Zuo-Guang. Ye Advanced Dielectric Piezoelectric and Ferroelectric Materials: Synthesis, Characterisation and Applications

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Handbook of dielectric, piezoelectric and ferroelectric materials980

Although the reactive MBE process produces perovskite superlattices of

the highest quality, the deposition rate of the MBE process is still too slow

to prepare perovskite superlattices for practical applications. Most of the

industrial manufacturing processes of oxide thin films are still by simple and

conventional RF-magnetron sputtering. Therefore, we tried to make BTO/

STO superlattices using a simple sputtering system as shown in Fig. 32.5(b).

A substrate is rotated with an air actuator to alternately face the RF-plasma

of BTO (A) and STO (B) targets. The thickness of each layer is determined

from the deposition time. Tsai et al.

prepared the BTO/STO superlattices

and Wu and Hung

made the PbZrO

/BaZrO

superlattices using RF-

magnetron sputtering systems. They confirmed the formation of superlattices

from the satellite peaks in XRD profiles. Although the RF-sputtering is a

promising process for practical applications, the quality of the superlattices

must be improved to obtain the desired properties.

32.3 Lattice distortions in artificial superlattices

Figure 32.6 shows the XRD profiles of BTO/STO and SZO/STO superlattices

made with the MBE system shown in Fig. 32.2. Clear satellite peaks indicate

the formation of superlattices. XRD reciprocal-space-mapping measurements

were performed using high-resolution XRD equipment (Bruker AXS,

Discover8). Typical reciprocal-space-mappings obtained for BTO/STO

superlattices are shown in Fig. 32.7. The highest peaks in the maps are the

002 diffractions of the STO substrates. Clear satellite peaks are observed in

[BTO

/STO

]

superlattices. The shift of diffraction spots to the x-direction

(a*-axis) in the maps indicates that the a-parameter (in-plane lattice parameter)

of the epitaxial film changed from that of the substrate due to the relaxation

of crystal lattices. In [BTO

/STO

]

superlattices, all satellite peaks lie on

the same a* line as the substrate, indicating that the strained lattice is formed

in the films without relaxation of crystal lattices. In this case, a large lattice

distortion was induced by the lattice mismatch between BTO and STO in

substrate and in superlattices. On the other hand, a diffraction spot of the

[BTO

/STO

]

is shifted in the x-direction from the substrate by the relaxation

of crystal lattice.

The variations of the a- and c-parameters with the periodicity of BTO/

STO and SZO/STO superlattices calculated from the diffraction angles of

002 peaks are shown in Fig. 32.8. It should be noted that all superlattices in

one series have the same total thickness (80 perovskite unit cells) and the

same chemical composition (Ba : Sr = 0.5 : 0.5 and Ti : Zr = 0.5 : 0.5). The

dotted lines in Fig. 32.8 indicate the lattice parameters of bulk samples. In

the case of BTO/STO superlattices, the a-parameters of superlattices with

the periodicities of 10 and 20 unit cells are identical to that of STO substrate,

indicating that almost completely strained lattices are formed in these

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Dielectric and optical properties of perovskite 981

superlattices. The a-parameter was relaxed to a large value when the periodicity

was increased to 40. The anisotropy of the crystal lattice has a maximum at

the periodicity of 10. On the other hand, the a-parameter of SZO/STO

superlattices increases with the periodicity. The c-parameter of the superlattice

with the periodicity of 10 is consistent with that of the ideally strained lattice

calculated from the unit cell volume of the bulk samples. The anisotropy of

the crystal lattice has the maximum value in this superlattice. The lattice

parameters of the superlattice with the periodicity of 40 are almost the same

as bulk SZO ceramics because the diffraction from the STO layer in the

relaxed superlattice is overlapped with that of the substrate and the lattice

parameters are calculated from the diffraction only from the SZO layer in the

superlattice.

The different behaviors in the variation of lattice parameters between

BTO/STO and SZO/STO superlattices in Fig. 32.8 are attributable to the

difference in the a-parameters of bulk samples of BTO

(0.3994 nm) and SZO

Substrate

Intensity/Arb. unitsIntensity /Arb. units

CuKα 2θ/deg.

70 806050403020

(a)

(b)

70 806050403020

32.6

XRD profiles of (a) [BTO

/STO

]

and (b) [SZO

/STO

]

superlattices.

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Handbook of dielectric, piezoelectric and ferroelectric materials982

(0.4100nm). As the SZO has a large a-parameter, the in-plane compressive

strain induced to the SZO layers from the STO substrate and the STO layers

in the superlattices cannot be retained with the increase of the periodicity,

giving rise to the relaxation of lattice strains, more easily than the case of

BTO/STO superlattices. The lattice parameters of the superlattices with a

periodicity of 1 have anomalous values, i.e. the c-parameters of the superlattices

markedly shrink in both cases. The formation of solid solution films due to

(a) [BTO

/STO

]

(b) [BTO

/STO

]

/STO

]

(d) [BTO

/STO

]

32.7

XRD reciprocal-space-mappings of BTO/STO superlattices.

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Dielectric and optical properties of perovskite 983

the interdiffusion of constituent elements is the reason for this phenomenon

but the lattice volume shrinkage observed in the SZO/STO superlattice cannot

be explained at present.

32.4 Optical property of artificial superlattices

32.4.1 Spectroscopic ellipsometry

Ellipsometry is an optical technique that can evaluate the optical constant

and film thickness of a thin film simultaneously. It is widely used for the

characterization of thin films and in-situ observation of growth process of

thin films.

41–46

The basic theory of ellipsometry was summarized in a book

written by Azzam and Bashara.

There are some reports on the ellipsometry

of semiconductor superlattices

48–52

but the studies on oxide artificial

superlattices are extremely limited except for our work on NiO/ZnO

superlattices prepared by the IBS process.

32.8

Variations of lattice parameters with the stacking periodicity of

(a) BTO/STO superlattices and (b) SZO/STO superlattices.

Identically strained

Stacking periodicity

(a)

4020101

Lattice parameter (nm)

0.42

0.41

0.40

0.39

0.38

Lattice parameter (nm)

0.43

0.42

0.41

0.40

0.39

0.38

Stacking periodicity

(b)

4020101

-axis

STO

BTO

0.5

TiO

-axis

STO

SZO

Sr(Ti

0.5

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Handbook of dielectric, piezoelectric and ferroelectric materials984

Figure 32.9 shows the rotating-analyzer type spectroscopic ellipsometer

used for the evaluation of ellipsometer angles, Ψ and ∆, of superlattices on

substrates. Reflection ellipsometry is a technique based on the measurements

of the states of polarization of the incident and reflected waves, leading to

the determination of the ratio ρ of the complex Fresnel reflection coefficients.

The ratio

ρ is represented in terms of ellipsometer angles by ρ = tan Ψ

exp(i∆). The rotation-analyzer ellipsometer becomes inaccurate when ∆ <

10° or ∆ > 170°

which is frequently encountered in the measurements of

transparent films.

55–58

To avoid this problem, a compensator (a quarter-wave

retarder) is inserted after the polarizer to change the polarizing state of

incident light. Polarized light from 350 to 850 nm in wavelength is provided

from a Xe lamp (75 W) through a computer-controlled monochrometer and

an optical fiber. The incident angle is varied from 50° to 80°. The refractive

indices of thin films were calculated using the three-phase model (ambient

thin films substrate). In the analysis, the superlattices were regarded as uniform

thin films along the thickness. The difficulty in the ellipsometric measurements

of superlattices is that the refractive index of the substrate is very close to

that of thin films. We measured the ellipsometer angles of STO substrates

very accurately to prepare database used for the analysis of thin films. Nonlinear

least-squares-fitting software was developed to determine the optical constant,

n* = n – iκ, where n is the refractive index and κ is the extinction coefficient,

from the complex Fresnel reflection coefficients (ρ) determined at different

incident angles. No theoretical assumption was used to evaluate the wavelength

dispersion of refractive index.

32.4.2 Optical constants of superlattices

The refractive index (n) and extinction coefficient (κ) of the BTO/STO and

SZO/STO superlattices determined by the ellipsometer system are shown in

Fig. 32.10 as a function of light wavelength. The refractive index decreases

with increasing wavelength for all specimens. High refractive indices at low

wavelengths are due to the effect of the fundamental absorption below

350nm. It was found that the BTO/STO and SZO/STO superlattices with the

periodicity of 10 had higher refractive indices than those of the other

superlattices over the whole wavelength range. The variation of refractive

index at a wavelength of 500nm with the stacking periodicity of the superlattices

is shown in Fig. 32.11. The refractive index shows a maximum at the periodicity

of 10 in both systems. The superlattices with a periodicity of 10 had the

highest anisotropy of crystal lattice as shown in Fig. 32.8. The result in Fig.

32.11 indicates that the lattice distortions induced by the lattice mismatches

change the electronic states affecting electronic polarizations in the superlattices,

giving rise to the variation of refractive index even though the averaged

chemical compositions of the superlattices are identical.

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Dielectric and optical properties of perovskite 985

DIO

Ellipsometry

control computer

A/D (data)

D/A (offset)

DIO (gain control)

GPIB

Incident angle

control

Wavelength

control

Light source

monochromator

Shutter & filter

control

Polarizer

Compensator

Sample

Analyzer

Detector

Signal

Analogue controller

Level

Offset

Meas

Power

Differential amplifier

Gan

GanMatInroads

Input

Output

Power

Radio

width

Offset

Input

32.9

Schematic illustration of rotating-analyzer type spectroscopic ellipsometer.

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Handbook of dielectric, piezoelectric and ferroelectric materials986

Wavelength (nm)

450350 550 650 750 850

Wavelength (nm)

450350 550 650 750 850

(b)

0.50

0.40

0.30

0.20

0.10

0.00

Extinction coefficient (κ)

[SZO

/STO

]

[SZO

/STO

]

[SZO

/STO

]

[SZO

/STO

]

Refractive index (

)

2.5

2.4

2.3

2.2

2.1

2.0

[SZO

/STO

]

[SZO

/STO

]

[SZO

/STO

]

[SZO

/STO

]

Wavelength (nm)

(a)

850750650550450350

Wavelength (nm)

850750650550450350

Extinction coefficient (κ)

0.25

0.20

0.15

0.10

0.05

0.00

Refractive index (

)

2.5

2.3

2.1

1.9

1.7

1.5

[BTO

/STO

]

[BTO

/STO

]

[BTO

/STO

]

[BTO

/STO

]

[BTO

/STO

]

[BTO

/STO

]

[BTO

/STO

]

[BTO

/STO

]

32.10

Optical constant of (a) BTO/STO and (b) SZO/STO superlattices as a function of wavelength.

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Dielectric and optical properties of perovskite 987

32.5 Dielectric properties of artificial superlattices

32.5.1 Electrodes and measuring principle and technique

The selection of substrate is extremely important for the growth of perovskite

superlattices. The (001)-oriented STO single crystal is frequently used for

the substrate of superlattice growth because of its high crystallinity and a

small lattice mismatch with perovskite films. However, for the electric

measurements, superlattices should be deposited on a conductive layer working

as a bottom electrode. The easiest way to meet this demand is the usage of

conductive Nb-doped STO single crystals. We have used this substrate at the

beginning of the research but it gave a serious problem of high leakage

current in the superlattices. Figure 32.12 shows the difference in the leakage

currents between the BTO/STO superlattices deposited on undoped STO and

on Nb-doped STO substrate. The leakage current was measured between two

neighboring electrodes of In on the film surface as shown in the drawing in

Fig. 32.12. The In electrode makes an ohmic contact with semiconductive

oxides. The superlattice deposited on the Nb-doped STO substrate showed a

Stacking periodicity

(a)

403020101

Refractive index (

)

2.4

2.3

2.2

2.1

2.0

1.9

Stacking periodicity

(b)

Refractive index (

)

2.27

2.26

2.25

2.24

2.23

2.22

403020101

32.11

Refractive index of (a) BTO/STO and (b) SZO/STO superlattices

measured at wavelength of 500nm.

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Handbook of dielectric, piezoelectric and ferroelectric materials988

higher leakage current although the substrate was not used as a bottom

electrode. On the other hand, the leakage current of the superlattice on

undoped STO was lower than the measuring limit of the electric current

meter used for the measurement. The high leakage current observed in the

superlattice on the the Nb-doped STO substrate could not be improved by

annealing films in oxygen atmosphere or variation of the stoichiometry of

the films. We believe that the high leakage current is due to the thermal

diffusion of Nb into the film. It may be that some of anomalous dielectric

behaviors reported for artificial superlattices on the Nb-doped STO substrates

may be due to the Maxwell–Wagner polarization between electrodes with

the Schottky barrier.

To avoid the problem of the high leakage current mentioned above, we

tried to measure the dielectric properties of the superlattices on undoped

STO using planar electrodes on the film. Farnell’s theory

is frequently

used to evaluate the dielectric permittivity of films measured with interdigital

electrodes. From this theory, the relation between the dielectric permittivity

of a substance and the capacitance measured with interdigital electrodes is

given by:

= K(ε

+ 1)

= 6.5 + 1.08 + 2.37

() ()

32.1

where C

is the capacitance per unit length, ε

is the dielectric permittivity of

the substance, D is the width of the finger and L is the distance between the

center of two neighboring fingers in interdigital electrodes. The capacitance

Voltage (V)

Electric current (nA)

0–0.5–1.0 0.5 1.0

On undoped STO

On Nb-doped

STO

10000

100000

1000

100

Substrate

Thin film

Top

electrode

(In)

Micro-prober

32.12

Leakage current of BTO/STO superlattices on STO and Nb-

doped STO substrate.

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Dielectric and optical properties of perovskite 989

of a film on a substrate (C) is represented by the capacitance due to the film

and that due to the substrate C

as follows:

C = C

+ (C

– C

)[1 – exp(–4.6h/L)] 32.2

where h is the thickness of film. By combining Eqs. (32.1) and (32.2), the

dielectric permittivity of the film is calculated from the capacitances C and

the permittivity of the substrate ε

. However, Eqs. (32.1) and (32.2) are

accurate only under the conditions that the permittivity of substrate and film

is 50 or less, the finger width D and the space between fingers (L – D) are

equal and the ratio of the film thickness h to the space between fingers

(D – L) is 0.2 or more. These conditions cannot be satisfied in the case of

superlattices with a thickness of about 32nm (80 unit cells of the primitive

perovskite lattice). Therefore, electromagnetic (EM) field analysis (Sonnet,

EM) was employed to calculate the film permittivity from the capacitance

measured with interdigital electrodes. The validity of Farnell’s theory was

simulated at first. The parameters used for the simulation are as follows: the

dielectric permittivity of the substrate is 300 (STO), the film thickness (h) is

32nm, the finger-to-space ratio D/(L – D) is fixed at 0.5 and the finger width

D is changed from 5 to 50µm. The thickness of the substrates and that of the

air above the electrode were 0.5 mm and 10mm, respectively. The results of

the simulation using Farnell’s theory and the EM analysis are compared in

Fig. 32.13 where the capacitance is normalized to that simulated for the

substrate without film. The normalized capacitance increases with decreasing

finger width D in both Farnell’s theory and the EM analysis. Although

Farnell’s theory gave a relatively good approximation when the film permittivity

was low, the capacitance calculated from Farnell’s theory became higher

than that from the EM analysis as the dielectric permittivity of the film

increased. This result indicates that Farnell’s theory overestimates the

permittivity of ultra-thin superlattices and that the EM analysis is indispensable

to determine the dielectric permittivity of the superlattices with high dielectric

permittivity.

The required finger width of interdigital electrodes for the measurements

of superlattices was determined using EM analysis. In this analysis, the

admittance calculated for a substrate (ε

= 300) was compared with that

calculated for the substrate with a film (30nm, ε = 1000). The ∆Y defined by

∆Y = (Y

– Y

)/Y

, where Y

is the admittance of the substrate and Y

is the

admittance of the film and the substrate, is shown in Fig. 32.14 as a function

of the finger width of interdigital electrodes. The ∆Y increases with decreasing

finger width, indicating that the contribution of the film to the admittance

increases with decreasing finger width. The result in Fig. 32.14 shows that

the finger width of interdigital electrodes should be less than 10µm to obtain

reliable admittance data of the film. Based on this analysis, the finger width

was determined to be 5 µm in the final design and the simulation model as

shown in Fig. 32.15.

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