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

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Handbook of dielectric, piezoelectric and ferroelectric materials990

Film permittivity

500040003000200010000

1.25

1.20

1.15

1.10

1.05

1.00

Normalized capacitance

1.03

1.02

1.01

1.00

Film permittivity

900700500300

Farnell_5um

EM_10um

Farnell_10um

EM_5um

Farnell_5um

EM_5um

Farnell_10um

EM_10um

EM_25um

EM_50um

32.13

Capacitance variation with film permittivity and the finger

width of interdigital electrodes calculated using Farnell’s theory and

EM analysis. Capacitance in the

-axis is normalized to the

capacitance calculated for substrate only (without the film). The

notation of Farnell_5um, for example, means the capacitance

calculated from the Farnell’s theory for interdigital electrodes with a

finger width of 5µm.

DDD

Thin film

SrTiO

substrate SrTiO

substrate

Finger width

(µm)

6050403020100

0.14

0.12

0.10

0.08

0.06

0.04

0.02

0.00

∆

= (

–

)

32.14

Change of ∆

= (

–

with the finger width

interdigital electrodes obtained by the EM analysis.

is the

admittance of only substrate (ε

= 300) and

is the admittance of a

film (30nm, ε = 1000) with substrate.

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Dielectric and optical properties of perovskite 991

Another problem in the dielectric measurement of superlattices is the

anisotropy of dielectric properties. The crystal lattices in the superlattices

are distorted in one direction as shown in Fig. 32.8, indicating that the

dielectric permittivity along the film plane (ε

) and that along the film thickness

(ε

) must be different. Figure 32.16 shows the variation of admittance with

the number of fingers in the interdigital electrodes (Fig. 32.15) obtained by

the EM analysis. In this analysis, the relative dielectric permittivity along the

film plane (ε

) was fixed at 5 × 10

and that along the film thickness (ε

) was

changed from 1.0 × 10

to 7.5 × 10

. The values of admittance calculated are

identical in spite of the variation of ε

as shown in Fig. 32.16, leading to a

very important conclusion that the permittivity measured for superlattices

using interdigital electrodes in Fig. 32.15 is the permittivity along film plane

(ε

) of the superlattices.

32.5.2 Dielectric property

Dielectric permittivity of BTO/STO superlattices

The interdigital electrodes shown in Fig. 32.15 were formed on the film

surface using electron beam lithography. The admittance between the

fingers of the interdigital electrodes was measured using impedance

analyzer (HP4294A) connected to a micro-prober system (Measure Jigu,

WN365A1).

300mm

305µm

Thin film

300mm

Port 2

100µm

Port 1

electrode

5µm

32nm

0.5mm

Thin film

SrTiO

substrate

= 300

32.15

Final design and the model of the EM analysis of interdigital

electrodes on superlattice films.

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Handbook of dielectric, piezoelectric and ferroelectric materials992

The dielectric properties of BTO/STO superlattices are shown in Fig.

32.17. The frequency dispersion of capacitance (Fig. 32.17a) indicates that

the capacitance (dielectric permittivity) of the BTO/STO superlattices does

not depend on frequency significantly and that the permittivity of [BTO

STO

]

superlattice is much higher than that of other superlattices. The

dielectric loss tangents of all superlattices are several % or less (Fig. 32.17b).

The dielectric permittivity of superlattices was calculated by fitting admittance

calculated with the EM analysis to that observed. The EM analysis was

repeated with changed permittivity of the superlattices until the best fit was

obtained. The dielectric permittivity so obtained for the BTO/STO superlattices

at 110 MHz is shown as a function of the stacking periodicity of the superlattices

in Fig. 32.17(c). The BTO/STO superlattice with the stacking period of 10

unit cells of perovskite lattice shows the highest permittivity of 33 000

which is remarkably higher than those reported previously.

10,12

However, the

highest permittivity was very sensitive to the quality of superlattices and it

varied from 16000 to 35000 with a slight variation of the deposition conditions.

The charge (Q) vs. voltage (V) curve of the [BTO

/STO

]

superlattice

measured with the interdigital electrodes at 132.5Hz is shown in Fig. 32.17(d).

A linear relation is observed in the Q – V curve. Bulk ceramics of the BTO–

STO system also exhibit large dielectric permittivity with the relaxor or the

diffuse phase transition behaviors. The high permittivity of the bulk ceramics

is accompanied with the nonlinearity of the dielectric permittivity, and it can

be explained by the electric-field-induced orientation of thermally fluctuating

Interdigital electrodes

with finger number 5

Number of fingers

151311579

3.0

2.5

2.0

1.5

1.0

0.5

0.0

Admittance (

) × 10

–4

)

Substrate

Thin film

= 5 × 10

= 10 × 10

– 7.5 × 10

32.16

Admittance as a function of the number of fingers in

interdigital electrodes obtained by the EM analysis. In the analysis,

the permittivity along the film plane (ε

) was fixed at 5 × 105 but that

along the film thickness (ε

) was varied from 1.0×105 to 7.5 × 105. The

admittance is independent of ε

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Dielectric and optical properties of perovskite 993

Frequency (MHz)

(b)

100800604020

Tan δ

1.0

0.8

0.6

0.4

0.2

0.0

[BTO

/STO

]

[BTO

/STO

]

[BTO

/STO

]

[BTO

/STO

]

Stacking periodicity

(c)

403020101

Relative permittivity

40000

30000

20000

10000

(d)

–75

–50

–25

Charge (µQ)

–25 –15 –5 501525

Voltage (V)

[BTO

/STO

]

Frequency (MHz)

(a)

0 20 40 60 80 100

[BTO

/STO

]

[BTO

/STO

]

[BTO

/STO

]

[BTO

/STO

]

Capacitance (pF)

4.0

5.0

3.0

2.0

1.0

32.17

Dielectric properties of BTO/STO superlattices: (a) frequency dispersion of capacitance; (b) frequency dispersion of

loss tangent; (c) relative dielectric permittivity at 110 MHz as a function of stacking periodicity of superlattices; (d)

charge vs. voltage curve of [BTO10/STO10]4 superlattices.

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Handbook of dielectric, piezoelectric and ferroelectric materials994

spontaneous polarization in the polar nano-regions. This type of dipole

polarization always shows nonlinear dielectricity and dielectric dispersion at

relatively low frequencies. However, the high permittivity of the superlattices

does not show any nonlinear behaviors, as shown in Fig. 32.17(d) and the

dielectric relaxation is not observed at frequencies up to 110MHz. We think

that this is a truly remarkable and anomalous dielectric behavior of the

superlattice.

The enhancement of the permittivity was also confirmed in the BTO/STO

superlattices prepared with the RF-magnetron sputtering system shown in

Fig. 32.5(b). The admittances measured with a planar electrode on the [BTO

STO

]

superlattices and on the Ba

0.5

TiO

thin film are shown in Fig.

32.18 as a function of frequency. The planar electrode was designed to

contact a ground–source–ground three terminal probe (Cascade Microtech.)

for high-frequency measurements. The straight lines to fit the experimental

data in Fig. 32.18 were obtained from the EM-analysis. The relative permittivity

of the [BTO

/STO

]

superlattices deposited at 600°C was determined to

be 850, which was much higher than that of the Ba

0.5

TiO

thin film

deposited at 750°C (ε

= 280). The relative permittivity of the [BTO

/STO

]

superlattices was about 750, which was lower than the superlattice with the

periodicity of 10. These results are consistent with those obtained for

superlattices made with the MBE system, indicating that the formation of

superlattices enhanced the permittivity and the degree of enhancement is

enlarged in the superlattices with the periodicity of 10. It is also an important

and anomalous behavior that the superlattice film deposited at a higher

temperature of 650°C showed a lower permittivity (ε

= 510) than that

deposited at 600°C (ε

= 850). This phenomenon can be interpreted by

Frequency (GHz)

2.5 3.02.01.51.00.50.0

10.0

8.0

6.0

4.0

2.0

0.0

Admittance (

) × 10

–3

0.5

TiO

film at 750°C (ε

= 280)

[BTO

/STO

]

at 650°C (ε

= 510)

[BTO

/STO

]

at 600°C (ε

= 850)

32.18

Admittance of BTO/STO superlattices and Ba

0.5

TiO

thin

film as a function of frequency. The solid lines were obtained by the

EM analysis.

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Dielectric and optical properties of perovskite 995

taking into account an interdiffusion of Ba and Sr at the boundary of each

layer during the deposition at high temperatures. Although the enhancement

of the permittivity was confirmed by the superlattices prepared with a different

deposition process, the permittivity of RF-sputtered superlattices was much

lower than that prepared with the MBE process. This is obviously due to the

imperfection of superlattice structures in the sputter-derived films. We could

not, in fact, observe clear satellite peaks in the XRD analysis of the sputter-

derived films. The enhancement of the permittivity is sensitive to the quality

of superlattices. However, the enhancement of the permittivity in the films

deposited with a simple sputtering process has an important meaning for the

practical applications of perovskite superlattices. Decoupling capacitors on

Si-chips are currently demanded for the noise reduction and the stable electric-

current supply to the LSI circuits. The BTO–STO thin films are regarded as

one of the candidates for this application because of their relatively high

permittivity with low loss, but the permittivity at low deposition temperatures

still need to be enhanced at the present. The formation of superlattice-like

structures using simple sputtering process may give a new solution to satisfy

the requirements to the capacitor films.

Mechanism of permittivity enhancement in BTO/STO superlattices

Although the Maxwell–Wagner effects due to the electric conduction have

been pointed out as a mechanism of dielectric enhancements in oxide

superlattices,

we do not think that the anomalous dielectric behavior shown

in Fig. 32.17 is due to these effects because the superlattices showed relatively

low loss tangents, a linear Q–V relation (leakage current gives round shape

in the curve) and dielectric enhancement at high frequencies. It should be also

be noted that the result of dielectric enhancement is consistent with the change

of refractive index (Fig. 32.11) as well as the lattice distortions (Fig. 32.8).

The relaxation of crystal lattices and the stress directions in a BTO film,

a Ba

0.5

TiO

film and a BTO/STO superlattice on a STO substrate are

depicted in Fig. 32.19. A large in-plane compressive stress is applied to the

BTO films from the substrate because of the lattice mismatch between BTO

and STO. The BTO lattices near the substrate are distorted to elongate its c-

parameter (lattice parameter along the film thickness) while keeping the a-

parameter (lattice parameter along the film plane) to achieve the lattice

matching with the STO substrate. These strained lattices are relaxed with

increasing film thickness by introducing dislocations. The similar stress should

be applied to the (Ba

0.5

)TiO

film but the stress is lower than the case of

BTO film because of the smaller lattice mismatch between (Ba

0.5

)TiO

and STO. Therefore, the strained lattices are remained thicker than the case

of the BTO films. In the case of superlattices, the similar compressive stress

is applied to the first BTO layer from the substrate to distort the crystal

WPNL2204

Handbook of dielectric, piezoelectric and ferroelectric materials996

STOSTOSTO

(Ba

0.5

)TiO

BTO

BTO film Solid solution film Superlattice

BTO

STO

BTO

STO

BTO

STO

BTO

STO

32.19

Models of lattice relaxation and the direction of stresses in

films deposited on STO substrates.

lattices of the BTO, but these strained lattices of BTO are not relaxed because

the next STO layers are deposited on the strained BTO lattices to give a new

compressive stress. Owing to the stress induced by the STO layers in the

superlattices, the strained BTO lattices remain up to the film surface. Although

a large stress and a strain are thus induced into the BTO layers, the stress and

strain in the STO layers in the superlattices should be very small because the

stress is hardly induced to the STO layers from the strained BTO layers or

the STO substrate with the same a-parameter.

The ideal cases of the strained lattice formation are observed in the BTO/

STO superlattice with the periodicity of 10, where the a-parameter of the

superlattice is consistent with that of STO (Fig. 32.8). As the staking periodicity

increases to 40, the strained lattices were relaxed as indicated by the change

in the a-parameter. The elongation of c-parameter of BTO lattice stabilizes

and/or enhances the spontaneous polarization of BTO layers along the film

thickness. It should be recalled that the result of the EM analysis indicated

that the permittivity measured with interdigital electrodes was that along the

film plane. This means that the electric field applied in the dielectric

measurements using interdigital electrodes is perpendicular to the direction

of the spontaneous polarization of BTO layers, which is analogous with the

permittivity measurement of a tetragonal BTO single crystal along its a-axis.

It is known that the permittivity along the a-axis of the tetragonal BTO is

much higher than that along the c-axis because of flat potential wells in the

lattice and/or the rotation of spontaneous polarization with electric fields

which contribute to the dipole polarizations. We believe that this is the

mechanism of the enhancement of dielectric permittivity in the BTO/STO

superlattices formed on the STO substrate. The permittivity observed in our

study was much higher than previously reported because we only used planar

electrodes in the permittivity measurements.

WPNL2204

Dielectric and optical properties of perovskite 997

Temperature dependence of permittivity of BTO/STO superlattices

Temperature dependence of the dielectric permittivity provides important

information for understanding the mechanism of the dielectric anomaly of

the superlattices. The high permittivity of BTO-STO ceramics is accompanied

by the phase transition at the Curie point. Even in the relaxors, the formation

of polar nano-regions can be regarded as a precursor phenomenon of the

phase transition. As far as the phase transition is concerned with the generation

of high permittivity, the permittivity inevitably varies with temperature. Figure

32.20(a) shows the complex dielectric permittivity of Ba

0.6

0.4

TiO

ceramics

as a function of temperature.

The ceramics show a large permittivity peak

at about 5°C corresponding to the first-order phase transition. The room

temperature permittivity of about 6000 is due to the tailing of the peak,

therefore the temperature stability of high permittivity cannot be expected in

the ceramics. The real dielectric permittivity of the BTO/STO superlattices

1MHz

100MHz

1GHz

3GHz

Temperature (°C)

(b)

160140120100806040200

25000

20000

15000

10000

5000

Relative permittivity

[BTO

/STO

]

[BTO

/STO

]

[BTO

/STO

]

Temperature (°C)

(a)

3000

1500

ε″

806040200–20–40

15000

12000

9000

6000

3000

ε′

32.20

Temperature dependence of dielectric permittivity;

(a) Ba

0.6

0.4

TiO

ceramics; (b) BTO/STO superlattices.

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Handbook of dielectric, piezoelectric and ferroelectric materials998

with different compositions is shown in Fig. 32.20(b) as a function of

temperature. The permittivity of the [BTO

/STO

]

superlattice is about

19000 at room temperature, which is lower than the result in Fig. 32.17. This

discrepancy is due to the sensitivity of permittivity to the quality of the

superlattices. The dielectric permittivity of the [BTO

/STO

]

superlattices

is higher than other superlattices, namely [BTO

/STO

]

and [BTO

/STO

]

Again, the enhancement of the permittivity in the superlattices with a periodicity

of 10 was confirmed. As for the temperature dependence of the permittivity,

the permittivity increases in all superlattices with increasing temperature

and no peak of the permittivity is observed in the temperature range up to

150 °C. These results strongly suggest that the high permittivity of the

superlattices is not concerned with the phase transition but is caused by the

temperature-stable lattice distortions induced by the lattice mismatch between

STO and BTO.

Artificial ferroelectricity in SZO/STO superlattices

Figure 32.21(a) and (b) shows capacitances and dielectric loss tangents of

the SZO/STO superlattices. It is notable that a large dielectric relaxation was

observed in the superlattices with the periodicity of 1 and 10, which was not

observed in the BTO/STO superlattices in Fig. 32.17. The dielectric loss

tangent of the [SZO

/STO

]

superlattice steeply increases in the low-

frequency region, which obviously indicates the effect of electric conduction.

This superlattice also shows a high extinction coefficient in the optical

frequencies (Fig. 32.10b). We believe that the high loss and high leakage

current observed only in this superlattice are concerned with overlapping of

electron clouds caused by the lattice shrinkage of this superlattice (see the

result of the XRD analysis in Fig. 32.8b). A dielectric loss peak was also

observed at 250kHz in the [SZO

/STO

]

superlattice. The dielectric loss

peak indicates that a polarizing species with a relatively long relaxation time

exists in this superlattice. A similar dielectric loss is observed in the [SZO

STO

]

superlattice but its frequency is lower than that of the [SZO

/STO

]

superlattice. The dielectric loss of the [SZO

/STO

]

superlattice slightly

increases in the low-frequency region. This may be due to the tailing of the

dielectric loss peak at lower frequencies. The peak frequency seems to decrease

with increasing periodicity of superlattices.

The variation of the relative permittivity at 110 MHz with the periodicity

of superlattices is shown in Fig. 32.21(c). The permittivity of the superlattice

with a periodicity of 1 is not reliable because of its high leakage current. The

permittivity decreased with increasing periodicity over the periodicity of 10,

which is similar to the behavior of the BTO/STO superlattices, but the maximum

permittivity of the SZO/STO superlattices is lower that of the BTO/STO

superlattices (Fig. 32.17c).

WPNL2204

Dielectric and optical properties of perovskite 999

32.21

Dielectric properties of SZO/STO superlattices: (a) frequency dispersion of capacitance; (b) frequency dispersion of

loss tangent; (c) relative dielectric permittivity at 110MHz as a function of stacking periodicity of superlattices;

(d) Charge vs. voltage curve.

Dielectric permittivity

20000

15000

10000

5000

Conductive

Stacking periodicity

(c)

403020101

(d)

–200

200

–8 –6 –4 –2

2468

Voltage (V)

[SZO

/STO

]

[SZO

/STO

]

Charge (µQ)

Frequency (Hz)

(b)

Tan δ

[SZO

/STO

]

[SZO

/STO

]

[SZO

/STO

]

[SZO

/STO

]

Frequency (Hz)

(a)

Capacitance (pF)

[SZO

/STO

]

[SZO

/STO

]

[SZO

/STO

]

[SZO

/STO

]

[SZO

/STO

]

WPNL2204