A Thin Film Piezoelectric Transformer for Silicon Integration by Timothy Russell Olding A thesis submitted to the Department of Physics in conformity with the requirements for the degree of Master of Science (Engineering) Queen's University Kingston, Ontario. Canada June, 1999 O Timothy Russell Olding
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A Thin Film Piezoelectric Transformer
for Silicon Integration
by
Timothy Russell Olding
A thesis submitted to the Department of Physics in conformity with the requirements for the degree of Master of Science (Engineering)
Queen's University
Kingston, Ontario. Canada
June, 1999
O Timothy Russell Olding
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Abstract
Many applications in the electronics industry now require small, low profile
components with a high efficiency of operation. Electromagnetic transformers,
which consist of wire turns around a magnetic core, are unsuitable for integration
as mid-scale microelectronic components. A thin film piezoelectric transformer has
promise as a possible alternative. Radial mode thin film piezoelectric transformers
with a diameter of 1-2 mm and piezoelectric layer thickness of 1-2 pm have a
predicted operating range of 0.5-1 -0 MHz with vo&age gains of 0.1 -7 0. depending
on the dimensions and quality of the film. The device has been modelled using
Mason's model for piezoelectric transformers. The piezoelectric layers of the
transformer have been produced using an acetic acid based lead zirconate titanate
(PZT) solgel process. A stable solution chemistry and consistent thermal
processing route have been developed for producing multi-layer fully crystallized
PZT coatings of high electrical quality and thicknesses up to 5 pm, which is suitable
for transformer production. The coatings are piezoelectrically active and have been
characterized. One and two layer thin film transformers have been produced using
a process suitable for the manufacturing environment which employs standard
photo-lithographic and wet chemical etching techniques. A one layer thin film
transformer with a PZT layer thickness of 2 pm and a diameter of 5.1 mm yields a
voltage gain of 2.25 at 400 kHz. the resonant frequency of the device. The voltage
gain can easily be altered by changing the dimensions of the device or the driving
and output electrode patterns of the transformer.
Acknowledgements
I would like to thank my supervisor Dr. Michael Sayer for giving both his
guidance and a great degree of freedom for exploring new ideas. His refreshing
optimism and excitement about the project helped me greatly.
I would also like to thank the people at the Materials & Metallurgical
Department at Queen's University. Gennum Corporation, Datec Corporation, Royal
Military College (RMC), Canadian Microelectronics Corporation (CMC) and
Photonics Research Ontario (PRO) for their technical expertise and use of
equipment: Joyce Cooley, Charlie Cooney, Michael Watt, David Barrow, Ted
Petroff, Stewart Sherrit, Yasser Jamanni and Jeff Kablfleisch. My work was made
significantly easier because of your contributions. I would particularly like to
acknowledge and thank Stewart Sherrit for his assistance in transformer modelling.
Wthout him, I would likely still be working on the model. I would also like to thank
Gennum Corporation and Materials and Manufacturing Ontario for their financial
assistance and BM HiTech for supplying me with PZT disks.
My gratitude goes to the members of the Applied Solid State group for their
friendship, help and being available to listen to my successes and frustrations: Katia
Dyrda, Sarah Langstaff, Brian Leclerc, Marc Lukacs, Guofeng Pang and Lichun
Zou. I would particularly like to thank Marc Lukacs, Brian Leclerc, and Lichun Zou
for the many times they have helped me in my work.
Last, but not least, I would like to thank my wife Joy for loving and
supporting me in all my "mixing, baking and cookie cuttingn, and for making me
leave my work at work. And most importantly, I thank God for giving me
perspective and purpose in my work. His promise is true: "But seek first His
kingdom and His righteousness, and all these things will be given to you as well-"
For "what good will it be for a man who gains the whole worid, yet forfeits his
FIGURE 4.5.2.1 : Effect of solvent on crystallization of a PZT film ........... 78 FIGURE 4.6.1 : (a) Zr propoxidell7 isopropoxide 2.8 pm thick film (b) Zr
FIGURE 4.7.1 : Frequency response of (a) Zr butoxidemi butoxide ....... based film(b) Zr butoxidemi isopropoxide-based film 82
FIGURE 4.8.1. Impedance response of a PZT film with Cr-Au electrodes .... 84 ....... FIGURE 4.8.2. Impedance response of a PZTfilm with Pt electrodes 85
........ FIGURE 5.1.2. Flip-chip technique for reducing substrate clamping 92 ..... FIGURE 5.1 -3: (a)-@) Two layer and (d) one layertransformer designs 93
....................... FIGURE 5.2.1 : Transformer production process 94 ......................... FIGURE 5 - 2 2 Modified transformer structure 96
....................... FIGURE 5.2.3. Masks for one layer transformer 97 ................. FIGURE 5.3.1 : Two layer thin film transformer response 98
............ FIGURE 5.3.2. Two layer bulk ceramic transformer response 100 ................ FIGURE 5.3.2. One layer thin film transformer response 101
FIGURE 5.4.1. Schematic of a thin film transformer voltage converter ..... 103
vii
List of Tables
TABLE 3.1 -1 : Deposition parameters .............................. 33 TABLE 3.6.1 : Sputtering conditions ............................... 41 TABLE 3.1 0 .I : HP41 94A specifications [9] .......................... 47 TABLE3.11.1. PZTetch ......................................... 50 TABLE 4.3.1 : Chemicals for acetic acid-based PZT sol-gel ............. 64 TABLE 4.3.1 -1 : Reaction between alkoxide precursors ................. 65 TABLE 4.3.3.1 : Effect of solvent on solution stability ................... 69 TABLE 4.4.3.1 : RTA processing schedule ........................... 75 TABLE 4.8.1 : Material parameters for a PZT film on a Si (I 1 1) substrate . . 87
List of Symbols and Abbreviations
a A B C CRT CSD CVD Cii d D d, DMM DRAM DTA DTG E EEPROM e i j E f FeRAM F r G GA-XRD IMO I kP 4 MOD n N NMR P PCT Qm r R RTA RTP Sij S
disk radius area susceptance capacitance, Curie constant cathode ray tube chemical solution deposition chemical vapour deposition elastic stiffness lattice spacing dielectric displacement piezoelectric charge coefficient digital multimeter dynamic random access memory differential thermal analysis derivative therrnog ravimetric analysis electric field electrically erasable programmable read-only memory piezoeiectric coefficient relative dielectric constant frequency ferroelectric random access memory radial force conductance glancing angle x-ray diffraction inverse mixing order current radial mode electromechanical coupling constant thickness mode electromechanical coupling constant metallorganic deposition diffraction order term transformer turns ratio nuclear magnetic resonance density piezoelectric ceramic transformer mechanical quality factor radius resistance rapid thermal annealer rapid thermal processing elastic compliance strain
s,, SEM
T C
TGA
complex scattering parameter scanning electron microscope thickness stress, temperature Curie temperature therrnog ravimetric analysis radial displacement speed of sound voltage radial velocity admittance impedance angular frequency wavelength AC conductivity Poisson's ratio diffraction angle
1. Introduction
Polycrystalline ceramics have long been recognized as having unique
structural and electronic properties that could be extended to a wide variety of
applications. Structural ceramics are finding use as mechanical components in
engines and other machinery. Electronic ceramics have a wide range of use, from
passive oxides such as silica (SiOJ and alumina (A1,03) which are used as
substrates and insulators in electronic circuits [I], to active oxides such as zirconia
(Zr0.J which is used to manufacture the high temperature oxygen sensors used in
automobile engines [2]. Some of the ceramics with a more complex crystal
structure, such as the perovskite barium titanate (BaTiO,) and lead zirconate
titanate PbZr03-PbTiO, (PZT) compounds which have useful ferroelectric andlor
piezoelectric properties are used in capacitors, mechanical resonators, ultrasonic
transducers, pressure sensors, optical switches and other devices 131.
The development of thin film technology has allowed for the integration of
electronic ceramics with semiconductor technology, raising the possibility of a new
range of electronic devices. There is currently a great deal of interest in employing
1
the ferroelectric properties of some of the electronic ceramics in high density
capacitors for dynamic random access memory (DRAM) [4] and nonvolatile
ferroelectric memory (FeRAM) (51. Integrated couplingldecoupling capacitors and
filter capacitors to replace off-chip ceramic capacitors are also being developed [6]-
The piezoelectric properties of thin film electronic ceramics such as PZT are also
being employed in a variety of applications, including ultrasonic sensors and
focussed high frequency ultrasound sources for medical applications, mechanical
strain and pressure sensors in a range of applications including automobile pre-
ignition and timing sensors and diaphragm actuators for fluid flow valves, and
positioning sensors and actuators m. The major difference in piezoelectric device
development as opposed to ferroelectric memory and integrated capacitor
development is the requirement for thicker films which leads to different deposition
techniques.
A wide variety of thin film deposition techniques exist that can be
summarized in two broad categories [8]. Physical techniques include thermal and
electron beam evaporation; dc, radio frequency, and ion beam sputtering; and laser
ablation. Chemical techniques include spray pyrolysis, chemical vapour deposition
(CVD), and chemical solution deposition (CSD) which includes metal organic
decomposition (MOD) and sol-gel processes. The sol-gel process is particularly
suitable for the production of thick (greater than 1 pm) piezoelectric films in terms
of ease, time of processing, and low capital cost. The sol-gel process is the thin film
deposition technique employed in this work.
I 1 Piezoelectricity and Ferroelectricity
Piezoelectrics and ferroelectrics are closely associated in that they both are
part of the class of polar dielectrics. A polar dielectric is characterized by having
internal dipoles that may be aligned under an applied electric field to produce a net
dipole moment or polarization. The polarization is enhanced beyond that occurring
in any dielectric because of the asymmetry in the crystallographic structure of the
unit cell. In general, the centre of charge of the unit cell does not coincide with its
centre of mass, leading to a localized electric dipole moment within the unit cell.
Polar dielectrics are found in thirty of the crystal classes and within twenty of these
classes is the sub-group of piezoelectrics [9]. Piezoelectrics are distinguished by
the phenomenon of producing a surface charge when subjected to an external force
(termed the piezoelectricdirect effect) and conversely, a mechanical distortion when
subjected to an external electric field (termed the piezoelectric converse effect). Of
the twenty classes in which piezoelectrics are found, ten contain pyroelectrics,
which are characterized as having a spontaneous polarization in the absence of an
external electric field or mechanical stress. Within the pyroelectric subgroup are the
ferroelectrics, in which the direction of spontaneous polarization may be changed
by changing the direction of an externally applied electric field [I 01.
One of the important features of a ferroelectric is its Curie temperature. This
is the temperature above which the spontaneous polarization in the material
disappears. In this state the material is termed to be paraelectric. Since the
permittivity (E) of the material is directly dependent on the polarization, it also varies
with temperature. The relationship between the permittivity and temperature is
described by the Curie-Weiss law [I I]:
where C is the Curie constant. T is the temperature, and T, is the Curie
temperature. At temperatures near to Tc the permittivity of the material will be very
large. depending on the crystallographic direction in which the measurement is
made-
An important material with superior properties for piezoelectric applications
is PZT, a solid solution of PbZr0,-PbTiO, which is both ferroelectric and
piezoelectric. P A , along with many ferroelectric materials, crystallizes in the ABO,
perovskite crystal structure shown in Fig 1 .I .l . The large (A) cations are similar in
size to the oxygen ions and occupy the comers of a cubic unit cell. The small cation
"A" site
"6" site
Owgen
FIGURE 1.1 .I : ABO, perovskite crystal structure
(B) sits in the body centre of the cube and the oxygen ions are situated on the cube
faces. For P A , the large cations are lead (Pb) and the small cations are either
zirconium (Zr) or titanium (Ti). Above its Curie temperature, PZT is in the cubic
perovskite structure and is paraelectric. Below its Curie temperature. PZT becomes
ferroelectric, and depending on its composition, is in either a tetragonal or
rhombohedra1 phase (shown in Figure 1.1 -2). In the tetragonal phase, the cell is
* 0 6 Pbsite
e----e Q
0 zrm site
a Oxygen
FIGURE 1 .I -2: P A (a) tetragonal and (b) rhombohedral crystal structures
stretched along one side and has its direction of polarization parallel to the longest
side. In the rhombohedral phase. the cell is stretched along the body diagonal with
its polarization along the diagonal.
The Ti/Zr ratio in PZT determines whether the material will be in the
tetragonal or rhombohedral phase. The phase diagram for PZT(Figure 1 .I .3) shows
the regions where the various phases exist, with an important feature being the
% PbrlO 3 PbZr0: P b E 0 3
FIGURE 1 -1 -3: PZT phase diagram [I 01
morphotropic phase boundary between the tetragonal and rhombohedra1 phases.
PZT with a composition near this boundary has been shown to have excellent
ferroelectric and piezoelectric properties [lo], suitable for the production of
piezoelectric devices.
'1.2 Piezoelectric Transformers
With the onset of miniaturization, many applications in the electronics
industry now require small, low profile components with a high efficiency of
operation. Electromagnetic transformers, which consist of wire turns around a
magnetic core, are among the most bulky devices on a circuit board and are not
compatible with the requirements for most mid-scale microelectronic applications.
A significant amount of effort has been spent on the difficult task of producing
electromagnetic micro-transformers using thin film technology, but with limited
success [I 2,131
Piezoelectric ceramic transformers (PCTs) made from PZT bulk ceramic
have recently received considerable attention, particularly as voltage sources in
inverters used to drive the backlights of liquid crystal displays [14). Other
applications currently being studied include the use of PCTs as voltage sources for
air cleaners using a light load and voltage sources for computers with a medium or
heavy load 1141. PCTs were originally developed as high voltage generating
transformers for a high impedance load, having the advantage of a high step-up
ratio, relatively small size and low cost PCTs have been reported to have
operational efficiencies in excess of 90% [I 51.
The basic construction of a piezoelectric transformer involves two
mechanically coupled electrically insulated resonators (Fig.1.3.1). When an AC
signal with a frequency near the frequency of mechanical resonance is applied to
the input resonator, strong mechanical vibrations occur due to the piezoelectric
converse effect. This vibration is transferred to the output resonator, inducing a
charge on its electrodes due to the piezoelectric direct effect. Either a step-up or
step-down in voltage can be observed, depending on the dimensions of the
resonators and the electrical and mechanical qualities of the material used. This
is due to the impedance transformation of the load by the mechanical impedance
of the transformer.
0
vo Output Resonator
- Input Resonator
FIGURE 1.3.1: Operating principle of a piezoelectric transformer
Until recently piezoelectric transformers could only produced with quality in
bulk ceramic form, limiting its potential for silicon integration. It is now possible to
manufacture piezoelectric films of sufficient thickness and quality to make thin fiim
piezoelectric transformers via a sol-gel process. Producing piezoelectric
transformers using thin films allows for the possibility of integration with
conventional silicon technology, simple manufacturability of devices and access to
frequency ranges which are inaccessible using bulk ceramic manufacturing
techniques.
To be viable, several features are desirable in a thin film piezoelectric
transformer. It should operate at an efficiency comparable to that of
electromagnetic transformers and have an operational frequency range compatible
with available signal sources. The frequency range of use will likely be greater than
100 kHz and less than 10 MHz. The useful voltage gain range would be from 0.1
to 10 for most applications. The device must be small and of low profile in order to
achieve silicon integration and should be easily manufacturable using thin film
techniques.
1.3 Sol-Gel Science
Sol-gel technology was first developed as a new approach to the preparation
of glasses and ceramics as coatings on different substrates. There are basically
two different kinds of sol-gel technology 1161. The first kind of sol-gel starts with a
colloidal suspension of particles in a liquid forming a sol which is then destabilized
to form a gel. The second kind involves the polymerization of organometallic
precursors such as metal alkoxides to produce a gel network. In this thesis, only
sol-gel processing based on organometallic precursors will be discussed.
The organometallic precursor-based sol-gel process is conceptually quite
simple. A solution is made with appropriate molecular precursors containing the
elements of the desired compound in an organic solvent. The solution is
polymerized to form a gel, then the gel is dried and fired to remove the organic
components and form an inorganic oxide.
The most common precursors for making sol-gel solutions are alkoxides of
composition M(0-R)n, where R is an alkyl radical (methyl, ethyl, etc.). Their
properties are key to the preparation process. Additional oxides can be introduced
to multi-component systems as inorganic or organic salts. For PZT, zirconium and
titanium are usually introduced in the form of alkoxide precursors, whereas lead is
introduced as a salt. One important feature of the zirconium and titanium alkoxides
is that they are highly reactive toward water. This presents a problem with
premature gelation of these components during solution preparation, but can be
overcome by adding a chelating organic ligand to the solution to control the
hydrolysis rates of the alkoxides.
The sol-gel process has several advantages compared to conventional glass
and ceramic processing routes- Homogeneous multi-component systems of correct
composition can easily be obtained by mixing the corresponding molecular
precursor. The temperatures required for materials processing can be significantly
lowered due to the fact that the materials are mixed at the molecular level in solution
and diffusion distances are small. A variety of techniques such as spray, dip, paint
and spin coating exist for film fabrication and the viscosity, surface tension, and
solution concentration can be easily adjusted to meet specific requirements.
1.4 Thesis Objective
The objective of this thesis was to design and produce a thin film PZT
piezoelectric transformer with suitable operating parameters for device applications.
The device was modelled using Mason's model for piezoelectric transformers [I 71-
Different thin film sol-gel processes were evaluated for producing piezoelectric
resonator layers of suitable thickness with appropriate electrical and piezoelectric
properties. A stable solution chemistry and consistent thermal processing route
were developed for a multi-layer process capable of producing greater than 5 pm
thick PZT films. The film properties were characterized using glancing angle x-ray
diffraction (GA-XRD), dielectric analysis and high frequency impedance analysis.
The transformer was produced via the sol-gel process using standard photo-
lithographic and wet chemical etching techniques.
The outline of this thesis is as follows: Chapter 2 contains the model for the
thin film piezoelectric transformer. In Chapter 3, the tools and methods used forthe
production and characterization of the PZT films are outlined. In Chapter 4, the sol-
gel process used for the fabrication of the thick PZT films is described, as well as
the results from the characterization of the PZT films. The subject of Chapter 5 is
the practical implementation of the thin film piezoelectric transformer and potential
applications, Chapter 6 contains a discussion of the results and conclusions from
this work.
References
R. R. Tummala, Ceramic Bulletin, 67, 752 (1988).
G. Fisher, Ceramic Bulletin, 65, 622 (1 986).
M. Sayer and K. Sreenivas, Science. 247, 1056, (1990).
L. ti. Parker and A. F. Tasch, IEEE Circuits and Devices. 17 Jan (1990).
J. F. Scott and C. A. Araujo, Science, 246. 1400 (1989).
V. Chivukula, J. Ilowski, I. Emesh, D. McDonald, P. Leung and M. Sayer,
Integrated Ferroelectrics, 10 (4), 247 (1 995).
M. Sayer. D. A. Barrow, R. Noteboom, E. Griswold and 2. Wu, Science and
Technology of Electroceramic Thin Films, Kluwer Academic Publisher,
Netherlands (1 995).
L. I. Maissel and R. Glang (eds.), Handbook of Thin Film Technology,
McGraw-Hill, New York (1 970)-
E. C. Henry, Electronic Ceramics, Doubleday & Company, Inc., New York
(1 969).
B. Jaffe. W. R. Cooke and H. JaRe, Piezoelectrics, Academic Press, New
York (1 991).
J. C. Burfoot and G. W. Taylor, Polar Dielectrics and fheir Applications,
University of California Press. Los Angeles (1 979).
T. Yachi et al., lEEE Power Electronics Specialists Conference, 20 (1 991).
C. R. Sullivan and S. R. Sanders, IEEE Power Electronics Specialists
Conference, 33 (1 993).
K. Nagata, J. Thongrueng, K. Kato, Japanese Journal of Applied Physics:
Part 1, 36 (9). 61 03 (1 997).
K. Sakurai eta/., Japanese Journal of Applied Physics, 37. Part 1,56,2896,
(1 998).
G. Yi and M. Sayer, Ceramic Bulletin, 70 (7). 1 173 (1 991)
W. P. Mason. Electromechanical Transducers and Wave Filters, D. Van
Nostrand Co., 205, (1948).
2. Transformer Desian
Many piezoelectric transformer designs have been introduced since C. A.
Rosen proposed a piezoelectric transformer operation in length extensional mode
[I-31. The basic principle of operation is to apply an AC voltage to one resonator
at the frequency of mechanical resonance causing it to strongly vibrate. This
resonator is bonded to another resonator, which also begins to vibrate and
produces an output voltage due to the piezoelectric effect. The voltage gain of the
transformer is a function of the input and output impedances of the device and is
limited by how well vibration transfer occurs between the two resonators. These
transformers have been manufactured using bulk piezoelectric ceramic and most
of them operate in the 200-300 kHz range. It has been difficult to achieve a
piezoelectric transformer with a power density as high as that found in conventional
electromagnetic transformers. One solution has been to use a new structure for a
piezoelectric transformer operating in the second thickness extensional vibration
mode [3], and this seen a considerable amount of success. Another way to
approach the design of a piezoelectric transformer is to transfer the device to the
realm of thin film technology. Moving to thin film technology drastically changes the
device dimensions and the consequent frequency range of operation, opening a
new range for the design and use of piezoelectric transformers. The structures that
can be produced using thin film technology are also significantly different. This
chapter focuses on the design of a piezoelectric transformer for production via thin
film technology.
2.1 Mode of Operation
Several vibration modes could be used for piezoelectric transformer
operation. The five most common modes used for piezoelectric ceramic materials
analysis [4] are shown in Figure 2.1.1 along with the recommended geometrical
aspect ratio and the direction of poling marked by an arrow. Some of these can be
dismissed immediately from consideration. Length extension mode transformers
have previously been investigated and found to be unsuitable for power conversion,
as they have a large internal impedance leading to undesirable power loss. The
resonator structure also cannot be produced easily using thin film technology. The
thickness extensional and thickness shear modes have fundamental mechanical
resonance frequencies f,, and f, respectively of:
where t is the resonator thickness, c, is the elastic stiffness of the material under
constant dielectric displacement D (in reduced form) and p is the density of the
piezoelectric material. For thin film thicknesses of 1-1 0 pm, the resonant frequency
of these modes is in the hundreds of megahertz to gigahertz range, which is
unsuitab!e for most applications. Finally, the length thickness mode has the
weakest coupling constant of all five modes for the conversion of mechanical to
electrical energy and vice versa. This leaves the radial mode structure as the most
promising candidate for use in a thin film piezoelectric transformer. Other modes
such as the bending mode of a bar and the torsional mode of a rod are too
complicated to produce using thin film technology.
(a) Radial &tension (D > 20t)
(c) Thickness Shear (w , w > 201)
(e) Length Extension (L > 5w . Sw,)
* )
FIGURE 2-1 .I : Transformer vibration modes
2.2 Radial Mode Resonator
The analysis of piezoelectric resonators can be approached on a continuum
basis for simple resonator structures using the wave equation and the linear
piezoelectric constitutive equations. However, it is often more convenient to use an
equivalent circuit approach where both the electrical and mechanical portions of the
resonator are represented by electrical equivalents. The equivalent circuit approach
has a distinct advantage overthe direct wave equation approach in that the versatile
methods of network theory can be employed. To the extent that the original
assumptions and boundary conditions used to obtain the equivalent circuit are valid.
the equivalent circuit can be considered an exact representation of the piezoelectric
resonator.
Much of the original work on equivalent circuits for piezoelectric resonators
was completed by Mason [5]. His work on equivalent electromechanical circuits for
piezoelectric resonators was then extended to piezoelectric transformers [I ,2.6] by
drawing an analogy between piezoelectric and conventional electromagnetic
transformers. A standard electromagnetic transformer is made of two coils coupled
by a magnetic field. An AC voltage applied to one coil generates a magnetic field
which passes to the other coil and induces a voltage. The coupling can be
increased by guiding the magnetic flux through a iron or ferrite core. The
transformer ratio is equal to the ratio of coil winding turns. In a piezoelectric
transformer, an inductor is analogous to a mass, a capacitor to a spring, and a coil
with distributed inductance and capacitance to a section of acoustic line (i-e. a
mechanical resonator). Thus, the two coils of an electromagnetic transformer are
analogous to two mechanically coupled, electrically insulated mechanical
resonators.
To obtain an equivalent electromechanical circuit for a radial resonator, one
may note that a derivation of the radial mode resonance impedance equation has
previously been developed for radial mode vibrations in a thin disc by Meitzler.
O'Bryan and Tiersten [7]. However, a review of the basic derivation with the
assumptions made and boundary conditions used is useful toward understanding
the limitations of the equivalent circuit model. The piezoelectric equations
governing the radial mode resonance are:
where T, S, E and D are the stress, strain, electric field and dielectric displacement,
and rand u, are the radius and radial displacement. These equations have been are
derived from the linear piezoelectric constitutive equations and are transformed to
a cylindrical coordinate system for convenience of calculation. The radial material
constants are defined in terms of standard cartesian constants as:
The radial material constants q3', c+', and e,: are the permittivity, elastic stiffness.
and piezoelectric constant respectively. The standard cartesian material constants
SF, and d,, are the free permittivity, elastic compliance under a constant
electric field. and the piezoelectric charge coefficient respectively. When a
sinusoidal voltage is applied to the piezoelectric resonator, the time dependence of
the fields TI S, E and D can be taken into account by an exponential eqwt term:
The wave equation for a thin disc is:
The general solution of the wave equation for a steady state vibration is of the form:
where A is a constant, J,(x) is a first order Bessel function and vP is the speed of
sound in the piezoelectric material, equal to:
The derivative of u, with respect to r can be evaluated using the relation
Then
This eqt ration (2.2.15) and equation 2-2-12 may then be s
(2.2-1 5)
)ubstituted into the first
piezoelectric equation (2.2.1) and this, combined with the boundary condition T, =
0 at r = a (the disk radius) gives:
With some rearranging,
A =
Then ur equals
Now, using the second piezoelectric equation (2.2.2), the current I in the
piezoelectric resonator is:
Substituting for the value of A, the current is then
The voltage is found by integrating E3 to get the voltage V = -E3 t, where t is the disk
thickness. The admittance is then
The admittance equation may be simplified using the following equations:
2 (~13')Z
(k') = ~ 3 3 ~ c11P
to obtain:
This equation may be written as:
where C, is the radially clamped capacitance, N is the turns ratio of the transformer,
and Z, is the specific acoustic impedance of the acoustic line, equal to:
*aZ cJJP Cp = (2.2.29)
t
These equations form the basis of an equivalent electromechanical circuit for a thin
disk radial mode resonator:
Electric Acoustic Port CP Port
FIGURE 2.2. I : Equivalent circuit for a radial resonator
where F, and v, are the radial force and velocity at the acoustic port of the resonator.
To confirm the validity of this equivalent circuit, the open and short circuit
impedances on the acoustic ports were checked, giving the right results. The
displacement and radial velocity were also checked and they are consistent with
each other.
For a free resonator, the acoustic port is shorted and the electrical
impedance is:
The effect of a substrate (Figure 2.2.1 -2) on which the piezoelectric layer is
deposited is to lower the voltage drop across the acoustic port of the resonator. It
is assumed that the radial strain is the same in both the piezoelectric layer and the
- . - Piezoelectric ,-- -
t s
v Substrate
FIGURE 2-2.2: Effect of the substrate on the radial resonator
substrate, which means that their acoustic elements have to be in series. The
specific acoustic impedance (ZJ of the substrate is:
and the equivalent circuit for the radial resonator modified by the substrate is:
Electric Port
Acoustic Port
FIGURE 2.2.3: Equivalent circuit for a radial resonator on a substrate
The electrical impedance of the resonator is then:
2.3 Radial Mode Transformer
In the radial mode transformer there are two piezoelectric disks of different
material properties and geometries (Figure 2-33). To understand the operational
dependence of the transformer on the material and dimensional parameters of the
device, the disks are assumed to be substrate-free. A voltage is applied to one
disk, and the voltage across the other disk is measured. An important quantity to
< 2 hours c 24 hours c 2 weeks c 3 months 5 months +
0.094 1 e 1 hour
4.3.4 Mixina Order
Precipitates and gels are difFicult to avoid in the modified acetate process,
where lead acetate trihydrate dissolved in acetic acid is added to the metal
alkoxides. This is particularly true for solutions employing zirconium propoxide (70
wt.% in I-propanol) andlor titanium isopropoxide precursors. This is probably due
to the fact that when acetic acid is added first to the metal alkoxides, as in the IMO
method, the alkoxides can be sufficiently chelated before trace amounts of water
associated with lead acetate trihydrate are introduced. The modified acetate
method introduces water and acetic acid simultaneously to the metal alkoxides, with
the potential of causing localized hydrolysis of the metal alkoxides before they are
69
chelated. It is possible with careful solution preparation to avoid hydrolysis in both
methods though. if the lead acetate trihydratelacetic acid solution is dehydrated
before mixing with the metal alkoxides by heating it at a temperature slightly above
100°C. An indepth analysis has been completed to investigate the difference
between the acetate and IMO methods of chemical addition using 'H and 13C
nuclear magnetic resonance (NMR) spectroscopy [S]. Overall, the IMO solution
displayed less ester formation and less water is formed in solution. One way to
explain this result would be to note that the solution with a greater degree of
chelation would have less free acetic acid to react and form esters. This is
consistent with the proposal that metal alkoxides in solutions prepared using the
acetate method are more susceptible to hydration and consequently, local
inhomogeneities, by the simultaneous addition of the acetic acid and lead acetate
trihydrate together in solution-
4.4 Thermal Processing
The method of processing sol-gel derived P A thin films depends largely on
the thickness of the individual film layers. If the film is thin (< 0.1 pm), it can be fired
directly on a surface heated to 350-400°C until the organics have been removed
from the film, then annealed at a higher temperature [I]. For thick films in the range
of 5-1 0 pm prepared by a multi-layering process, it is preferable to have a larger
individual layer thickness. When these film layers (> 0.2 pm thick) are fired directly
after deposition at 350-40O0C, the buildup of internal stress due to removal of
organic components and the corresponding volume shrinkage usually causes
cracking. In light of this behaviour, it is desirable to know the temperatures at which
the various organic components are released from the film and the percentage
weight loss at any given temperature. From this, a thermal processing schedule can
be established-
4-4.1 Simultaneous TGAfDTA Analvsis
The results from a TGCVDfA analysis of a zirconium butoxide (80 wt.% in 1-
butanol)/titanium butoxide-based sol-gel prepared by the modified I MO method are
shown in Figure 4.4.1 .I. The solution was heated at a rate of 1 O°C/min. The TGA
TGA
Temperature ("C)
FIGURE 4.4.1 -1 : TGNDTA analysis of a butoxidabased IMO PZT sot-gel [21]
results show weight loss versus temperature. Most of the weight loss occurs below
a temperature of approximately 180°C. The derivative therrnogravimetric results
(DTG) combine the results from the TGA and DTA analyses to show rate of weight
loss versus temperature. Important temperatures in these results are 100°C and
285OC, at which the rate of weight loss peaks and the potential for failure of the film
layer increases. The peak in weight loss at 1 OO°C is due to the removal of free
acetic acid, water and alcohol and peak at 285°C corresponds to the decomposition
temperature for lead acetate [I 71.
The TGNDTA results shown in Figure 4.4.1 -2 are for the same PZT solgel
solution dried at a temperature of 150°C prior to TGAlDTA analysis. This increases
d
f n - fn 0 -
-
FIGURE 4.4.1.2: TGAiDTA results for a PZT sol-gel dried at 150°C
I
- I 1 I
- I I t
U) - I
UI DTG 1 1
c. - r *
cn - ; : - - 0 - a . u (D -
c I I 4 c 6 I I I I I 1 I I I I I I I
z - 1
- I I
7 -- I-
- - - I I
I I
0 200 400 6d0 800 1000
Temperature ("C)
the sensitivity to changes occurring at higher temperatures. In the TGA results. it
is important to note that weight loss is still occurring up to a temperature of -600°C-
Thus, one might expect that PZT films prepared using this solution will not
crystallize well when annealed at temperatures below 600°C. In fact. since the
temperature ramp rate in a furnace or an RTA is much greater than the ramp rate
of 1O0C/min and the hold time is not especially long, a temperature greater than
600% will be needed to sufficiently crystallize the film layer. This has been
confirmed in other work completed at Queen's University [21]. The DTG results in
this second case show another broad relatively flat peak in rate of weight loss
centered at approximately 400°C which was not obvious in the previous analysis
(Figure 4.4.1.1). This peak is due to the pyrolysis of the remaining organic
components in the film. One further point of interest is that TGAIDTA analyses
completed on solutions with zirconium propoxide (70 wt% in 1-propanol)/titanium
butoxide and zirconium propoxide (70 wt.% in 1 -propanol)/titanium isopropoxide
precursor combinations yield similar results.
4.4.2 Furnace Processing
Based on the above TGNDTA analysis, a processing schedule was
established for thermal processing. Individual layers were dried on a hot plate at
250 OC for 30 seconds, fired at on a second hot plate at 400 O C for 15-60 seconds
and annealed in a box furnace at 650 OC for 2 minutes. A final anneal of the
multilayer films for 15-30 minutes at 650 OC in a box furnace was performed. It was
important to perform the full processing schedule for each film layer. Although
attempts have been made to anneal up to four dried and fired film layers at a time,
these film layers were much thinner and diffusion distances in the film were
comparable. Without full processing of each film layer, residual organics tend to get
trapped in the film (as the diffusion distances are too large). One way to
compensate for this is to process for long periods of time. However, grain sizes in
the film then become unduly large and the film's dielectric, fernelectric and
piezoelectric properties suffer. The chosen schedule allows most of the free
organics to be released prior to the decomposition and removal of lead acetate,
which reduces the possibility of film cracking. An intrinsic stress relief mechanism
inherent in PZT processing is the shrinkage of the film as the lead acetate
decomposes to the more stable lead carbonate and acetic acid is evolved. Since
most stress relief processes are thermally activated, the stress relaxation time of the
film can be reduced by increasing the temperature. This prevents the buildup of
high internal stress in the film. Thus, firing the film at a temperature of 400°C (which
is significantly higher than 285OC) reduces the possibility of film cracking. This
intermediate temperature also facilitates the release of more organics, but not an
excessive amount as to promote film cracking. For this reason, firing at much
higher temperatures usually yields deleterious results. The films are fired at 650%
to properly crystallize the layer when past the point at which weight loss still occurs.
The final post-anneal for an extended period of time results in a slight improvement
in the dielectric properties of the film.
4.4.3 Ra~id Thermal Processinq
The RTA schedule used was very similar to that for furnace processing.
Individual film layers were dried on a hot plate at 250°C for 30 seconds, fired on a
hot plate at 400°C for 15 seconds, then processed in the RTA using the processing
schedule outlined in Table 4.4.3.1. One advantage of using RTA processing is that
the anneal times are cut in half and no final anneal is necessary. This minimizes
the damage to layers under the PZTfilm. This method of processing is suitable for
manufacturing environments.
TABLE 4.4.3.1 : RTA processing schedule
Act ion
Delay
11 Hold I 60 s I 650
- -
Hold
Ramp
Hold
Cool Down I 60 s I < 300
Hold Time I Ramp Rate
15 s
4.5 Glancing Angle X-ray Diffraction
The ABO, perovskite phase is the preferred crystal structure for PZT thin
films as it is the phase with strong ferroelectric and piezoelectric properties.
However, depending on the processing conditions, PZT thin films may crystallize in
Temperature PC)
< 200
- --
I 0 s
100 "CIS
15 s
--
285
400
400
an undesirable phase. In the literature on P A thin films, reference is often made
to a pyrochlore type structure that is observed as an intermediate phase during
fabrication. In general terms, pyrochlores are ternary metallic oxide with properties
isostructural with the mineral pyrochlore [(NaCa)(NbTa)O,fl and the general
formula &6,06X [22]. In oxide pyrochlores such as PZT, X is an additional oxygen
atom which is loosely attached to the lattice and often escapes to leave a non-
stoichiometric composition. Most pyrochlores have Curie temperatures at sub-zero
temperatures, and therefore do not exhibit ferroelectric or piezoelectric properties
at room temperature. In PZTfilm fabrication, a cubic intermediate phase has been
reported and referred to as pyrochlore. This is not strictly true, however, as no
verification has been provided on the precise crystal structure of the intermediate
phase. In this thesis the term pyrochlore phase is used for consistency with the
general sense used in literature; the phase observed has no ferroelectric or
piezoelectric properties and is not the perovskite s?ructure.
The JCPDS (Joint Committee on Powder Diffraction Spectra) file for P A is
included in Appendix 2. The peaks in the GA-XRD results for the PZT films were
identified using this standard.
4.5.1 Choice of Alkoxide Precursor
GA-XRD results for coatings processed from solutions based on the IMO
method consistently indicate a significant amount of the non-piezoelectric
pyroc h lore phase in p ropoxidelp ropoxide-based coatings, little or no p yroc hlo re
phase in the butoxidelpropoxide-based coatings and no pyrochlore phase in the
butoxidelbutoxide-based coatings, as shown in Figure 4.5.1.1. The pyrochlore
phase peaks are identified by (Py) and the perovskite phase peaks are identified by
their (hkl) crystallographic orientation. Variations in the perovskiie peak heights in
the results shown are due to texturing in the films. The samples shown were
processed with methanol as the solvent and had (a) no cracking on the 15'" layer,
(b) cracking on the 81 layer, and (c) cracking on the 3d layer. These films cracked
at a lower thickness compared to most of the samples that were due to a slower
spin speed of 1500 rpm leading to thicker individual layers. The fact that the
FIGURE 4.5.1 .l: Variation in crystallization with choice of alkoxide precursor: (a) Zr butoxidemi butoxide, (b) Zr butoxidem isopropoxide and (c) Zr butoxideni isopropoxide precursors.
zirconium butoxide (80 wt.% in 1-butanol) I titanium butoxide-based films do not
contain any measurable amount of pyrochlore phase indicate that they probably will
have the best dielectric and ferroelectric properties, which would make them the
preferred choice for alkoxide precursor.
4.5.2 Choice of Solvent
Films processed using the modified IMO method and zirconium butoxide (80
wt.% in l-butanol) and titanium butoxide as alkoxide precursors do not show an
appreciable difference in crystallization when different solvents are used. The films
for which the GA-XRD results are shown (Figure 4.6.2.1) are all in the range of 1.8 -
2.0 pm thick. No pyrochlore phase is observed, regardless of the solvent used.
FIGURE 4.5.2.1 : Effect of solvent on crystallization of the P A film. The solvent used in the films were (a) ethanol (b) methanol (c) water and (d) butanol.
4.6 Scanning Electron Microscopy
Films processed by the modified IMO method, with the various combinations
of aikoxide precursors and methanol as a solvent are shown in Figure 4.6.1. Films
deposited from a sol-gel solution with zirconium propoxide and titanium
isopropoxide (Figure 4.6.1 a) tend to crack at the fewest layers, with an approximate
upper limit of 3 pm at 0.2 pmllayer. The next films to crack were those containing
zirconium butoxide and titanium isopropoxide (Figure 4.6.1 b), with an approximate
upper limit of 4 pm at 0.2 pmllayer. An upper limit has not been established for the
zirconium butoxide and titanium butoxide-based coatings, as crack-free coatings of
greater than 5 pm thickness have been produced (Figure 4.6.1~). The pictures of
the coatings shown in Figure 4.6.1 were taken using a scanning electron
microscope and have a 10000~ magnification.
FIGURE 4.6.1 : (a) Zr propoxideni isopropoxide 2.8 pm thick film (b) Zr butoxidemi isopropoxide 3.5 pm thick film (c) Zr butoxide Ki butoxide 4.4 pm thick film
All of the films appear dense and individual film layers are not observable, which are
both desirable results. It is difficult to say whether the columnar structure seen in
the SEM images is a crystallographic result, or a result of the cleaving of the
samples to obtain an edge for examination. As expected, much thicker films were
produced using the butoxide/butoxide-based P A solgel, due to greater solution
stability and although not confirmed, probably fewer local inhomogeneities.
SEM images for Alms processed with different solvents exhibit no appreciable
difference in density, appearance or thickness. The choice of solvent does not
affect the maximum attainable film thickness-
4.7 Electrical Characterization
Samples processed using the IMO method consistently have a permittivity
of 11 00-1 300 and a loss tangent of 1-2% for the zirconium butoxide/titanium
butoxide and zirconium butoxide (80 wt.% in 1-butanol) I titanium isopropoxide-
based coatings, depending on the thickness of the coatings. The dielectric
response for the films shown in Figure 4.7.1 are reasonably consistent over the
range of 1 kHz to 1 MHz. The zirconium propoxide (70 wt.% in I -propanol)/titanium
isopropoxide coatings were of poorer quality, with dielectric constants of 600-900
and loss tangents of 3.5%. Up to 2 pm thick films wlh dielectric constants of 1000-
I 100 and loss tangents of 2-3% have also been produced using the modified
acetate method of chemical addition when zirconium butoxide (70 wt.% in 1-
butanol) and titanium butoxide are used as alkoxide precursors. However, it is
difficult to obtain consistent results using this method. When either titanium
0 200 400 600 800 1 000
Frequency (kHz)
FIGURE 4.7.1 : Frequency response of (a) Zr butoxidemi butoxide based film (b) Zr butoxidemi isopropoxide-based film (c) Zr propoxidem isopropoxide-based film
isopropoxide or zirconium propoxide are used, it becomes difficult to avoid the
formation of transient gels in solution during the solution preparation process, with
a corresponding decrease in film quality. This is consistent with the proposal that
metal alkoxides in solutions prepared using the acetate method are more
susceptible to hydration and consequently, to local inhomogeneities formed by the
simultaneous addition of the acetic acid and lead acetate trihydrate together in
solution. The IMO process is a preferable method of chemical addition.
4.8 Piezoelectric Characterization
The impedance response for the thickness mode resonance of the PZT films
was anaIyzed using an HP8753D network analyzer over the range of 150-700 MHz.
The results for resistance and reactance normalized against frequency are shown
in Figures 4.8.1 and 4.8.2 for a 5 pm thick zirconium butoxide (80 wt.% in 1-
butanol)ltitanium butoxide-based film. The film was produced on a 500 yrn thick
platinized Si(1ll) wafer from a sol-gel solution prepared using the modified IMO
method. Electrodes were formed by sputtering a top layer of platinum on one of the
PZT films and evaporating chrome-gold electrodes the other. Two hundred micron
square electrodes were cut out by laser machining using a Kr excimer laser (231.
The films was poled at 180 O C and 6 Vlum for 20 minutes prior to laser machining.
The effect of the substrate on the piezoelectric response of the P A film is
to significantly broaden the thickness mode resonance envelope and to constrain
the response to the frequencies of thickness mode resonance in the substrate. The
result is the "diffraction grating-liken features in the impedance response. A fit to the
impedance response of the films may be obtained from a one-dimensional model
of thickness mode vibrations for a piezoelectric film on a substrate developed by
Lukacs et al. [24]. The fits from this model, which uses Newton's force laws and the
linear constitutive piezoelectric equations, are shown in Figures 4.8.1 and 4.8.2.
Five complex material parameters may be obtained from the fit to the data, which
yields a total of ten material constants. One important feature to note is the
dispersion in the material parameters over the frequency range (i.e. the material
constants have a slight frequency dependence). Because the resonance is quite
1e+5 2e+5 3e+5 4e+5 5e+5 6e+5 7e+5 8e+5
Frequency (kHz)
FIGURE 4.8.1: Impedance response of a 5 urn thick P A film with Cr-Au electrodes
1e+5 2e+5 3e+5 4e+5 5e+5 6e+5 7e+5 8e+5
Frequency (kHz)
FIGURE 4.8.2: Impedance response of a 5 urn thick PZT film with Pt electrodes
broad, dispersion has a significant effect. This subject has been examined
extensively in other work [25]. In this work, the five peaks in the center of the
resonance envelope were fit. with the results summarized in Table 4.8.1. The
effects of dispersion can be seen away from the resonance, where the peaks in the
fit are shifted with respect to the peaks in the data. The material parameters are
assumed to be frequency-independent in the model, and cannot compensate forthe
effects of dispersion.
The results from the fit for the ten material constants are summarized in
Table 4.8.1. The electromechanical coupling constant (kJ is comparable to that
obtained from the solgel composite coatings which yield k, values in the range of
0.25-0.35 [23]. However, the thin film &value is less than the bulkceramic coupling
coefficient, which typically has a magnitude of 0.6-0.72 [26]. This is primarily due
to mismatch between the P A film and the substrate which leads to strain and
constraint of motion in the film by the substrate. A preferred crystallization direction
can be induced in the P A in keeping with the crystallographic orientation of the
substrate. In thicker films (s 1 pm), this effect of substrate clamping on the film is
reduced, but the strain induced by the substrate still has the effect of lowering the
magnitude of k, 1271. Further improvements could be made in the poling process,
which has not been optimized. However, the parameters obtained from the analysis . of the piezoelectric response of the PZT thin films demonstrate the adequacy of
PZT sol-gel films for use in piezoelectric devices, and in particular, a thin film
piezoelectric transformer.
TABLE 4.8.1 : Material parameters for a PZT film on a Si (1 11) substrate
Dasfic stift.lass (Pm (Wm3 (2289 & 0.004) xlb + i(252 i 0.04) xl d (1.841 k 0.003) x l b + i(1.08 f 0.05) xld a a s t i c ~ ( ~ e ) 4'' (Nfd) (1.789 k0.001) x?O1' + i(6.06 k0.17) xl0' (1.783 e0.001) x10" + i(5.86 k0.21) xlff S(ray Impedance c (Q) (220 k 0.09) + i(O.23 r 0.1 0) (4.30 20.07) - i(0.036 k 0.082)
4.9 Summary
A stable solution chemistry and a consistent thermal processing route have
been developed to produce multi-layer solgel lead zirconate titanate (PZT)
piezoelectric coatings of high electrical quality. Up to 5 pm thick fully perovskite and
piezoelectrically active crack-free coatings with permittivity of 1100-1 300 and loss
tangents of 1-2% can be produced with careful attention to the choice of titanium
and zirconium alkoxide precursors, the choice of solvent, the method of solution
preparation, and the thermal processing schedule. The optimum sol-gel recipe
used is found in Appendix 3. The films were deposited on platinized silicon,
spinning for 30 seconds at 3000 rpm. Individual layers were dried on a hot plate at
250 OC for 30 seconds, fired on a second hot plate at 400 OC for 15-60 seconds and *
annealed in either a box furnace at 650°C for 2 minutes or an RTA at 650°C for 1
minute. The film properties meet the design specifications for the production of a
thin film piezoelectric transformer.
References
G. Yi and M. Sayer, Proceedings of the 8" International Conference On the
Applications of Ferroelectrics. (1 992).
G. Yi, Z. Wu and M. Sayer, Journal Applied Physics. 64,2717 (1988).
R.W. Schwartz, R.A. Assink and T.J. Headley, MRS Symposium
Proceedings, 243, 245 (1 992)-
S-RGurkovich and J.B. Blum, Ferroelectrics, 62, 189 (1 985).
K.D. Budd. S.K. Dey and D.A. Payne, Proceedings of the British Ceramic
Society, 36. 107 (1 985).
Y.L. Tu and S.J. Milne, Journal of Materials Science, 30, 2507 (1995).
G. Yi and M. Sayer, Ceramic Bulletin, 70. 1 173 (1 990).