Temperature-dependent dielectric nonlinearity of relaxor ferroelectricPb0.92La0.08Zr0.52Ti0.48O3 thin filmsBeihai Ma, Zhongqiang Hu, Shanshan Liu, Sheng Tong, Manoj Narayanan et al. Citation: Appl. Phys. Lett. 102, 202901 (2013); doi: 10.1063/1.4807665 View online: http://dx.doi.org/10.1063/1.4807665 View Table of Contents: http://apl.aip.org/resource/1/APPLAB/v102/i20 Published by the American Institute of Physics. Additional information on Appl. Phys. Lett.Journal Homepage: http://apl.aip.org/ Journal Information: http://apl.aip.org/about/about_the_journal Top downloads: http://apl.aip.org/features/most_downloaded Information for Authors: http://apl.aip.org/authors

Temperature-dependent dielectric nonlinearity of relaxor ferroelectricPb0.92La0.08Zr0.52Ti0.48O3 thin films

Beihai Ma,1,a) Zhongqiang Hu,1 Shanshan Liu,1 Sheng Tong,2 Manoj Narayanan,1

Rachel E. Koritala,2 and Uthamalingam Balachandran1

1Energy Systems Division, Argonne National Laboratory, Argonne, Illinois 60439, USA2Nanoscience and Technology Division, Argonne National Laboratory, Argonne, Illinois 60439, USA

(Received 29 March 2013; accepted 8 May 2013; published online 22 May 2013)

Rayleigh analysis has been used to investigate the temperature dependence of the dielectric response

of relaxor ferroelectric Pb0.92La0.08Zr0.52Ti0.48O3 films grown on platinized silicon substrates by

chemical solution deposition. The irreversible contribution to dielectric permittivity maximizes at

50 �C and decreases with further temperature increase; while the intrinsic/reversible contribution is

weakly dependent on temperature. The relaxor ferroelectric transition temperature Tm increases from

160 �C to 172 �C when the frequency increases from 1 kHz to 100 kHz. The dielectric nonlinearity

decreases with temperature: falling from 0.012 cm/kV at room temperature to 0.005 cm/kV at 225 �Cin tests at 1 kHz. VC 2013 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4807665]

Ferroelectric lead zirconate titanate (PZT) systems have

been intensively studied in recent years because of their de-

sirable ferroelectric and piezoelectric properties, which make

them potentially useful for various applications such as

nonvolatile digital memories, piezoelectric sensors, micro-

electro-mechanical systems, electro-optical components, and

decoupling capacitors.1–4 The properties of ferroelectric

materials strongly depend on the displacement of the domain

walls. The physical operations of these ferroelectric devices

are significantly influenced by the polarization states and do-

main wall movements under external stimuli such as temper-

ature, stress, and electric field. The contributions to dielectric

and ferroelectric properties can be separated into intrinsic

and extrinsic types, which originate from the single domain

contribution and domain wall motions, respectively.5,6

Several models have been proposed to estimate the domain

wall contributions to the properties of ferroelectric ceramics.

Li et al. extended a phenomenological model to include non-

linear contributions.7 Zhang et al. reported an experimental

method to separate the extrinsic and intrinsic contributions

to the piezoelectric and dielectric response.8 Domain wall

mobility depends on many factors, such as grain structure,

crystalline orientation, space charge, stress distribution, and

defects in the material under investigation.9,10 The relation-

ship between intrinsic and extrinsic responses to an external

applied field of ferroelectric materials can be analyzed in a

manner analogous to magnetization in the ferromagnetic sys-

tems described by the Rayleigh law.11 Even though domain

wall movement and dielectric nonlinearity of ferroelectric

films have been extensively investigated,11–13 majority of the

investigations were focused on piezoelectric PZT and other

ferroelectric materials that exhibit large remanent polariza-

tion. Recently, lanthanum-doped PZT (PLZT) thin films

attracted renewed interest because of their potential for

energy harvesting and energy storage applications.14–17 In

PLZT systems, the degree of relaxor nature is dependent on

the lanthanum content. The ferroelectric long-range order is

broken when the incorporation of La3þ ions causes an excess

of A-site vacancies. This fact results in the formation of

polar nanoregions (PNRs) that are related to the origin of the

relaxor ferroelectric properties in the materials. In this letter,

we report the temperature- and frequency-dependent ferro-

electric and dielectric properties of relaxor ferroelectric

Pb0.92La0.08Zr0.52Ti0.48O3 (PLZT) films grown on platinized

silicon substrates that were measured using small oscillation

fields. By means of a Rayleigh analysis of the data, we were

able to quantify the intrinsic/reversible and irreversible con-

tributions to the dielectric response and to gain a better

understanding of the fundamental physics governing the

domain wall mobility in relaxor ferroelectric PLZT films.

Pb0.92La0.08Zr0.52Ti0.48O3 (PLZT) films were grown on

platinized silicon (PtSi) substrates by chemical solution dep-

osition. Prior to coating, PtSi substrates (500-nm-thick ther-

mally oxidized silicon dioxide coated with 20-nm-thick

titanium oxide and 200-nm-thick platinum (Pt)) were ultra-

sonically cleaned in distilled water, then wipe-cleaned with

acetone and methanol in sequence. A PLZT precursor

solution of 0.5M concentration was prepared by a modified

2-methoxyethanol synthesis route using an appropriate

amount of titanium isopropoxide, zirconium n-propoxide,

lead acetate trihydrate, and lanthanum nitrate hexahydrate.

The PLZT solution contains 20% excess lead to compensate

for the lead loss during heat treatments. Details about stock

solution preparation were reported earlier.18 Before being

used for coating, the PLZT precursor solution was filtered

through polytetrafluoroethylene (PTFE) syringe filters

(Restek Corp., Bellefonte, PA) with 0.22-lm open pore size.

The filtered PLZT precursor solution was spin coated with a

Laurell WS400 spin processor (Laurell Technologies, North

Wales, PA) on PtSi substrates at 3000 rpm for 30 s, followed

by pyrolysis at 450 �C for 5 min, and annealing (crystalliza-

tion) at 650 �C for 5–10 min. After every three layers,

additional annealing was performed at 650 �C for 10 min.

Solution coating and firing were repeated to produce films

of desired thickness. All pyrolysis and annealing were

a)Author to whom correspondence should be addressed. Electronic mail:

bma@anl.gov. Telephone: 630-252-9961. Fax: 630-252-3604.

0003-6951/2013/102(20)/202901/5/$30.00 VC 2013 AIP Publishing LLC102, 202901-1

APPLIED PHYSICS LETTERS 102, 202901 (2013)

performed in air-filled Lindburg tube furnaces. Each layer of

PLZT coating results in a film thickness of �0.115 lm as

determined from scanning electron microscopy (SEM) meas-

urements. Crystalline structure and residual stress of the film

were studied with a Bruker AXS D8 diffraction system. Pt

top electrodes with thickness of �100 nm were deposited by

electron-beam evaporation through a shadow mask to obtain

�250-lm-diameter capacitors. A Signatone QuieTempVR

probe system with heatable vacuum chuck (Lucas Signatone

Corp., Gilroy, CA) was used for electrical characterization.

An Agilent E4980A precision LCR Meter was used to deter-

mine the capacitance and dissipation factor at different fre-

quencies, oscillation and bias fields. A Radiant Technologies

Precision Premier II tester measured the polarization-applied

field (P–E) hysteresis loops.

Figure 1 shows the room-temperature X-ray diffraction

(XRD) pattern of a six-layer PLZT film grown on (111) tex-

tured PtSi substrate. XRD data revealed that the PLZT films

are well crystallized without preferred orientation. All peaks

can be indexed according to a pseudo-cubic perovskite struc-

ture (JCPDS 56-0900), as shown in Fig. 1. The two tiny

peaks at 2h of �34� and �36� marked by open squares are

the PLZT (111) and Pt (111) diffraction peaks associated

with Cu-Kb radiation. The Pt (200) and Pt (220) peaks are

clearly visible from the regular 2h scan diffraction pattern.

The preferred (111) orientation of the PtSi substrates was

verified on the basis of XRD patterns at various tilt angles.

We observed maximum intensity for the Pt (200) peak at a

tilt angle of �55� and for the Pt (220) peak at a tilt angle of

�35�. The cross-sectional SEM image of the six-layer PLZT

film on PtSi (Fig. 1, inset) revealed a dense and uniform

microstructure free of cracks and delamination. The thick-

ness of the PLZT film was determined to be �690 nm from

the SEM image. In addition, an average grain size of

�25 nm was determined from atomic force microscopy

(AFM), and a residual tensile stress of �380 MPa was meas-

ured by x-ray diffraction sin2w method.19

Figure 2(a) shows the relative permittivity (e0) and

dielectric loss (tan d) measured as a function of applied bias

field. The measurement was conducted at room temperature

with an Agilent E4980A LCR meter using a small signal am-

plitude of 100 mV. The curves indicate relative permittivity

e0 � 1200 and dielectric loss tan d� 0.04 at zero applied

field. Both parameters decrease with applied bias filed. The

P–E hysteresis loops measured with various maximum

applied fields are shown in Fig. 2(b). The P–E loops are slim

and indicate low coercive field and small remanent polariza-

tion, which are likely due to small domain dimension and

lack of long-range order in the PLZT films.20 Slim hysteresis

loops with small remanent polarization are desirable charac-

teristics for energy storage applications.14,17

Figure 3(a) shows e0 as a function of frequency meas-

ured between 500 Hz and 500 kHz. Measurements were con-

ducted with a small oscillation signal (E ¼ E0 sin xt) of

various signaling amplitude E0. As shown in Fig. 3(a), e0

increases with increasing ac field amplitude E0 but decreases

with increasing frequency. The linear dependence of e0 on

the logarithm of frequency indicates that extrinsic factors

such as motions of defect charge species and domain wall

movement are the contributing factors to the polarization

under low applied ac field. To quantitatively assess the con-

tribution of the extrinsic effect on permittivity, we plotted e0

as a function of E0. As shown in Fig. 3(b), data measured at

various frequencies fit well to the Rayleigh law21

e0¼e0initþa0E0; (1)

where e0, e0init, a0, and E0 are the real permittivity, initial

(zero field) permittivity, irreversible Rayleigh coefficient,

and the applied ac field amplitude, respectively. Note that

FIG. 1. Room-temperature XRD and cross-section SEM (inset) for six-layer

PLZT film on PtSi.

FIG. 2. (a) Relative permittivity and dielec-

tric loss and (b) P-E hysteresis loops meas-

ured at room temperature on Pt/PLZT/PtSi

capacitors as a function of applied field.

202901-2 Ma et al. Appl. Phys. Lett. 102, 202901 (2013)

e0initin Eq. (1) consists of contributions to permittivity from

the intrinsic lattice polarizability and reversible domain wall

motion. Reversible domain wall motions account for the part

of the domain wall that would, if the field were suddenly

removed, return to the original position, i.e., the state prior to

application of the ac field. The factor a0E0 in Eq. (1) repre-

sents the irreversible displacement of the walls, which

accounts for �25% of the total measured dielectric permit-

tivity at E0¼ 25 kV/cm. The corresponding Rayleigh param-

eters derived from least square fitting of the experimental

data to Eq. (1) are summarized in Table I. The ratio of irre-

versible-to-reversible contributions to dielectric nonlinearity

(a0/e0init) decreases with increasing frequency at room tem-

perature. The a0/e0init ratio determined in this study for PLZT

grown on PtSi substrates is comparable to those reported for

PZT films grown on PtSi substrates.11,22

The low-field P–E hysteresis loops can be described by

analogy to magnetic domain movement with the following

equation:11

P ¼ ðe0init þ a0E0ÞE 6a0

2ðE2

0 � E2Þ; (2)

where the “þ” sign corresponds to decreasing field while the

“�” sign corresponds to increasing field, and E0 stands for

the maximum field applied during the P–E loop measure-

ments. A low-field P–E loop, where E0¼ 72 kV/cm and

frequency¼ 100 Hz, is shown in Fig. 3(c). Experimental data

fit well to Eq. (2).

Figure 4 shows the dependence of e0init, a0, and their

ratio (nonlinearity) with temperature. As shown in Fig. 4(a),

the relaxor ferroelectric transition temperature Tm (corre-

sponding to maximum e0init) was determined from a least

square fitting to a parabola equation. Tm increases from

160 �C to 172 �C when the frequency is increased from

1 kHz to 100 kHz (as illustrated in the Fig. 4(a) inset) exhib-

iting relaxor ferroelectric behavior. We observed a reduced

transition temperature for PLZT grown on PtSi substrates

when compared to those grown on nickel substrates.23 X-ray

diffraction analysis19 revealed that the 690-nm-thick PLZT

film grown on platinized substrates has tensile residual

stress of �380 MPa. This tensile stress leads to reduced Tm

and broadened temperature dependence.23 The irreversible

Rayleigh coefficient a0 peaks at temperature of �50 �C(as shown in Fig. 4(b)) and it decreases with further increase

in temperature. The irreversible Rayleigh coefficient decreases

from �15 cm/kV at room temperature to �7 cm/kV at 225 �Cwhen measured with frequency of 1 kHz. Similarly, the dielec-

tric nonlinearity (a0=e0init) decreases with increasing tempera-

ture from 0.012 to 0.005 cm/kV under the same conditions, as

shown in Fig. 4(c). These data measured at room temperature

are in good agreement with those reported for PZT films of

similar thicknesses.22 The PNRs in locally disordered relaxor

ferroelectric PLZT films are weakly coupled. Mean correlation

FIG. 3. Relative permittivity of Pt/PLZT/

PtSi capacitor measured as function of

(a) frequency and (b) ac field amplitude,

and (c) low-field PE hysteresis loop.

TABLE I. Room-temperature Rayleigh parameter measured for 690-nm-

thick PLZT films grown on PtSi substrates.

Frequency (kHz) a0 (cm/kV) e0 init a0/e0 init (cm/kV)

1 13.82 6 0.40 1218.3 6 5.3 0.0113

10 12.12 6 0.57 1154.1 6 7.5 0.0105

100 9.90 6 0.49 1098.5 6 6.3 0.0090

202901-3 Ma et al. Appl. Phys. Lett. 102, 202901 (2013)

strength of a “connected” network composed of high density

PNRs can be modulated by random fields stemming from struc-

tural and chemical disorder in multivalent relaxors.20 The

decrease in Rayleigh coefficient a0 is likely caused by the

reduction in total PNR volume (both static and dynamic frac-

tions) with increasing temperature.24 The decrease in a0 may

also attribute to increased relaxation time (s) at higher tempera-

tures.25 Diffused temperature dependence in e0init and decreas-

ing a0 lead to a significant decrease in dielectric nonlinearity

a0=e0init with rising temperature. Our results demonstrated that

both intrinsic/reversible and irreversible contributions to dielec-

tric permittivity are temperature dependent.

Figure 5 shows e0init and a0 measured as a function of

frequency at various temperatures. At each temperature, the

relative permittivity was measured at 15 frequencies ranging

from 200 Hz to 200 kHz. Data were fit to Eq. (1) to calculate

e0init and a0 for each frequency and temperature. As shown in

Figs. 5(a) and 5(b), both e0init and a0 decrease linearly with

the logarithm of frequency and can be expressed as26,27

e0init ¼ e0 � e lnðf Þ; (3)

a0 ¼ a0 � a lnðf Þ: (4)

Fitting data in Fig. 5(a) into Eq. (3), we calculated

e0¼ 1401.8 6 2.4 and e¼ 26.54 6 0.26 at 25 �C. The e0

value is, in fact, the extrapolated value for e0init at 1 Hz. The

slope of the curve, e, also known as the “frequency scaling

parameter,” is plotted in the Fig. 5(a) inset as a function

of temperature. Similarly, using Eq. (4), we calculated

a0¼ 19.76 6 0.11 cm/kV and a¼ 0.838 6 0.012 cm/kV at

room temperature. The temperature-dependent frequency

scaling parameter associated with the Rayleigh coefficient is

plotted in the Fig. 5(b) inset. Both frequency scaling parame-

ters decrease with increasing temperature, as shown by the

FIG. 4. Temperature dependence of (a) re-

versible (intrinsic) contribution to permittiv-

ity, (b) irreversible Rayleigh coefficient, and

(c) ratio of irreversible-to-reversible contri-

butions of Pt/PLZT/PtSi capacitors.

FIG. 5. Frequency dependence of (a) revers-

ible/intrinsic contribution to permittivity and

(b) irreversible Rayleigh coefficient meas-

ured at various temperatures; corresponding

scaling parameters are plotted in insets as a

function of temperature.

202901-4 Ma et al. Appl. Phys. Lett. 102, 202901 (2013)

Fig. 5 insets. This finding indicates a reduced domain wall

movement, which is related to the finite time dependence of

domain wall motion. Our data indicate that both the reversi-

ble and irreversible domain wall motion decreased with the

frequency, as the intrinsic relative permittivity should be

independent of frequency in this range.28

In summary, we investigated the nonlinear dielectric

response of PLZT films grown by chemical solution deposi-

tion on PtSi substrates under low ac sweeping field. At room

temperature and 1–100 kHz, the irreversible domain wall

displacement accounts for �25% of the total measured

dielectric permittivity at E0¼ 25 kV/cm. We observed

maxima for the irreversible Rayleigh coefficient at �50 �C.

The irreversible Rayleigh coefficient decreased >50%, from

�15 cm/kV to �7 cm/kV, when the temperature increased

from 50 to 225 �C at 1 kHz. The intrinsic/reversible contribu-

tion to dielectric permittivity exhibits a broad temperature de-

pendent behavior. In addition, the maxima for e0init versus T are

frequency dependent: Tm increases from 160 �C to 172 �Cwhen the frequency is increased from 1 kHz to 100 kHz. The

ratio of irreversible-to-reversible contributions to dielectric non-

linearity (a0=e0init) decreases with temperature at frequencies of

1–100 kHz: dropping from 0.012 cm/kV at room temperature to

0.005 cm/kV at 225 �C in tests at 1 kHz. We observed good

logarithmic dependency with frequency for both e0init and a0.Frequency scaling parameters of both reversible/intrinsic and

irreversible components decrease with temperature.

This work was funded by the U.S. Department of

Energy, Vehicle Technologies Program, under Contract No.

DE-AC02-06CH11357. The electron microscopy was

accomplished at the Electron Microscopy Center at Argonne

National Laboratory, a U.S. Department of Energy Office of

Science Laboratory operated under Contract No. DE-AC02-

06CH11357 by UChicago Argonne, LLC.

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