0

Basic Laboratory

Materials Science and Engineering

Chemical Solution Deposition of

Lead Zirconate Titanate Thin Films M107

Stand: 30.09.2015

Aim: Deposition of PZT thin films by CSD and determination of di- and piezoelectric properties.

Contents

1 Introduction 1

2 Basics 2

2.1 Chemical Solution Deposition (CSD) 2

2.2 Lead Zirconate Titanate (PZT) 5

2.3 Double Beam Laser Interferometer (DBLI) 9

3 Experimental 11

3.1 Fabrication of the PZT precursor solution 11

3.2 Deposition 11

3.3 Measurements of di- and piezoelectric properties of oriented PZT thin films 12

4 Report 13

5 References 14

6 Appendix 15

1

Chemical solution deposition of lead zirconate titanate thin films

1 Introduction

Ever since high piezoelectricity was found in Pb(ZrxTi1-x)O3 or PZT, PZT ceramics have become the most

successful piezoelectric materials in practical applications over the past 50 years. Currently, PZT

materials are widely used in commercial applications such as actuators, transducers, and sensors. [1]

The trend of miniaturization and integration led to the development of micro-electro-mechanical-

systems (MEMS). Typically these systems consist of a substrate (silicon wafer) and a functional thin

film deposited on top. For this diverse techniques have been developed and adapted for the deposition

of functional thin films. A method which allows for the fabrication of high quality coatings and is

simultaneously a versatile and non-expensive process is the Chemical Solution Deposition (CSD)

method.

The advantages of this technique are self-evident. It is a simple and economical technique, as the

fabrication does not need expensive machinery or apparatuses. In addition it offers high flexibility, as

one can produce materials with a wide range of stoichiometries and additional dopants. CSD could be

seen as an umbrella term for several solution based techniques, like the sol-gel process, the chelate

process, and metallo-organic decomposition (MOD). However, in reality for compositions containing

more than one metal ion, a clear differentiation of defined processes is not possible. A mixture of the

above mentioned processes will be used for the fabrication of metalorganic solutions. These solutions

are the basis for the fabrication of functional oxide thin films. For this, the solutions have to be

deposited on suitable substrates and have to be converted by a pyrolysis reaction and crystallization

processes into the desired oxidic phase.

2

2 Basics

2.1 Chemical Solution Deposition (CSD)

General [2, 3]

The starting point of the CSD technique is always a solution. The most prominent starting materials for

such solutions are metal organic or inorganic compounds. These could be metal alkoxides, salts of

organic acids (acetates, lactates), metal organic compounds (pentandionates), or salts of inorganic

acids (nitrates, chlorides). However, the most popular starting reagents are metal alkoxides. These are

compounds consisting of a positively charged metal ion and a negatively charged moiety of an alcohol.

Metal alkoxides can be produced by several routes. Two examples are given in equations 1 and 2. The

advantages of metal alkoxides are the good solubility in organic solvents, the good miscibility with

other organic compounds and solvents, and the extremely high reactivity. A disadvantage is the

sensitivity to humidity and water due to the high reactivity.

25252 222 HONaHCOHHCNa Equation 1

HClCHOCHTiCHOHCHTiCl 4])([)(4 423234 Equation 2

Sol-Gel Process

The sol-gel process is based typically on alkoxides as starting reagents dissolved in organic solvents.

The reactions in the sol-gel process lead to the formation of oligomers with M-O-M bridging bonds.

In the first step, the alkoxides react with water with the formation of partially hydrolyzed alkoxides

and alcohol:

yROHHOORMOyHORM yyxx )()()( 2 Equation 3

In the second step, the partially hydrolyzed alkoxides react to form oligomers with M-O-M bridging

bonds. These condensation reactions lead to the elimination of water (equation 4) or alcohol (equation

5).

ROHORMOMROHOORMORM xxxx 111 )()()()()( Equation 4

OHORMOMROHOORMOHROM xxxx 21111 )()()()()()( Equation 5

3

The reaction kinetics depend on the kind of alcohol moiety and the kind of solvent. Another possibility

is to restrict the amount of water and control the addition. This can be controlled by different factors

including the kind of alkoxide, solvent, alkoxide concentration, water concentration, and kind of

addition. Manipulating these factors leads to variations of the hydrolysis and condensation reactions.

One commonly used method to manipulate the reactivity is the alcohol exchange:

xROHORMOHxRORM xx ´)(´)( Equation 6

The aim is to exchange more reactive alcohol moieties with less reactive ones. An example would be

the exchange of methanol or ethanol by 2-methoxyethanol or 1,3-propanediol.

The method described above is also known as the polymeric route. A second route is called the colloidal

route. In contrast to the polymeric route, the alkoxides will hydrolyze completely to a metal hydroxide

with water under evolution of alcohol (Equation 7). The hydrolysis can be done by adding the alkoxide

drop-wise into pure water or by adding the appropriate amount of water drop-wise to the alkoxide. In

this case the alkoxide should be dissolved in an organic solvent.

xROHOHMOxHORM xx )()( 2 Equation 7

A condensation of the metal hydroxide occurs simultaneously. The hydroxide reacts to form an oxide

(Equation 8). Both reactions are visible by formation of a cloudy, in transparent precipitate. By adding

a small amount of acid (e.g. nitric acid), the precipitate should disperse and a clear solution of a

colloidal sol arises. The acid causes the formation of a charged layer around the particles and so isolates

each particle preventing agglomeration. This method is called electrostatic stabilization.

OHxMOOHM xx 22 2)( Equation 8

Chelate Method

The strong tendency of precursors like alkoxides to polymerize excessively and precipitate can be

reduced by chemical modification. The main aim is to alter the chemical nature and structure of the

precursor. Most often in these processes, compounds such acetic acids, acetylacetone (more precisely:

2,4-pentandionate), or amine compounds are employed, since these compounds readily react with

alkoxides. The reaction involves the formation of new species that possess physical and chemical

characteristics that are more attractive in terms of solution stability and film formation behavior. [2]

4

CH3

CH

2

CH3

O O

CH3

CH

CH3

O OH

Equation 9: Keto and enol form of acetylacetone (2,4-pentandionate)

Acetylacetone is by far the most frequently used stabilizer for metal alkoxides. Acetylacetone and

other β-diketones, (R1-C(=O)-CR2H-C(=O)-R3) are compounds which undergo a rapid keto-enol

tautomerism. They possess a reactive hydroxyl group in the enolic form (R1-C(=O)-CR2=C(R3)-OH),

which may attack the alkoxide in a similar way as a simple alcohol, leading to the corresponding

alcoholysis reaction with the release of the original alkoxy group as an alcohol (equation 9).

The second oxygen atom of the β-diketonate ligand is able to form an additional bond to the central

metal atom of the modified alkoxide, hence forming a chelate complex (equation 10). These chelate

complexes have higher stability constants than the original metal alkoxide, which is the driving force

for the reaction. As a further result, the bidentate ligand is less readily hydrolyzed than the remaining

OR-groups upon exposure to water. This leads to a higher stability of the corresponding precursor

solutions. [3]

CH3

CH

CH3

O

CH3

CH

CH3

O

O

Ti

CH3

CH

CH3

O

CH3

CH

CH3

O

CH3

CH

CH3

O

CH3

CH

CH3

O

CH3

CH

CH3

O

Ti

CH3

CH

CH3

O

CH3

C

H2

CH3

O O

CH3

CH3

OH

+

+

Equation 10: Reaction of Titanium isopropoxide with acetylaceton.

Metallo-Organic Decomposition (MOD)

Typically long chained metallo-organic source materials are dissolved in an inert solvent. Due to the

long chain nature and the inert solvent, a minimum of reactivity is obtained.

5

Film preparation

Such solutions can used for the preparation of thin films by spin coating, dip coating, or other

techniques, such as spray pyrolysis.

Spin coating allows the preparation of thin films on flat substrates. The apparatus used for spin coating

is called a spin coater. An adequate amount of a solution is dropped on a rotating substrate. The sol

spreads on the surface and forms a film. In a second step the rotation increases and the excess sol is

removed by centrifugal forces. In this step, the volatile solvent evaporates and a dry, thin, metal

organic film is formed. The thickness of the film depends on the viscosity, the concentration of the sol,

and on the angular speed. With increasing angular speed the film thickness decreases.

Dip coating also allows for the preparation of thin films on adequate substrates. The apparatus used

for dip coating is called a dip coater. The substrate is immersed at a constant speed into a tank

containing the solution. The substrate is withdrawn, again with a constant speed, after a sufficient

dwell time. Outside the tank, the volatile solvent evaporates and a dry, thin, metal organic film is

formed. The thickness of the film depends on the viscosity, the concentration of the sol and on the

withdrawing speed. With increasing withdrawing speed the film thickness also increases.

During film formation, the sol is transformed into a gel by evaporation of the solvent and particles or

polymeric chains approaching each other. The resulting gel is a system consisting of a solid,

deformable, three-dimensional network and a liquid. In the last step, the residual solvent and

remaining organic or inorganics must be removed. This is done via pyrolysis and results in an

amorphous, oxidic solid structure. Via annealing at temperatures of about 500°C, this solid can be

transformed into a crystalline and dense material.

2.2 Lead Zirconate Titanate (PZT)

Lead zirconate titanate is one of the most popular ferroelectric materials. Ferroelectrics are insulating

and are considered dielectric materials. They show the pyroelectric as well as the piezoelectric effects.

Another characteristic is the existence of electric dipoles due to the structure. In contrast to linear

dielectrics, ferroelectrics show spontaneous polarization. The polarization is associated with distinct

crystallographic orientations. By applying an electric field, the direction of the polarization can be

reversed. The polarity reversal is characterized by a pronounced hysteresis behavior (Fig. 1 (a)). The

source of the behavior is found in the ferroelectric domain structure. These are areas in a crystal with

adjacent polarization orientation. Due to energy minimization, neighboring domains show opposite

polarization directions. Polycrystalline materials contain countless crystals with random orientations;

they are isotropic. The net electrical polarization is zero (compare Fig. 1 (b)). By applying an electrical

field, domains oriented suitably to the field direction will align. At higher external fields, less well-

oriented domains contribute to the polarization (Fig. 1 (c)).

6

Fig. 1: (a) Ferroelectric hysteresis and domain configuration (b) at zero field and (c) at applied electric

field. Note the piezoelectric displacement D for an applied electric field.

The properties of ferroelectric materials are strongly associated with their structures. Many

ferroelectric materials crystalizes in the perovskite structure with the formula ABO3. A and B are

cations, whereby B ions are found in an octahedron of O ions. These [BO6] octahedrons form across

common edges a 3 dimensional network. The A ions are located in the vacancies of the network in a

12-fold cuboctahedral coordination. The ideal cubic structure exist only at elevated temperatures.

Beyond a certain temperature, called the Curie temperature, the cubic structure transforms into a

structure with lower symmetry. For example: BaTiO3 transform at 120 °C from the high temperature

cubic phase into the low temperature tetragonal phase. The cell is c-axis distorted, the titanium ion is

no longer centered, and the oxygen octahedron will also be distorted. These processes lead to a

displacement of the charge balance point from the center of the cell. The result is a spontaneous

polarization.

Fig. 2: (a) Phase diagram of PbZrO3-PbTiO3 after Jaffe [5] and (b) revised phase diagram after Noheda

[7].

PZT ceramics are commonly used with compositions close to a nearly temperature independent

morphotropic phase boundary (MPB) separating tetragonal Ti-rich PZT from rhombohedral Zr-rich PZT,

at x = 0.48 PbTiO3 (see Fig. 2 (a)). MPB compositions show enhanced dielectric and piezoelectric

7

properties. It is generally accepted that the enhanced piezoelectric properties near the MPB result

from enhanced polarizability, arising from the coupling between two equivalent energy states of

tetragonal (t) and rhombohedral (r) phases, allowing optimum domain reorientation during the poling

process. In 1999, Noheda first discovered a monoclinic phase, sandwiched between r and t phases near

the MPB in PZT ceramics. A revised PZT phase diagram around the MPB is shown in Fig. 2 (b). This

discovery completely changed the well-accepted picture of the MPB, since this new phase acts as a

structural bridge between the r and t phases. [1]

In piezoelectric materials, upon application of a stress, charges develop on the surfaces of the

piezoelectric body (direct effect). The opposite effect works as well: a deformation occurs upon

application of an electric field (converse effect). Both effects are linear, at least at values of external

electric field and stress that are not too high. [4]

Fig. 3: Illustration of the (a) direct and (b) converse piezoelectric effect.

For ordinary solids, a stress T merely causes a proportional strain S, related by an elastic modulus, 𝑇 =

𝑌𝑆. Piezoelectricity is the additional creation of an electric charge by the applied stress. This is the

direct piezoelectric effect. The charge is proportional to the force, and it is therefore of opposite sign

for compression and tension. In terms of dielectric displacement D (charge Q per unit area) and stress

T, we may write 𝐷 = 𝑄 𝐴⁄ = 𝑑𝑇 (d expressed in coulombs/newton). There is a converse effect. An

applied field E produces a proportional strain S, expansion or contraction depending on polarity, 𝑆 =

𝑑𝐸 (d expressed in meters/volt). For both effects, the proportionality constant is the piezoelectric

constant d, which is numerically identical for both direct and converse effects.

𝑑 = 𝐷 𝑇⁄ = 𝑆 𝐸⁄ Equation 11

A high d constant is desirable for materials intended to produce motion or vibration, such as

transducers in ultrasonic cleaners or sonar. Another frequently used piezoelectric constant is g, which

gives the field produced by a stress. Its common units are meter volts/newton, simplified from

(volts/meter)/(newton/square meter). The g constant is related to the d constant by the permittivity:

𝑔 = 𝑑 𝜀𝑟𝜀0⁄ Equation 12

+

-

+

-

F

F

a) b)

+

-

+

-

F

F

a) b)

(a) (b)

8

A high g constant is desirable in materials intended to generate voltages in response to a mechanical

stress, as in a phonograph pickup. Additional piezoelectric constants which are only occasionally used

are e, which relates stress T to field E, and h which relates strain S to field E:

𝑇 = −𝑒𝐸 Equation 13

𝐸 = −ℎ𝑆 Equation 14

The piezoelectric constants are partial derivatives evaluated at constant stress (subscript T), constant

field (subscript E), constant displacement (subscript D) or constant strain (subscript S). The

definitions are: [5]

Ej

i

Tj

i

ijT

D

E

Sd

Equation 15

Tj

i

Dj

i

ijD

S

T

Eg

Equation 16

Ej

i

Sj

i

ijS

D

E

Te

Equation 17

Dj

i

Sj

i

ijS

E

D

Th

Equation 18

Fig. 4: Illustration of piezoelectricity for thin films.

The properties of a piezoelectric film cannot be compared to the corresponding bulk material. The film

is part of the composite structure film-substrate and the strain across the film-substrate interface

needs to be continuous, i.e. the film is fixed in the film plane, but free to move in off-plane direction.

With the converse effect (actuator), the in-plane stresses σ1, σ2,and the off-plane strain x3 are changed

9

as a function of the applied field E3 (see Fig. 4). The corresponding, directly measurable, piezoelectric

coefficients are the effective d33,f, which is obtained as follows from the bulk tensor properties: [4]

EE

E

fss

sddd

1211

13

3133,33 2

Equation 19

With 𝑑3𝑗 the piezoelectric constants and 𝑆𝑖𝑗𝐸 , the elastic compliance at constant electric field of the

bulk material.

2.3 Double Beam Laser Interferometer (DBLI)

A double beam laser interferometer (aixDBLI) will be used to determine the dielectric and piezoelectric

properties of PZT thin films.

Typically, the high resolution of laser interferometry is used for precise measurements of very small

mechanical deformations of thin-film structures. However, unavoidable sample or wafer bending lead

to large measurement errors. These can be eliminated by the differential measurement method used

in DBLI, which is shown in principle in Fig. 5. With this method, thin-film expansions can be measured

under electrical excitation with a resolution much better than 1 pm. [6]

Fig. 5: Beam path of the DBLI.

A more detailed description of the DBLI measurement principle and dielectric characterization method

can be found in the appendix.

10

Fig. 6 and Fig. 7 show example measurements of the large and small signal response, respectively, of

a 1 μm thick PZT film.

Fig. 6: Large signal measurement. (a) Ferroelectric hysteresis and (b) piezoelectric displacement.

Fig. 7: Small signal measurement. (a) Dielectric and (b) piezoelectric response.

11

3 Experimental

3.1 Fabrication of the PZT precursor solution

Before you start: read the safety data sheets listed in the appendix for the chemicals used in this

experiment!

Source materials are:

Lead acetate trihydrate (C4H6O4Pb*3H2O), 379.33 g/mol

Zirconium propoxide (70 wt.-%) Zr(OPrn)4, 327.57 g/mol

Titanium butoxide Ti(OBu)4, 340.36 g/mol

2-methoxyethanol (C3H8O2), 76.09 g/mol

Acetylacetone (C5H8O2), 100.12 g/mol

We want to produce 5ml of sol with a concentration of 0.4 mol/l. At first you have to calculate the right

amount of the source materials to use. Keep in mind that the desired composition of PZT is given with

Pb1.1(Zr0.52Ti0.48)O3. Due to the volatility of lead oxide at elevated temperatures, an excess of 10 % will

be used.

In the first step, lead acetate will be dissolved into 2 ml of 2-methoxyethanol in a beaker at room

temperature. In a flask, 1 ml of 2-methoxyethanol and 1 mol of acetylacetone (1 mol acetylacetone

relative to 1 mol alkoxide) are introduced. After mixing, the alkoxides are introduced (first zirconium

propoxide). After mixing, we add the Pb solution drop-wise. In the next step, you heat the solution for

one hour while the solution is stirred with a magnetic stirrer and the vaporized solution is cooled and

flows back. Finally, you fill up the solution with 2-methoxyethanol in order to reach 5 ml solution

volume.

3.2 Deposition

After the fabrication of the sol, we want to deposit a substrate. For this we use samples of Si with a

thin SiO2 film and a 150 nm thick Ti/Pt film sputter deposited on top of that. The Pt film has different

functions. At first, it serve as a seed layer due to the strong orientation ((111) orientation) and the

small mismatch of the Pt lattice constant and the lattice constant of PZT. Additionally, the Pt film later

acts as a bottom electrode for the plate capacitor-type device. The deposition of the PZT film on these

substrates is done by spin coating with a spin coater (Laurel WS-400BX-6NPP). The instructor will

12

explain the handling of the spin coater in detail. It is important to choose the preset program “B”. As

usual, the coating program is subdivided into two steps. In the first step, the machine rotates at

800 rpm for 8 s. During this step you have to drop an adequate amount of the solution on the sample.

This is done by using a pipette to approach the sample through a small hole in the lid of the spin coater.

In the next step, the coater rotates for 20 s at 3000 rpm. In addition to that, you should always confirm

that the machine is connected to compressed air. In order to keep the sample at the right position

during rotation, we have to hold the sample in place with a vacuum, and that is done by a vacuum

pump. Thus before starting the procedure, you have to switch on the vacuum, and, of course, before

removing the sample, you have to switch it off. We want to deposit on our samples four times.

Therefore, we repeat this whole procedure four times, and between each deposition we heat up the

sample to 300 °C on a hotplate for 30 seconds. Finally, the film is crystallized at 700 °C for 10 min.

3.3 Measurements of dielectric and piezoelectric properties of oriented PZT thin films

Two samples will be investigated. Both samples are prepared by CSD. The differences between the

samples are shown in the XRD diffraction patterns in Fig. 8. The PZT film of one sample shows a strong

(111) orientation, the other a strong (100) orientation. Both samples were prepared in the same way,

with the same solution, deposited on identical substrates with an identical Ti/Pt seed layer. The

difference is, that for the (100) oriented PZT film, a PbO film was additionally deposited on the Pt film.

The result is a change in the orientation of the subsequently deposited PZT film.

Fig. 8: XRD diffraction pattern of a (a) (111) oriented and (b) (100) oriented PZT film. Note the

logarithmic scale of the intensity.

Piezoelectric properties are strongly connected to the structure of the investigated PZT film. In general,

a randomly oriented film shows a smaller piezoelectric response then an oriented film, and a (100)

oriented film is superior to a (111) oriented ones. [8]

13

4 Report

Introduction

Keep the introduction as simple as possible; just make the main points.

Experimental

Make a short description of experiments and give the calculated weights.

Results and discussion

Discuss the most probable reactions during the solution preparation based on the mechanisms given

in chapter 2.1 and based on the observations taking during the experiments.

Plot the ferroelectric hysteresis (polarization vs the electric field) and extract the main characteristic

values (coercive field, remnant polarization). Compare and discuss the values of the two differently

oriented PZT films.

Calculate, based on the capacitance-voltage data, the dielectric constant 𝜀𝑟 and plot 𝜀𝑟 vs the electric

field for the two differently oriented PZT films.

Plot the piezoelectric constant d33,f vs the electric field for the two differently oriented PZT films. Extract

the piezoelectric constant at zero field. Compare the data.

For all extracted data: compare the different values extracted from plots with published ones.

14

5 References

[1] Priya, S., & Nahm, S. (Eds.). (2011). Lead-free piezoelectrics. Springer Science & Business Media.

[2] Schwartz, R. W., & Narayanan, M. (2009). Chemical solution deposition—basic principles (p. 33-76).

John Wiley & Sons: Hoboken, NJ, USA.

[3] Schneller, T., Waser, R., Kosec, M., & Payne, D. (Eds.). (2013). Chemical Solution Deposition of

Functional Oxide Thin Films. Springer.

[4] Muralt, P. (1997). Piezoelectric thin films for MEMS. Integrated Ferroelectrics, 17(1-4), 297-307.

[5] Jaffe, B., Cook, W., & Ceramics, H. J. P. (1971). Academic Press. New York

[6] Prume, K., Tiedke, S., & Schmitz-Kempen, T. Double-Beam and four-point.

[7] Noheda, B., Cox, D. E., Shirane, G., Gonzalo, J. A., Cross, L. E., & Park, S. E. (1999). A monoclinic

ferroelectric phase in the Pb(Zr1-xTix)O3 solid solution. Applied physics letters, 74, 2059.

[8] Ledermann, N., Muralt, P., Baborowski, J., Gentil, S., Mukati, K., Cantoni, M., ... & Setter, N. (2003).

{1 0 0}-Textured, piezoelectric Pb (ZrxTi1−x)O3 thin films for MEMS: integration, deposition and

properties. Sensors and Actuators A: Physical, 105(2), 162-170.

15

6 Appendix

DBLI (excerpt from DBLI user manual, Aixacct)

Using the converse piezoelectric effect, the electric field induced displacement of the sample is

measured. Since the small thickness of thin films limits the voltage applicable to the samples, the

displacements are in the angstrom range. The non-linear piezoelectric response of ferroelectric

materials for different applied electric fields requires an even higher resolution of about 1 - 10pm.

Interferometric techniques are one approach to achieve such high resolutions. Of the different

interferometric methods, homodyne interferometers are most commonly used. Using an active

stabilization of the operating point, two optical path schemes have been developed over time: the

single-beam Michelson interferometer measures the displacement of only one surface of a sample,

whilst the double-beam Mach-Zehnder measures the displacement difference between the two major

surfaces of the sample. Since the single-beam technique does not take sample motion into account, it

is prone to errors resulting from sample bending. Therefore, the double-beam technique is the

superior method for measuring ferroelectric thin films. Measuring only the displacement difference,

any motion of the sample along the optical path is successfully suppressed. Hence, bending of the

sample cannot contribute to the measured displacement. The disadvantage of this technique is a

reduced resolution (10-3 – 10-2 angstrom), resulting from the increased optical path length and loss of

light intensity in the system. The optical path of the double-beam laser interferometer used in this

work is shown Fig. 9. The laser beam, generated by an intensity stabilized He-Ne laser, passes the

diaphragm and a shutter before it is reflected by the two mirrors M1 and M2 to the front side of the

setup. The beam passes then the λ/2 plate P1 before entering the polarizing beam splitter (PBS1) on

the upper rail. The diaphragm keeps reflected light out of the laser and the λ /2 plate is used to rotate

the laser beam polarization. Rotation of the polarization determines the amount of intensity

transmitted and reflected in the beam splitter (PBS1). The transmitted beam is used as a measurement

beam and has a longer beam path. Hence, the losses in this beam are higher than in the reflected

beam, which is used as a reference beam. Higher losses can also result from less than optimal reflection

of the sample surface and counterbalanced by increasing the intensity of the measurement beam. The

measurement beam travels along the upper rail, passes the λ /4 plate P2 and is reflected downwards

in the mirror M3. After being focused by the lens L1, the beam is reflected on the upper surface of the

sample. Afterwards, the beam travels back to the beam splitter PBS1. By passing the λ /4 plate P2

twice, the polarization is rotated 90° resulting in a downward reflecting in PBS1. In PBS2, the

measurement beam is reflected again and travels along the lower rail. It is reflected (M4) and focused

(L2) again, this time on the lower sample surface. Another λ /4 plate P3 is used for polarization rotation.

When the beam reaches PBS2 it is transmitted to the non-polarizing beam splitter BS3. Inside BS3, half

the beam is transmitted and half is reflected upwards to the photo detector. The reference beam,

which is reflected upwards in PBS1, passes the λ /4 plate P4 and is reflected on the mirror M7 seated

on a piezoelectric actor. This so called reference mirror can be shifted along the beam path to change

the path length of the reference beam and to control the operating point of the interferometer. Since

the λ /4 plate P4 turns the polarization, the reference beam is transmitted through PBS1 on its way

back and passes PBS2. After being transmitted again, the beam is reflected in the mirrors M5 and M6

until it reaches the beam splitter BS3. It reaches BS3 in the same polarization state as the measurement

beam. Therefore, the superposition of both beams in BS3 results in the desired interference. The

combined beam is broadened by lens L3 to enlarge the center of the interference pattern. The center

intensity of the pattern is finally measured by the photo detector.

16

Fig. 9: Beam path of the DBLI.

The most common measurements done with laser interferometers are the characterization of the

electrically induced large signal strain S and the calculation of the piezoelectric small-signal coefficient

d33.

The large signal displacement D or strain S is calculated directly from the intensity variations in the

center of the interference pattern. A varying electric field with an amplitude higher than the coercive

voltage is applied to the sample and the thickness change is measured. Since no noise reduction

hardware is used during this measurements, the strain signal has to be improved by averaging over

many cycles of the electric field (see Fig. 6).

Utilizing Lock-In amplification in hardware or software, it is possible to boost the Signal-To-Noise ratio

(SNR) significantly. In order to use these techniques it is necessary to have a nearly linear relation

between applied electric field and thickness change of the sample. Therefore, these methods are

limited to small-signal measurements, where only intrinsic effects contribute to the electromechanical

sample strain. To characterize the sample behavior for different defined sample states, two electric

fields have to be used. The sample characterization itself is done by a high frequency field with small

amplitude (small-signal field). The state of the sample is changed by a bias field which is either varied

stepwise or with a very low frequency. Both fields are superimposed and applied to the sample. The

Lock-In amplification cancels out any effects arising from the bias field and only measures the small-

signal response. By dividing the response by the amplitude of the small-signal field, the small-signal

coefficient d33 is calculated (see Fig. 7).

17

Safety data sheets

Lead acetate trihydrate

Zirconium propoxide

Titanium isopropoxide

2-Methoxyethanol

Acetylacetone

18

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