinnamon et al. demonstrated that with equal effectiveness low permittivity layers perpendicular or parallel to the film thickness can be used to model experimental data sets showing a thickness dependent dielectric response [23].
The present data set brings further into question the interfacial dead layer model. This is not to say that low permittivity layers at the interface do not exist. Clearly electrostatic models prove that these effects are finite, however, the present results illustrate that microstructural aspects of ferroelectric crystals have a dramatic effect on the dielectric response, and for the purpose of reproducing bulk-like properties in thin films, efforts to optimize microstructure and crystal structure should receive maximum attention.
142 4.1.4 Summary
(Ba0.6Sr0.4)TiO3 thin films have been deposited on Ni foils. Metal-insulator-metal capacitors were fabricated by co-firing the BST thin films with Pt top electrodes. The dielectric properties were shown to improve substantially by increasing the sputtering temperature up to 400 oC. The increase in the permittivity and the tunability was attributed to the increase in grain size. The ferroelectric anomaly also became sharper with the increased grain size. The best sample of this work exhibited a room temperature permittivity of 1800, a tunability ratio of 10:1, and a loss tangent less than 1.5% at 10 kHz. This work shows that Ni can be a strong candidate as a flexible substrate for embedded capacitors in printed wiring boards. The permittivity of BST on Ni can likely be further improved by increasing the annealing temperature closer to bulk sintering temperatures of BaTiO3.
Acknowledgements
The authors would like to acknowledge the support of DuPont Electronic
Technologies, Research Triangle Park, North Carolina.
4.2 Hot Sputtering of Barium Strontium Titanate on Copper Foils
Even though the processing temperatures on copper are lower than that of nickel’s, copper still has a few advantages. It is inexpensive, widely available, easier to process due to its smooth surface, and has lower resistivity. Therefore, to compare with the nickel data
143 (Ba0.6Sr0.4)TiO3 films were also sputtered on bare copper foils at manipulator temperatures
ranging from 100 to 400 °C. The films were subsequently fired at 900 °C for 30 min. at a pO2
of 10-13 atm for densification and crystallization. XRD patterns of the as-deposited and fired
films are shown in Figure 4.10. The intensities were plotted using a logarithmic scale for
easy identification of any second phases. The as-deposited films are partially crystalline and
become completely crystallized after the firing.
Figure 4.10a shows that copper oxide-Cu2O forms above 300 °C. It is important to
note that the (111) Cu2O peak observed in the sample deposited at 350 °C disappears after the annealing at 900 °C under reducing atmosphere. This indicates that copper oxide reduces
back to copper and/or dissolves into the BST.
144 Figure 4.10 XRD patterns of the (a) as-deposited samples and (b) those fired at 900 °C.
After firing, Pt top electrodes were dc magnetron sputtered through shadow masks.
Figure 4.11 shows an optical microscope image of a 0.5 mm diameter Pt electrode on a BST film. All films were subsequently exposed to a reoxidation anneal at 500 °C for 30 min.
-8 under a pO2 of 10 atm.
145 Figure 4.11 Optical microscope image of a 0.5 mm diameter Pt electrode.
The room temperature permittivity-field curves for the films deposited at temperatures ranging from 100-400 °C are shown in Figure 4.12. The measurements were made at 10 kHz. Typical paraelectric field dependent permittivity curves were observed, with permittivity maxima at zero and falling to saturation at high fields.
146 Figure 4.12 Permittivity and loss tangent vs. field curves for the samples sputtered in the range of 100-300 °C.
The maximum permittivity values increased from 900 to 1050 with the increase in sputtering temperature from 100 to 300 °C. The highest tunability, which is given as the ratio of max (permittivity at zero bias) to min (permittivity at 35 V), was obtained from the sample sputtered at 300 °C with a value of 6:1. The samples sputtered at above 300 °C showed high dielectric loss values could not stand to applied dc bias. This was attributed to the presence of
147 the as-deposited Cu2O interface layer as observed by XRD and the microstructural
instabilities that are expected during its reduction to Cu metal.
Ultimately, the oxidation of copper limits the temperature at which BST can be
deposited which limits the ultimate crystal quality and microstructure of the final film after
post-annealing. Nickel, has much slower oxidation rate compared to copper in the processing
temperature range of BST thin films [36, 37]. Therefore, higher deposition temperatures can
be achieved by using nickel foils. Consequently, the benefits of hot sputtering observed in the
Ni system could not be appreciated with Cu.
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153 CHAPTER 5. PROCESS-PROPERTY RELATIONSHIPS IN
CHEMICAL SOLUTION DEPOSITED BARIUM TITANATE
THIN FILMS
Chapter 5 corresponds to a manuscript that was submitted to Acta Materialia
Seymen M. Aygün1, Patrick Daniels1, William Borland2 and Jon-Paul Maria1
1North Carolina State University, Department of Materials Science and Engineering, Raleigh,
NC 27695
2DuPont Electronic Technologies, Research Triangle Park, NC 27709
5.1 Abstract
Residual gas analyzer (RGA) techniques were used to analyze furnace gas atmospheres in real time during the thermal processing of chemically solution deposited
BaTiO3 films. This in situ probe enabled quantitative investigation of firing parameters including ramp rate, time, and oxygen partial pressure, and their relationship to crystal structure and microstructure development in complex oxides formed from metalorganic precursor solutions. The ability to monitor organic removal and barium titanate phase formation using an RGA was instrumental in identifying heat treatments that optimized structure and properties. Very slow ramp rates resulted in higher porosity, larger grain size, and a dramatic drop in the capacitor yield. Very fast ramp rates produced similar trends, however, the mechanisms were distinct. These observations are understood by considering
154 the profiles of organic removal and perovskite nucleation as measured by residual gas
analysis. The effects of oxygen partial pressure on barium titanate formation and
microstructure development were also explored. Grain size increased with increasing pO2
while there was no appreciable influence on density and capacitor yield. Optimal firing
-13 parameters, i.e., 20 °C/min ramp rate at a pO2 of 10 atm maximized permittivity,
minimized loss tangents, and produced dramatic improvements in microstructure uniformity
and density. Downstream analysis of furnace gas is a generically applicable means to better
understand synthesis methods that are complicated by simultaneous mechanisms of precursor
decomposition, extraction of volatile components, and crystallization.
5.2 Introduction
Chemical solution deposition (CSD) of barium titanate is an attractive low cost
synthesis method suitable for large-scale production. CSD has many advantages including
high purity, compositional homogeneity, straight-forward variation of stoichiometry, and
control over phase formation and microstructure development. Initial investigations of
solution based barium titanate processing were intended to decrease the processing temperatures and obtain fine sized high purity powders [1-4]. Analogous methods were first applied to synthesize barium titanate thin films by Yanovskaya et al. [5]. Since these
pioneering reports, solution based barium titanate powders and thin films have been prepared
using multiple precursor chemistries. The most popular ones include sol-gel approaches with
alkoxide solutions [6-9], metalorganic and oxalate salt decomposition [10-13], and hybrid
routes utilizing carboxylates and alkoxides [14-17]. These studies revealed the importance of
155 solution chemistry and firing parameters on the phase evolution and the microstructural
development of barium titanate.
In conventional bulk synthesis, the transformation pathway of barium titanate
involves diffusion and reactions between micron-sized BaCO3 and TiO2 powders. These
processes require temperatures in excess of 1100 °C, whereas in thin films, the temperatures
are lowered due to the mixing on the nanometer scale [4]. Additionally, there are other
transformation pathways for barium titanate formation depending on the solution chemistry, which also affect the crystallization temperature. Gopalakrishnamurthy et al. were the first to report the crystallization of barium titanate through an intermediate oxycarbonate phase with the chemical formula Ba2Ti2O5CO3 [10]. The authors identified this phase using TGA/DTA
and chemical analysis for the decomposition of barium titanyl oxalate tetrahydrate. Kumar et
al. also observed the presence of a weakly crystalline phase for the decomposition of their
citrate based organic precursors [11]. Based on the TGA, XRD, and Raman data it was
concluded that the compound had again a stoichiometry close to Ba2Ti2O5CO3. In addition to
the metalorganic and oxalate routes, this oxycarbonate phase was also formed during the
processing of both sol-gel and hybrid chemistries [6, 14, 15]. Hasenkox et al. studied the role
of precursor chemistry in the transformation pathway for barium titanate formation. Utilizing
various chain length Ba-carboxylates and Ti-alkoxide precursors it was demonstrated that the
formation of the intermediate oxycarbonate depends on the barium precursor, and this phase
shifts the crystallization to higher temperatures. The higher density and permittivity obtained
in these films were attributed to the elevated crystallization temperature.
156 The heat treatments applied to metalorganic layers are similarly important in determining structure since in the course of firing a number of physical and chemical processes are required to extract organics, crystallize, and densify. After the drying step, which in principle removes only residual solvent, a xerogel is formed. Subsequent heat treatments promote organic removal, which involves thermolysis, condensation reactions, and the formation of carbonate species. These reactions and structural relaxation consolidate the xerogel [18, 19]. With increasing temperatures, densification occurs by viscous sintering until crystallization. After crystallization solid-state sintering becomes the predominant densification mechanism. The final microstructure and the dielectric properties are influenced by each of these processes which are interdependent. For instance, incomplete organic removal prior to crystallization can interfere with nucleation, while over aggressive drying can produce brittle xerogels which crack upon organic removal and crystallization. As such, these processes must be fundamentally understood and purposefully engineered in order to optimize physical and electrical properties.
Recently, the film-on-foil approach, which started with platinum substrates [20], was applied to base metal foils by firing the films in reducing atmospheres to avoid substrate oxidation [21-23]. The higher thermal budget allowed by the thin and compliant foils compared to rigid substrates were shown to enhance the crystal quality and the dielectric properties of barium titanate thin films [24, 25]. The present work investigates the effects of firing parameters on the dielectric properties of these solution deposited barium titanate films on copper foils. The larger processing temperature window afforded by these substrates is ideally suited to in situ monitoring of furnace gases by mass spectroscopy, which can be used
157 to quantitatively study the organic extraction and barium titanate formation reactions as a
function of temperature and time. It is the hypothesis of this investigation that in situ analysis
of furnace gasses can be used to monitor the processes of organic removal and BaTiO3
formation as a function of time, temperature, and heating rate, and that this information will
provide a better understanding of the mechanisms that regulate structure evolution. This
information will in turn improve our ability to optimize materials properties and
performance, and the approach is generically applicable to many materials systems. The
authors note that other researchers have used mass spectrometry and thermal gravimetric
analysis to monitor phase formation in metalorganic precursors, however, the current study
offers a unique improvement. The present results analyze the heat treatment process in the
exact samples used for electrical and structural analysis. Most importantly, the high surface- to-volume ratio of the thin film embodiment is conserved. This is in contrast to conventional
studies where a crucible of precursor with much smaller surface area (thus access to the gas
phase) is subject to heat treatment. As such, a unique insight is available regarding the
relationships between organic extraction and property development.
5.3 Experimental Procedure
Barium titanate precursor solutions were prepared using a process developed by
Ihlefeld et al. which utilizes hybrid-chelate chemistries [22]. The barium precursor was
prepared by dissolving barium acetate (99% Sigma-Aldrich) in glacial acetic acid (99.99%
Sigma-Aldrich) and the titanium precursor was prepared by mixing titanium isopropoxide
158 (99.999% Sigma-Aldrich) with acetylacetone (99% Sigma-Aldrich). The precursors were
mixed in Ba:Ti ratio of 1:1 and diethanolamine was added to obtain a molarity of ~0.3 M.
The films were spin coated on 18 μm thick copper foils (Oak-Mitsui PLSP) at 3000 rpm for
30 s and then dried on a hotplate at 250 °C for 5 min. The process was repeated 6 times to get the desired final film thickness of ~0.6 μm. Then the films were fired in a 3-zone tube furnace for organic removal and crystallization under reducing atmospheres. The pO2 was adjusted by flowing nitrogen and forming gas (1% H2 balanced with nitrogen) and ranged
from 10-15 to 10-11 atm by varying the gas flow rates which were flown through a water
-11 bubbler at room temperature. A pO2 of 10 atm was obtained by flowing 400 sccm nitrogen
-13 and 5 sccm forming gas, a pO2 of 10 atm was obtained by flowing 400 sccm nitrogen and
-15 20 sccm forming gas, and a pO2 of 10 atm was obtained by flowing 100 sccm forming gas.
The pO2 was monitored using a solid-state oxygen sensor located in the hot zone. The films were heated to 900 °C with various ramp rates and held at that temperature for 30 min. The rapid heat-up experiments were performed by sliding the samples into the hot zone at 900 °C using an o-ring sealed transfer arm. The exhaust line of the furnace was connected to an
SRS-RGA200 residual gas analyzer (RGA) system using stainless steel tubing and a leak valve. The line was kept at >120 °C to minimize gas condensation. The total pressure in the
RGA was 110-5 Torr. The exhaust gas partial pressures of nitrogen, water, carbon dioxide,
oxygen, and hydrogen were monitored as a function of time and temperature. The large and
uniform hot zone of the 3-zone tube furnace enabled simultaneous firing of four 5 cm 2.5
cm thin film samples in order to achieve suitable signal-to-noise ratios from the RGA. The
159 RGA data were fit using the software IGOR Pro (WaveMetrics, Inc) such that peak areas
could be calculated and quantitatively compared.
X-Ray diffraction (XRD) was used to confirm phase formation using a Bruker AXS
D-5000 diffractometer equipped with a HighStar area detector. The local probing was
performed by Raman spectroscopy (Renishaw Ramascope) using an Ar laser with a 514 nm
wavelength. The planar and cross-sectional microstructural characterizations were performed with a Hitachi S-5500 scanning electron microscope (SEM) and a JEOL 6400F Field emission SEM, respectively. For accurate film thickness calculations, the samples for cross- sectional characterization were prepared by sandwiching the films in between silicon pieces and polishing down to 0.05 μm using alumina slurries. Grain sizes were calculated via the linear intercept method using the film surface images.
Dielectric measurements were used to evaluate electrical properties. To do so, test capacitors were made by depositing platinum top electrodes by dc magnetron sputtering through shadow masks to complete the metal-insulator-metal capacitor stack. Reoxidation anneals were conducted to reduce oxygen vacancy populations produced by the highly reducing crystallization anneals, as is customary for base metal electrode capacitor processing [26]. The anneals were performed in a controlled atmosphere furnace at 500 °C
-8 for 30 min. under a pO2 of 10 atm. Dielectric properties including capacitance and loss
tangent as a function of dc bias and temperature were measured using an HP 4192A
Impedance Analyzer and an MMR Technologies, Inc. Joule-Thomson thermal stage.
Capacitance-voltage measurements were made by doing forward and backward sweeps
between –10 and 10 V with 0.5 V steps using an oscillating voltage of 0.05 V at 10 kHz.
160 Temperature dependence measurements were made by cooling the sample from 500 K down
to 100 K with a 5 K/min rate using the same ac signal.
5.4 Results and Discussion
Our preliminary experiment was designed to assess feasibility and to ensure the
absence of artifacts with potential to obfuscate the measurements, to do so, three sets of hot
-13 plate dried barium titanate thin films were fired at 900 °C under a pO2 of 10 atm with a
ramp rate of 20 °C/min. Organic extraction and barium titanate phase formation was
monitored in situ by recording the changes in the partial pressures of the exhaust gases, specifically carbon dioxide, since it is emitted in substantial quantities during both processes
of interest. The total gas flow passed through the furnace was doubled and tripled with
respect to our standard flow of 400 sccm. The partial pressure profile of CO2 vs. time and
temperature for all three experiments is shown in Figure 5.1. The data show that the
temperatures at which pCO2 reach a maxima are the same, thus we can be confident that
issues associated with gas residence time in the furnace or condensation during the path
between sample and RGA do not interfere with our analysis. To further ensure that these
measurements are free from artifacts, the peaks were curve fit and the total areas under the
carbon dioxide curves were calculated, i.e. the total signals obtained during each heat
treatment. The calculated area for the doubled and tripled flow rate was 1/2 and 1/3 of that
calculated for the standard flow rate respectively. This is consistent with the expectation that
161 increasing the flow rate will reduce the partial pressure of CO2, which is determined by
sample volume thus fixed.
Figure 5.1 Changes in the partial pressure of carbon dioxide as a function of time and temperature for different flow rates.
Examining the general curve shapes reveals two features, pressure maxima at 510 °C
and 810 °C. The former is attributed to the organic removal process and the latter is
attributed to the barium titanate formation [6, 10, 11, 13]. Previous researchers have observed
similar temperatures for organic thermolysis and BaTiO3 formation reaction, however the
reported temperatures were lower. This observation can be understood by recognizing that in
these reducing atmospheres the absence of oxygen slows the volatilization of carbon containing species. The data are not shown, but reference measurements were made for
precursor gels fired in flowing air and pure forming gas, in the former, BaTiO3 formation
162 reactions occurred at lower temperatures while in the latter, reactions shifted to higher temperatures, These data alone are valuable as they enable us to identify the thermal budget needed to fully remove residual carbon and complete the BaTiO3 solid-state reaction. Fig. 5.1 clearly shows that at ramp rates of 20 °C/min temperatures > 800 °C need to be achieved before the BaTiO3 formation reactions are complete. This persistance of carbon was also observed in chemical solution deposited barium titanate films on nickel foils which were fired at temperatures as high as 1000 °C in reducing atmospheres [27].
Temperature-dependent phase formation and film crystallinity were analyzed by ex situ X-Ray and Raman analyses as shown in Figure 5.2. To make a meaningful comparison with the RGA data, samples were extracted directly from the hot zone (via transfer arm) of the furnace thus quenched from temperatures between 550-900 °C in 50 °C intervals. A different sample was used for each temperature. The X-ray data in Fig. 5.2 identifies the intermediate oxycarbonate phase (Ba2Ti2O5CO3) above 600 °C. This phase precedes the onset of barium titanate crystallization which initiates at temperatures above 750 °C. It can be seen from the narrowing of the diffraction lines in Fig. 5.2 with temperature that the crystallinity of barium titanate improves, which is consistent with the RGA data showing a steady decrease in carbon content. The temperature-dependent Raman analysis also supports these results. With increased annealing temperature, an increasing peak intensity and the appearance of the bands near 305 and 715 cm-1 indicate crystallographic refinement via the appearance of a tetragonally distorted structure [28]. This combination of RGA and structural characterization enables us to make an important observation - the property improvements seen in solution-deposited oxides with increasing annealing temperature result not only from
163 an increased thermal budget and it’s ability to reduce crystal mosaicity, the improvements are also associated with the removal of residual carbon which persist in measurable quantity to temperatures higher than often used in thin film processing.
164 Figure 5.2 (a) X-Ray diffraction patterns and (b) Raman spectra of the barium titanate thin films.
The effects of ramp rate on the phase formation, microstructure, and the dielectric
properties were similarly investigated by monitoring furnace gasses for 900 °C anneals using
1 °C, and 3°C/minute ramp rates. Figure 5.3 shows the plots as a function of time and
temperature. Decreasing the ramp rate decreased the temperatures at which the CO2 maxima were observed. This result is expected from a kinetic perspective since the reactions which produce CO2 require diffusion within the film. To quantitatively validate this interpretation,
the total area under the carbon dioxide curves, i.e. the signals obtained from each ramp rate
were calculated. The total area under the peaks for each firing condition remained constant
suggesting that the same final chemical assembly results despite the changes in furnace
ramping rate.
165 Figure 5.3 Changes in the carbon dioxide partial pressure as a function of time and temperature for the ramp rates of (a) 3 °C/min and (b) 1 °C/min.
166 The impact of ramp rate on film microstructures was studied using SEM. For this experiment, an additional sample was introduced, one in which the dried 6-layer precursor film was inserted directly into a hot furnace - for this sample we estimate the ramp rate to be
~ 100 °C/minute. The surface and the cross-sectional images of the films fired using 20
°C/min, 1 °C/min, and direct insertion are depicted in Figures 5.4 and 5.5. All films exhibited equiaxed grain morphology, which is typical for barium titanate [7, 15]. Reducing the ramp rate from 20 to 1 °C/min, increased the grain size from 85 nm to 105 nm, this increase in grain size however, was accompanied by a decrease in the density. Additional grain growth can be attributed to a larger thermal budget, while the density decrease can be understood by comparing the RGA plots shown in Fig. 5.3. There is substantially more time during which the organic components are exposed to elevated temperatures at low heating rates. This provides for more extensive condensation reactions within the precursor gel which stiffen the network [18]. Consequently, the stiff gel cannot consolidate uniformly as the organic is removed and a porous final microstructure results. Furthermore, the lower crystallization temperatures observed at low ramp rates present detrimental effects on density. Early crystallization leads to incomplete densification, since solid state sintering which relies on diffusion of crystallized BaTiO3 is much slower than viscous sintering which can occur in the xerogel prior to complete BaTiO3 formation [29, 30]. For these reasons, the shift of both
RGA CO2 peaks to lower temperatures contributed to a lower final density.
167 Figure 5.4 Plane view images of the samples fired with (a) 20 °C/min, (b) 1 °C/min, and (c) rapid ramp rates.
The sample which was fired using a rapid ramp, i.e. direct insertion into the hot zone at 900 °C, also had a lower density than the sample fired using a 20 °C/min ramp. This is contrary to both of the organic removal and crystallization arguments discussed above.
However, it is important to note that there are intrinsic limits to these synthesis trends. A large gas volume must be evolved during the thermal decomposition stages regardless of the ramp rate. When ramp rates are rapid, and the total film thickness is ~ 1 m, gasses become trapped internally within the films, which frustrates gel consolidation and creates porosity after firing. SEM analysis in Fig. 5.4 also reveals an increase in the grain size from 85 to 120
168 nm for samples prepared by direct insertion. We attribute this to the relative rates of nucleation and growth as a function of temperature. That is, larger grains can be obtained by quickly passing the lower temperature range where the nucleation rate is high, thus reaching the higher temperature range where growth processes dominate with a smaller number of crystal nuclei [31].
Figure 5.5 Cross-sectional images of the samples fired with (a) 20 °C/min, (b) 1 °C/min, and (c) rapid ramp rates.
169 The permittivity versus applied bias curves for the samples fired using this series of ramp rates are shown in Figure 5.6. The sample set was measured at room temperature and
10 kHz. Typical nonlinear curves were obtained with hysteretic behavior expected for ferroelectric barium titanate. Two general trends are observed from the data. First, the permittivity is lowest for samples fired at 1 °C/min and 3 °C/min, and second, the loss
Figure 5.6 Permittivity versus applied bias curves for the samples fired with a ramp rate of (a) rapid, (b) 20 °C/min, (c) 3 °C/min, and (d) 1 °C/min.
170 tangent is highest for the slowest ramp rates. Low field permittivity reduces from 1500 to less
than 1200 when the ramp rate is changed from rapid to 1 °C/min.
The importance of the ramp rate is further illustrated by capacitor yield analysis.
Large numbers of dot capacitors for statistical dielectric measurements were prepared as
follows. A 5 cm 2.5 cm foil was spin coated with 6 layers and dried. This sample was
subdivided into quarters, each fired at one of the previously discussed thermal profiles. 200
0.5 mm capacitor dots were prepared and measured for each firing schedule and the number
of working capacitors was determined. Functionality was defined as a capacitor loss tangent less than 0.1 at 2 V dc bias. Table 5.1 summarizes this yield data and the microstructural properties. It can be seen that the yield was reduced dramatically with decreasing ramp rate.
Whereas the higher ramp rates resulted in about 90 % yield, this was reduced to 70% and
27% when the ramp rate was reduced to 3 °C/min and 1 °C/min respectively. Additionally, it is important to note that while the direct insertion sample resulted in a similar yield as the 20
°C/min ramp rate, with many measurements it became apparent that the loss tangents were substantially higher for samples processed using the direct insertion method. Average loss tangents at 2V were 0.05 and 0.025 for samples processed by direct insertion and 20 °C/min ramping respectively. The trends linking yield, loss tangent, and temperature profiles are understood via a density argument. During slow ramp-up, extensive condensation reactions causes the gel to lose its viscoelastic nature, which promotes cracking during consolidation, and the yield decreases sharply. During direct insertion, the rapid process of thermolysis results in trapped gasses ultimately producing microstructural defects which promote
171 conductive pathways and elevate loss tangent values.
Table 5.1. Summary of the SEM and yield studies.
Firing Condition Grain Size (nm) Thickness (nm) Yield (%) rapid 115 620 90 20 °C/min 85 570 88
3 °C/min 100 600 70
1 °C/min 105 650 27
-11 pO2~10 120 550 88
-15 pO2~10 75 580 87
An additional parameter of importance during heat treatment of BaTiO3 on base metal
foils is the firing atmosphere, especially for nickel, which requires a much lower pO2 than
copper to avoid oxidation. For those reasons the effects of pO2 on the phase development were investigated. Changing firing atmosphere during the entire heat treatment is difficult to interpret since there will be consequence on organic removal as well as the BaTiO3 defect
equilibrium. To minimize this, firing atmosphere was varied for a set of samples after the
organic removal had been completed. For a 20 °C ramp rate, this condition occurs at ~700
°C, which was verified by RGA. To investigate the impact of atmosphere on crystallization
and microstructural development, a set of samples were fired (after identical organic
-11 -15 -13 removal) at a pO2 of 10 and 10 atm in addition to the 10 atm pO2, which was used in
the initial ramp rate experiments. The RGA data for the experiments are shown in Figure 5.7.
172 Figure 5.7 Changes in the carbon dioxide partial pressure as a function of time and temperature for the oxygen partial pressures of (a) 10-15 atm and (b) 10-11 atm above 700 °C.
173 The higher pO2 firing resulted in a similar carbon dioxide profile as the standard pO2
of 10-13 atm. The maximum for the barium titanate formation peak was observed at 810 °C.
Alternatively, for the low pO2 experiment, the peak maximum shifted to 910 °C. For the
-15 BaTiO3 crystallized at 10 atm pO2, there is a substantial (~ 4X) increase in the total carbon
dioxide partial pressure reported in Fig. 5.7. This is only an apparent increase attributed to
-15 the relative gas flow rates. A pO2 of 10 atm is obtained using 100 sccm forming gas, while
-13 10 pO2 is obtained with 400 sccm of N2 and 20 sccm of forming gas. As such, the CO2
produced is measured in the context of total gas flow. At this point, we cannot explain the
shift of barium titanate formation to higher temperatures, however, the shift is consistent with
literature observations when BaTiO3 is processed in atmospheres with low oxygen partial
pressures.
The plane view and cross sectional images of the pO2-variable sample set are shown in Figures 5.8 and 5.9. While the grain size and the thickness values were similar for the pO2
-13 -15 of 10 atm and pO2 of 10 atm, the high pO2 sample exhibited a larger average grain
-15 diameter. The grain size increased from 75 to 120 nm, when the pO2 was increased from 10
to 10-11 atm above 700 °C. However, it is important to note that the X-Ray analysis for this
sample revealed trace quantities of Cu2O. Therefore, the change in grain size cannot be
attributed solely to oxygen partial pressure at this point.
174 -15 Figure 5.8 Plane view images of the samples fired at a pO2 of (a) 10 atm and (b) 10-11 atm above 700 °C.
-15 Figure 5.9 Cross-sectional images of the samples fired at a pO2 of (a) 10 atm and (b) 10-11 atm above 700 °C.
175 Voltage dependent permittivity data for the pO2 series are shown in Figure 5.10. It is seen from Figure 5.10a that the high pO2 resulted in a low permittivity and a high loss tangent rapidly increasing at high fields. This was attributed to the presence of Cu2O as a second phase which degrades the dielectric properties. The sample, which was fired at 10-15
-13 atm pO2 resulted in similar permittivity and loss tangent values to the sample fired at 10 atm pO2. As it can be seen in Table 5.1, changing the pO2 did not have a noticeable effect on the capacitor yield. In all cases a yield of ~90 % was achieved.
-15 Figure 5.10 Permittivity versus applied bias of the samples fired at a pO2 of (a) 10 atm and (b) 10-11 atm above 700 °C.
5.5 Summary
Barium titanate thin films have been chemical solution deposited on copper foils utilizing hybrid-chelate precursors. It was shown that a combination of in situ analysis of furnace gasses and ex situ structural and electrical characterization can be used to monitor the
176 processes of organic removal and BaTiO3 formation as a function of time, temperature, and heating rate. This combination leads to better understanding of the mechanisms that regulate structure evolution and improves our ability to optimize materials properties and performance. The capacitor yield was improved from 27 % to 88 % with increasing the ramp rate from 1 °C to 20 °C/min. This also increased the permittivity and decreased loss tangents.
A permittivity of 1450 and a loss tangent of 0.035 was obtained with a 20 °C/min ramp rate
-13 and a pO2 of 10 atm. There was appreciable change in the dielectric properties with the variation of pO2 provided that the copper substrate was not oxidized.
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181 CHAPTER 6. HIGH DENSITY CHEMICAL SOLUTION
DEPOSITED BARIUM TITANATE THIN FILMS
Chapter 6 corresponds to a manuscript that is going to be submitted to Advanced Materials
Seymen M. Aygün1, William Borland2 and Jon-Paul Maria1
1North Carolina State University, Department of Materials Science and Engineering, Raleigh,
NC 27695
2DuPont Electronic Technologies, Research Triangle Park, NC 27709
Materials scientists have struggled since the mid 1950s to achieve in a thin film
embodiment the electromechanical response typical of a ferroelectric single crystal or a well-
prepared ceramic. The deviations are observed in all thermodynamic properties, however, the
most notable and most often characterized, is the suppression of radio frequency dielectric
permittivity. Permittivity suppression is generally attributed to a set of phenomena termed
scaling effects. These may be divided into two categories; the first is an intrinsic size effect,
which describes the destabilization of ferroelectricity consequent only to reduced crystalline
dimension. Since ferroelectricity is a cooperative phenomenon that involves the alignment of
neighboring electrical dipoles, if the ensemble of dipoles is too small, the energy reduction for dipole-dipole coupling cannot stabilize the polar phase. The second category encompasses extrinsic size effects, which correspond to all practical deviations from the ideal crystalline state that occur due to the practical limits of material synthesis, and the physical
182 necessity of crystal interfaces and boundary conditions. The more important extrinsic effects
include grain boundary volume and area; residual stress due to substrates, electrodes, and the
spontaneous ferroelectric strain; point and line defects; density; stoichiometry control; and
crystalline mosaicity [1, 2]. Scaling effects are particularly difficult to study because
avoiding these extrinsic influences becomes more difficult as synthesis techniques are steered to produce increasingly small crystals in an embodiment that can be electrically and physically probed.
Substantial progress in understanding scaling effects has been made. In ceramic systems for instance, the grain size effect in BaTiO3 was explained by a brick-wall model, in
which, permittivity is reduced due to the dilution of high permittivity grain interiors by
structurally defective low permittivity grain boundaries [3]. In thin film systems, many
authors observed a decrease in permittivity with decreasing thickness. Very often, an
explanation involving low permittivity and potentially ferroelectrically inactive interfaces is
used to explain these trends, however, it must be noted that models proposing geometries
without parasitic interface layers can be used with equal success [4-9]. Furthermore, these
simple interface layer approaches cannot explain the origin of transition temperature shifts
and increased transition diffuseness that often accompany reduced film thickness [5]. With
limited exceptions, the focus on interface-related effects has eclipsed the importance of
rigorous physical characterization and optimization of microstructure and crystalline quality
as a function of crystal dimension. Recently, a body of literature has evolved that
demonstrates the importance of thin film crystalline quality and its role in extrinsic scaling
effects. In most cases, these observations were enabled through novel synthesis methods
183 affording high temperature processing while maintaining small crystal size [10-14]. In
summary, thin metal foil substrates enable crystallization anneals above 1200 °C, which is
approximately 2X higher than the processing temperature limits of BaxSr1-xTiO3 on silicon
(~700 °C). Permittivities larger than 1800 were obtained in both chemical solution deposited
and sputtered films at grain sizes that were previously associated with intrinsic permittivity
limitations. In this report we contribute to the scaling-effects knowledge base by
demonstrating that understanding scaling-effects begins with fundamentally understanding
oxide thin film processing science. Developing a sophisticated synthesis ability enables a self
consistent parameterization of grain size, crystal quality, and microstructure effects and the
observation of room temperature permittivity values above 3000 in chemical solution
deposited barium titanate thin films.
Barium titanate thin films were obtained by spin coating stoichiometric barium
titanate precursor solutions on bare copper foils and 250 °C hot plate drying after each layer.
Each sample was coated with six layers. Precursor crystallization was performed using three
different firing approaches. In the first approach, all six layers were fired at the same time at
-13 900 °C under a pO2 of 10 atm. In the second approach, a two-step firing process was used
which included a 450 °C bake-out step after each hot plate dry and one final 900 °C anneal.
The third approach used a 900 °C anneal after the deposition and hot plate drying of each layer. Figure 6.1 shows the plane view scanning electron microscope (SEM) images for
BaTiO3 film surfaces produced by the three different firing approaches. From these images
grain sizes are calculated to be 100 nm, 120 nm, and 185 nm. The increase in grain size can
be attributed to two factors: an overall increase in thermal budget with increased firing time
184 and/or a more effective removal of organic precursor components. To better understand the
origins of grain growth a fourth sample was prepared in which 6 layers were deposited and
hot plate dried, and fired. In this case, however, the standard firing schedule was repeated 6
times to replicate the thermal budget of the third approach. In this sample, an intermediate grain size of 140 was measured, which indicates that for the each-layer-fired sample, grain growth can be roughly equally attributed to an increased thermal budget and more effective organic removal. The SEM images in Fig. 6.1 also indicate a substantial narrowing of grain size distribution for the material produced with high temperature firing steps after each spin- on layer.
Figure 6.1 Plane view images of (a) one-step, (b) two-step, and (c) each-layer-fired samples.
185 Polished cross-sectional samples were used to examine the film density and to measure the film thickness. Since density measurement is difficult to assess from surface imaging alone, film thickness was used as a comparative measure of density: the identical amount of precursor was used in each sample and BaTiO3 is not volatile at the temperatures used, thus differences in film thickness can be solely attributed to porosity. Accurate thickness was evaluated by numerous SEM measurements and averaging for each sample.
The irregularity of copper foil substrates necessitates this approach. Figure 6.2 shows SEM
Figure 6.2 Cross-sectional images of (a) one-step, (b) two-step, and (c) each-layer-fired samples.
186 cross-sectional images that compare the three deposition and annealing approaches.
Incorporating the 450 °C annealing step reduced film thickness from 570 nm to 550 nm,
while firing each spun-on layer provided an additional reduction to 520 nm.
Fracture surface cross section images were also taken to examine the change in
density and microstructure, these data are shown in Fig. 6.3. Reduced porosity is apparent
from the images as is a fully dense film for the each-layer-fired approach. Though difficult to
quantify, a similar increase in grain size is reflected in the fracture cross sections. These images also reveal no evidence of columnar microstructure, in all cases, multiple grains can be identified through the thickness. A summary of the grain size and the thickness values for the films are given in Table 6.1.
TABLE 6.1 Summary of the scanning electron microscopy results.
Firing Grain Size Thickness Schedule (nm) (nm) One-step 100 570 Two-step 120 550 Each-layer-fired 185 520
187 Figure 6.3 Fracture images of (a) one-step, (b) two-step, and (c) each-layer-fired samples.
188 Permittivity and loss tangent versus applied bias curves for the three firing conditions
are given in Figure 6.4a. Strongly non-linear curves were obtained with maxima at zero bias
and saturation at high fields. Fired-each-layer sample exhibit a permittivity of 3000, a 5
μF/cm2 capacitance density, and a dielectric tunability of 15:1. Dielectric tunability is a direct
measure of the extrinsic ferroelectric contribution to permittivity and it is a relative value that
can be compared directly without capacitor thickness. The electrical data demonstrate a dramatic increase in tunability, thus extrinsic contribution to permittivity, for the samples with optimized microstructure, i.e., fully dense and larger average grain diameter.
189 Figure 6.4 (a) Permittvity vs. applied bias and (b) temperature dependent permittivity curves for the three firing conditions.
The temperature dependent permittivity and loss tangent data are shown in Figure 6.4b. In comparison to bulk materials, the transition is broad and is likely due to the shift of the tetragonal/orthorhombic phase transition to higher temperatures which has been previously seen in fine-grained barium titanate [15, 16]. The temperature dependent data follows the same trend seen in Figure 6.4a, the optimized microstructure resulted in a room temperature permittivity value in excess of 3000. This permittivity value is much higher than the typical thin film values on platinized silicon (where maximum temperatures are limited to 600 °C to
700 °C), and higher than permittivity values for barium titanate films processed on foils where the maximum exposure temperature was also 900 °C. It is in fact on the order of the bulk values obtained by Frey et al. for ceramic samples with similar grain sizes [16]. As
190 mentioned previously, the each-layer-fired sample exhibits two primary differences from the
others: the grain size is larger and the density is higher. The exact quantity of permittivity
difference stemming from each factor cannot be accurately known, however, we can
speculate the following: From the dense film we calculate a permittivity of 3500 at room
temperature, if we dilute that material with 10 % porosity, assume a pore permittivity of 1,
and approximate with the dielectric mixing law for spheres in a matrix [17], we predict a
BaTiO3 permittivity of 2200. The measured effective permittivity for a 10 % porosity sample
is 1500, less than our prediction. Thus we may hypothesize that 10 % porosity reduced
permittivity by approximately 30 %, while the reduction in grain size that accompanies the
pores reduces the permittivity by an additional 30 %.
The importance of the structure-property relationships presently observed for density
and grain size become more apparent when compared with the previous work on barium
titanate and (Ba,Sr)TiO3 thin films. Figure 6.5 shows the grain size dependence of
permittivity data of the current work and data sets from the literature on both bulk and thin
film studies. The data sets include the thin film studies of Aygun et al., Ihlefeld et al.,
Laughlin et al., Nagata et al., and Daniels et al. on base metal foils, and bulk studies of Arlt et al. and Frey et al. [3, 10, 11, 15, 18-20] (We note that when BST data are included, permittivity values ~ 100 °C below the measured dielectric maxima are used as to maximize consistency of comparison to pure BaTiO3). These data are chosen for comparison because
they are similar in substrate, and/or prepared from very similar chemical solution or physical
vapor deposition systems. Perhaps most importantly, in all of these examples firing
temperatures in excess of 900 °C were used, thus crystal quality/mosaicity is appropriate for
191 comparison. Generally speaking, the entire data set reveals a logarithmic dependence
between permittivity and grain size. The bottom dashed line connects the data points of
Ihlefeld et al. and Daniels et al. In both studies, six layers of chemical solution deposited
barium titanate were fired using the one-step firing process thus similar density values are expected. The very large grain size of Daniels et al. was achieved via metastable dissolution of excess BaO in BaTiO3 and an associated mechanism of rapid solid-state transport.
Grouping these data is rationalized by their similar (and non-ideal) density values.
Figure 6.5 Grain size dependence of permittivity comparison for pertinent data sets in the literature.
192 The top dashed line connects the data points from Aygun et al., Nagata et al., and
Laughlin et al. These data represent thin films of BaTiO3 and (Ba,Sr)TiO3 prepared by a
combination of chemical solution and physical vapor deposition techniques on metal foils, however, in these cases the final microstructures approached full density.
The similar slopes of the two lines reveal the importance of grain size in ferroelectric
thin films, and the general agreement with the trend for polycrystalline materials seen by
Frey and Payne [3]. This suggests that the same brick wall model can be used to interpret all
data and that the presence of parasitic electrode interface layers are not needed to reproduce
these trends. We hypothesize that the vertical separation of the two data sets can be
interpreted by a straight-forward density argument. Physical vapor deposition approaches can easily produce fully dense layers, while achieving the same from a CSD approach requires a more challenging optimization. For instance, Nagata achieved very high density by incorporating a combination of rapid thermal anneals and high temperature crystallization anneals, which is an approach similar to that used in the present study [20].
Fig. 6.5 includes a third heavy dotted line that connects the permittivity data points for samples produced using the three firing schedules explored in this study. These samples differ in both grain size and density, but interestingly provide a connection between the two permittivity/grain-size trends. The logarithmic dependency is altered by the concomitant change in density.
This research demonstrates the dramatic enhancement in film density by understanding the processing science relationships that link organic removal, crystallization, and densification in chemical solution deposition. By applying an each-layer-fired approach,
193 effective extraction of organic components and the elimination of pores increase grain
boundary mobility and enhance grain growth kinetics. This method provided for superior
densification and the observation of thin film properties similar to those of well-prepared
ceramics. Fundamentally understanding these processing-sturcture relationships enabled a
unique experimental perspective on scaling effects in ferroelectric thin films: the ability to
manipulate microstructure via grain size and density with a degree of independence that
allows a number of pertinent data sets to be understood in a common context. Ultimately, we
demonstrate that for the size range investigated, scaling effects in ferroelectric thin films can
be explained by the same brick-wall model used for bulk ceramics, and that additional
interface-related phenomena are unnecessary. This understanding is solely enabled by
advancing processing science, and eliminating artifacts and extrinsic effects which obfuscate
interpretation.
6.1 Experimental
The precursor solutions were prepared by dissolving barium acetate in acetic acid and reacting titanium isopropoxide with acetylacetone. Then, the precursors were mixed in equimolar ratio to obtain stoichiometric barium titanate. Finally, diethanolamine was added to the precursor to obtain a molarity of ca. 0.3 M. The films were spin coated onto 18 μm copper foils (Oak-Mitsui PLSP) and then dried on a hotplate at 250 °C for 5 min. For the one-step firing, this process was repeated six times and the resulting films were fired at 900
-13 °C for 30 min under a pO2 of 10 atm. The low pO2 was achieved by flowing 400 sccm
194 nitrogen and 20 sccm forming gas (1 % H2 balanced with N2) through a water bubbler at
room temperature. For the two-step firing, the samples were baked at 450 °C under the same
reducing atmosphere for 15 min after each drying step. A final crystallization step was
performed at 900 °C for 30 min. For the each-layer-fired approach, the samples were fired at
-13 900 °C for 30 min under a pO2 of 10 atm after each drying step. Platinum top electrodes
were sputter deposited using shadow masks. After that, a reoxidation anneal was performed
-8 in a vacuum furnace at 500 °C for 30 min under a pO2 of 10 atm. Plane view images were
taken using a JEOL 6400F Field Emission SEM and cross-sectional characterization was
performed with a Hitachi SU-70 Field Emission SEM. Cross-sectional samples were
prepared by adhering the films in between silicon wafer using M-bond and then polishing
down to 0.05 μm using alumina slurries. Dielectric properties were measured using an HP
4192A Impedance Analyzer and an MMR Technologies, Inc. Joule-Thomson thermal stage.
Capacitance-voltage measurements were made by applying an ac signal of 0.05 V at 10 kHz
with a dc bias between –10 and 10 V. Temperature dependent measurements were conducted
with the same ac signal in the temperature range 100-500 K.
References
1. Newnham, R.E. and S. Trolier-McKinstry, Size effects in ferroics. Integrated
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2. Shaw, T.M., S. Trolier-McKinstry, and P.C. McIntyre, The properties of ferroelectric
films at small dimensions. Annual Review of Materials Science, 2000. 30: p. 263-298.
195 3. Frey, M.H., et al., The role of interfaces on an apparent grain size effect on the
dielectric properties for ferroelectric barium titanate ceramics. Ferroelectrics, 1998.
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4. Binder, K., Surface Effects on Phase-Transitions in Ferroelectrics and Anti-
Ferroelectrics. Ferroelectrics, 1981. 35(1-4): p. 99-104.
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7. Sinnamon, L.J., et al., Exploring grain size as a cause for "dead-layer" effects in thin
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8. Vendik, O.G., S.P. Zubko, and L.T. Ter-Martirosayn, Experimental evidence of the
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Control. J. Mater. Res., 2008. in press.
196 12. Dudkevich, V.P., et al., Internal Size Effect in Condensed Batio3 Ferroelectric-Films.
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16. Frey, M.H. and D.A. Payne, Grain-size effect on structure and phase transformations
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197 CHAPTER 7. CONCLUSIONS AND FUTURE WORK
7.1 Conclusions
This research demonstrates the dramatic enhancement in thin film dielectric properties by understanding the processing science relationships that link microstructure development, crystallization, and densification. Below is a summary of thesis outcomes:
• Permittivity values in excess of 2000 were achieved in sputtered Ba1-xSrxTiO3 films
through a combination of high thermal budget processing and co-firing with grain
sizes that are typically associated with strong suppression of the dielectric response.
• Achieving a large permittivity in a fine grain ceramic thin film revealed the
importance of microstructural aspects of ferroelectric thin films –specifically crystal
mosaicity - to reproduce bulk-like properties. These data indicate that the interfacial
capacitance models are not appropriate to describe scaling effects in ferroelectric thin
films.
• An in-situ gas analysis process was developed to monitor the effects of firing
parameters on phase formation of chemical solution deposited barium titanate thin
films. This new capability allows the processes of organic extraction and phase
formation to be quantitatively monitored in the technologically relevant form factor
of a thin film.
• The effects of firing parameters including ramp rate and oxygen partial pressure were
explored using the in-situ gas analysis process. The dielectric data and the
capacitance yield were correlated to the barium titanate phase formation and
198 microstructure development. A permittivity value of 1450 with a loss tangent of
-13 0.035, and a 90 % yield was obtained with a 20 °C/min ramp rate at a pO2 of 10
atm. Very fast and very slow ramp rates result in higher porosity, larger grain size,
and lower capacitor yield. There was no appreciable change in the dielectric
properties with the variation of pO2 provided that the copper substrate is not oxidized.
• Firing schedules for chemical solution deposited barium titanate were explored.
Using an each-layer-fired approach, dramatic densification and grain growth was
achieved through effective organic removal. A permittivity value of 3000, a 5 μF/cm2
capacitance density and a dielectric tunability of 15:1 were obtained.
• Understanding the processing-property relationships enabled a unique perspective on
scaling effects in ferroelectric thin films bridging grain size, crystal quality, and
density. This allowed a number of pertinent data sets to be compared and understood
in a common context to explain the scaling effects in ferroelectric thin films.
7.2 Future Work
The hot sputtering on nickel study investigated the effects of sputtering temperature on the final film structure and electrical properties. A firing temperature of 900 °C was used for crystallization. This temperature was chosen to be able to make a comparison with the films deposited on copper foils. However, films on nickel foils can be fired at temperatures in excess of 1300 °C (Tm of Ni is 1455 °C) which are close to the sintering temperatures of bulk barium titanate ceramics. These higher temperatures are likely to further improve the crystal
199 quality and the grain size. Possible challenges awaiting include the grain boundary grooving that can occur in nickel at those temperatures and the increased de-wetting of the co-fired electrode. Pre-annealing the nickel foils and optimizing the electrode thickness would be the first approaches to overcome these challenges.
Chemical solution deposition of barium titanate can also be performed on nickel foils to take advantage of the high processing temperatures. The each-layer-fired approach can be combined with high temperatures to the increase the grain size and crystal quality in addition to density. However, due to the higher surface roughness of nickel foils compared to that of copper, the process needs to be optimized. CSD experiments using pre-annealed and/or well- polished nickel foils should be performed. Again, a co-firing approach can be used to increase the capacitor yield.
Daniels et al. has demonstrated the possibility of achieving a grain size on the order of one micron by metastable dissolution of excess BaO in BaTiO3 and firing the samples at temperatures close to melting point of copper [1]. Combining this with the each-layer-fired approach, the ultimate grain size and density combination could be achieved for a barium titanate thin film and the exact properties of a bulk ceramic may be duplicated.
References
1. Daniels, P.R., et al., Property Engineering in BaTiO3 Thin Films by Stoichiometry
Control. J. Mater. Res., 2008. in press.
200