Intrinsic and extrinsic dielectric responses of CaCu3Ti4O12 thin filmsC. P. L. Rubinger, R. L. Moreira, G. M. Ribeiro, F. M. Matinaga, S. Autier Laurent et al. Citation: J. Appl. Phys. 110, 074102 (2011); doi: 10.1063/1.3644962 View online: http://dx.doi.org/10.1063/1.3644962 View Table of Contents: http://jap.aip.org/resource/1/JAPIAU/v110/i7 Published by the American Institute of Physics. Related ArticlesOrigin of the dielectric response in Ba0.767Ca0.233TiO3 Appl. Phys. Lett. 100, 102908 (2012) The extrinsic origins of high permittivity and its temperature and frequency dependence in Y0.5Ca0.5MnO3 andLa1.5Sr0.5NiO4 ceramics J. Appl. Phys. 111, 054106 (2012) The effect of the spatial nonlocality of the Kirkwood g-factor on the determination of the long wavelengthdielectric functions in dipolar fluids J. Chem. Phys. 136, 084502 (2012) Improved dielectric functions in metallic films obtained via template stripping Appl. Phys. Lett. 100, 081105 (2012) Dielectric and magnetic properties of Y3−xTbxFe5O12 ferrimagnets J. Appl. Phys. 111, 07A521 (2012) Additional information on J. Appl. Phys.Journal Homepage: http://jap.aip.org/ Journal Information: http://jap.aip.org/about/about_the_journal Top downloads: http://jap.aip.org/features/most_downloaded Information for Authors: http://jap.aip.org/authors

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Intrinsic and extrinsic dielectric responses of CaCu3Ti4O12 thin films

C. P. L. Rubinger,1,2 R. L. Moreira,2,a) G. M. Ribeiro,2 F. M. Matinaga,2 S. Autier Laurent,3,4

B. Mercey,3 and R. P. S. M. Lobo5

1Departamento de Fısica e Quımica, Universidade Federal de Itajuba, CP 50, 37500-903, Itajuba,Minas Gerais, Brazil2Departamento de Fısica, Universidade Federal de Minas Gerais, CP 702, 30123-901 Belo Horizonte,Minas Gerais, Brazil3Laboratoire CRISMAT, CNRS UMR 6508, ENSICAEN, 6 Bd du Marechal Juin, F-14050, Caen Cedex,France4Laboratoire de Physique des Solides, Universite Paris-Sud, CNRS, UMR 8502, F-91405 Orsay Cedex, France5Laboratoire de Physique et Etude des Materiaux, ESPCI, CNRS, Universite Pierre et Marie Curie, 10 rueVauquelin, F-75231 Paris Cedex 5, France

(Received 13 July 2011; accepted 17 August 2011; published online 4 October 2011)

CaCu3Ti4O12 thin films were epitaxially grown on (001) LaAlO3 substrates by pulsed laser

deposition under optimized growth conditions. The crystal structure and sample morphology were

characterized by x-ray diffraction, AFM, TEM, ellipsometry, and Raman spectroscopy. The dielec-

tric responses of the films were investigated in a large temperature range (5 to 375 K) by infrared

reflectivity and impedance spectroscopies. The films exhibited a colossal dielectric response, with

the dielectric permittivity reaching 104 at 100 Hz. The results obtained in a broad frequency range

allowed us to investigate the behavior of intrinsic and extrinsic dielectric responses of this material.

The room temperature centrosymmetrical cubic structure remains stable down to 5 K, though soft-

ening of the lower frequency infrared phonon modes indicates an incipient ferroelectric character.

The radio frequency dielectric response reveals two relaxations of extrinsic origin, a primary higher

frequency relaxation responsible for the colossal dielectric behavior and a secondary one of lower

frequency. The activation energies of these processes are compatible with the presence of shallow

defect levels created by oxygen vacancies. VC 2011 American Institute of Physics.

[doi:10.1063/1.3644962]

I. INTRODUCTION

CaCu3Ti4O12, henceforth referred to as CCTO, is a

perovskite-related oxide that presents a colossal dielectric

constant (CDC) of about 104 to 105 (at 100 Hz), in a wide

temperature range (100 to 600 K).1–4 The dielectric permit-

tivity abruptly lowers to a value of the order of 102 below

100 K,2,3 which is comparable with the infrared “static” per-

mittivity extrapolated to 1011 Hz.3 The CDC effect has been

demonstrated for CCTO bulky crystals,1–4 ceramics,5,6 and

for thin films.7–11 However, the origin of such an extraordi-

nary effect has been a matter of debate for many years.

Indeed, the crystal structure of CCTO remains centrosym-

metrical down to low temperatures (�5 K),1–3,12 which for-

bids ferroelectricity. Moreover, its low frequency (100 Hz)

dielectric permittivity remains approximately constant

between 100 and 600 K, with no signature of Curie-Weiss

behavior. The relaxor effect was also considered to explain

the CDC response of CCTO.3 Once again, the constancy of

the radio-frequency dielectric permittivity rules out this pos-

sibility (there is no signature of the Smolenski-Isupov law,

which requires decreasing permittivities with temperature).

Therefore, it has been now well accepted (and demonstrated)

that the main origin of the CDC effect in CCTO has an ex-

trinsic origin, i.e., it is linked to the semiconducting nature

of the material, and to the presence of intentional or non-

intentional charged defects that act as charge carriers.5,6,12–23

The very high dielectric permittivity of CCTO within

large temperature and frequency intervals turns it into a

highly suitable material for technological applications, such

as components of capacitive memories and mobile

phones.1,24 In particular, CCTO thin films allow one to fabri-

cate capacitors with very high capacitance for application in

specific devices, when compared with single crystals and

ceramics. Such CCTO thin films have been grown over dif-

ferent substrates (LaAlO3, SrTiO3, Pt/TiO2/SiO2/Si, Pt/Si or

LaNiO3/Pt) by pulsed laser deposition (PLD),7–11,25–28 metal

organic chemical vapor deposition29 or by sol-gel meth-

ods.30,31 The CCTO thin films grown directly over LaAlO3

and SrTiO3 single crystal substrates usually exhibit better

epitaxial quality because of better lattice parameter matching

and chemical compatibility.

In order to investigate the role of intrinsic and extrinsic

contributions for the CDC of CCTO we have performed infra-

red reflectivity and dielectric spectroscopic investigations of

optimized CCTO thin films, grown directly onto LaAlO3 sub-

strates. The low frequency infrared phonon modes show soft-

ening at low temperatures, which are responsible for an

increase of the “static” infrared dielectric constant from 80 at

room temperature to about 115 at 5 K. These changes follow

a Curie-Weiss law with negative Curie temperature, charac-

teristic of incipient ferroelectric materials. Radio-frequency

dielectric spectroscopy shows the CDC effect (dielectric

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

bmoreira@fisica.ufmg.br.

0021-8979/2011/110(7)/074102/8/$30.00 VC 2011 American Institute of Physics110, 074102-1

JOURNAL OF APPLIED PHYSICS 110, 074102 (2011)

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constant up to 104), however, the relaxation frequency reveals

an unexpected thickness dependency. The related complex

impedance plots show two slightly depressed arcs in all tem-

perature intervals investigated, which is characteristic of the

Maxwell-Wagner relaxation processes linked to a heterogene-

ous structure of the samples. The radio-frequency relaxations

are discussed together with ac-electrical conductivity and

activation energies, revealing the role of anionic defects on

the observed CDC effect.

II. EXPERIMENTAL

The CaCu3Ti4O12 thin films were grown by pulsed layer

deposition (PLD) over the (001) pseudo-cubic direction of

LaAlO3 (LAO) substrates. The substrates were cut into

square slabs (5 mm� 5 mm� 0.5 mm), in which the edges

were parallel to the [100] pseudo-cubic axes of LAO. A high

density and high purity CCTO target was prepared by a solid

state reaction route. The (001) LAO single crystals were cho-

sen as substrates because of the relatively small lattice mis-

match of 2.2% between the sample and substrate with this

growth direction (2a¼ 2� 3.778 A for LAO,32 and

a¼ 7.391 A for CCTO (Ref. 1)). A pulsed KrF excimer laser

(Lambda Physik) with a 248 nm wavelength with energy up

to 250 mJ was used for the epitaxial growth of the CCTO

films. The optimal conditions for producing highly epitaxial

films were determined by maximizing the intensity of the

strongest (004) diffraction peak of CCTO (Seifert XRD

3000P system with Cu Ka1 radiation), for films produced

after 6000 pulses.33 The optimized growth parameters were a

laser energy of 210 mJ, a repetition rate of 2 Hz, a target-

substrate distance equal to 51 mm, a substrate temperature of

740 �C, an oxygen atmosphere (0.20 mbar) during film

growth, and cooling (10 �C/min) to room temperature. The

films obtained under these conditions crystallized in a cubic

cell with a lattice parameter of 7.39 A, which is in agreement

with the unit cell parameter of the bulk CCTO.1 No evidence

for a secondary phase or a different growth direction relative

to the substrate was observed. Rocking curve measurements

performed around the most intense reflection (004) gave a

full width at half maximum of 0.56�, indicating good film

crystallization. The samples were also characterized by

atomic force microscopy (AFM) and transmission electron

microscopy (TEM, image and diffraction modes), which

showed good quality (surface roughness of 1.05 nm, homo-

geneous grains of approximately 100 nm diameter) and epi-

taxial ([001]CCTO//(001)LAO and [100]CCTO//[100]LAO) films.

These films presented adequate electrical and dielectric pa-

rameters compared to pure CCTO bulk samples that present

the CDC effect: an electrical resistivity of 200 X cm and a

dielectric constant at 100 Hz of 12 000, at room temperature.

The samples studied here were 160 nm (6000 pulses) and

320 nm (12000 pulses) thick, respectively. Film thicknesses

were determined by infrared reflectivity measurements and

confirmed by ellipsometry (Woollam M2000), from the

spectral fittings for finite systems.

Polarized micro-Raman scattering spectra of CCTO

films were collected in back-scattering configuration using

an Olympus confocal microscope attached to a Jobin-Yvon

T64000 spectrometer (objective: 80�, 600 grooves/mm dif-

fraction grating). The 532 nm line of an YVO4:Nd laser

(Coherent Verdi V6) with 4 mW at the sample’s surface was

used as the exciting source and the scattered light was

detected by a liquid-nitrogen-cooled charge coupled device

(CCD), after stray light rejection by an appropriate edge fil-

ter. The spectral resolution was better than 2 cm�1, and the

spectra were obtained by averaging four accumulations of

100 s. The scattering geometries, assured by polarizers and a

half-wave plate, were chosen with incident and scattered

electric fields oriented accordingly to the LAO pseudo cubic

directions. We used the classical notation (xixj), for incom-

ing (xi) and outcoming (xj) light beam polarizations.

Near-normal-incidence infrared reflectivity spectra were

measured from 30 to 8000 cm�1 in a Bruker IFS-66V Fou-

rier transform spectrometer, using appropriate combinations

of sources, beamsplitters and detectors, i.e., Hg lamp, Si and

Mylar-Ge beamsplitters, and Si bolometer below 700 cm�1;

SiC lamp, Ge-coated KBr beam splitter, and DTGS detector

above 500 cm�1. A gold mirror was used as a reference. The

spectra were recorded, in the whole range, at several temper-

atures from 5 to 300 K. The agreement between the reflectiv-

ity spectra in the overlapping regions was better than 1%.

The obtained spectra were treated within the classical Lor-

entz model for finite systems (including the substrate reflec-

tion), as discussed in the next section.

Two 300 A-thick gold electrodes of 2 mm� 5 mm each,

separated by 0.5 mm, were thermally evaporated on the top

surface of the CCTO films. Impedance measurements were

carried out on these samples using an HP4192 A impedance

analyzer, in the frequency range of 10 Hz to 10 MHz, with

an applied sinusoidal field of 100–1000 mVrms (no bias

field). All of the measurements were carried out in an Oxford

exchange gas cryostat from 375 down to 175 K. The cryostat

head was modified to use BNC connectors, such that thin 50

X teflon-coated coaxial cables were used inside the cryostat

from the connectors to the sample holder. The total coaxial

cable length was about 1 m, which allowed the HP4192 to

perform the measurements at the whole frequency range

with negligible parasitic effects. Open and short circuit cor-

rections were considered for the measurements.

III. RESULTS AND DISCUSSIONS

The crystalline quality and the epitaxial growth of the

CCTO films have been investigated in detail by Raman spec-

troscopy. CCTO crystallizes in the cubic Im�3 (Th, #204)

space group, with 20 atoms in the primitive cell.1 Group

theory analysis of CCTO crystal foresees eight active first-

order Raman modes at the Brillouin zone center (C-point),

which decomposition into irreducible representations gives

2 Ag� 2Eg� 4 Fg.12 Figure 1 presents the polarized Raman

spectra of the 320 nm CCTO film, for four different scatter-

ing configurations (relative to the LAO substrate), that

allows for separating the first-order modes of CCTO into

their respective symmetries. For the parallel-polarized meas-

urements, we used the configurations xx and x0x0, where x

and x0 mean, respectively, the (100) and (110) pseudo-cubic

LAO directions. Two crossed polarizations, xy and x0y0 were

074102-2 Rubinger et al. J. Appl. Phys. 110, 074102 (2011)

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also used, where the y and y0 directions are, respectively,

parallel to the (010) and (�110) LAO pseudo-cubic axes.

Supposing that the cubic CCTO axes are parallel to the

pseudo-cubic LAO ones, as suggested by XRD and electron

diffraction data, the used configurations would give the fol-

lowing selection rules for the Raman spectra of CCTO: xx (2

Ag� 2Eg); x0x0(2 Ag� 2Eg� 4 Fg); xy (4 Fg) and x0y0 (2Eg).

The spectra of Fig. 1 show well defined and well polar-

ized first-order Raman bands of our CCTO film. Indeed, as

shown by Kolev et al.,12 five of the eight predicted Raman-

active modes are strong enough to be discerned in the polar-

ized Raman spectra of the CCTO single crystals, appearing

at 292 cm�1 (F2 g symmetry), 445 cm�1 (Ag), 499 cm�1

(Eg), 511 cm�1 (Ag), and 575 cm�1 (Fg). These five modes

have been discerned in the spectra of our PLD films, at

approximately the same positions (after fitting with Lorent-

zian lines), and with the correct symmetries, confirming that

the cubic CCTO axes are parallel to the pseudo-cubic LAO

ones. The depicted peak positions and the symmetries for

cubic CCTO are indicated in the figure. The mode at 499

cm�1 (single crystal) presented a considerable upshift to 505

cm�1 (160 nm film, not shown here) or 503 cm�1 (320 nm

film). For the other modes (except for the band at 575 cm�1),

a small upshift of, at most, 2 cm�1 was observed for the thin-

ner sample (160 nm). The upshifts were always smaller for

the thicker sample, tending to the values of the single crys-

tal,12 indicating that this frequency upshift is a consequence

of small stresses induced by the substrate. It is worth notic-

ing that the observed wavenumber upshifts presented by our

samples are smaller than those observed by other authors on

their PLD films, showing that the stresses in our films are

well relaxed.25,27 Moreover, our results show a very well ori-

ented film, in contrast with the results of Litvinchuk et al.25

(CCTO onto LAO substrate) and Srivastava et al.27 (CCTO

onto Pt/Si), whose spectra showed broad bands that could

not be resolved by polarization, which is characteristic of

randomly oriented films.25

Besides the characteristic Raman modes of CCTO, the

spectra of Fig. 1 show some additional features: four bands

relative to the LAO substrate (three allowed first-order

modes at 124, 154, and 487 cm�1 and a faint defect-induced

mode at 201 cm�1),34 and five weak additional bands of the

films (marked by asterisks) that are not first-order Raman

modes at the Brillouin-zone center of CCTO. Some of these

bands were also observed by other authors, in particular, the

defect mode around 620 cm�1 observed in single crystals (at

high temperatures),12 PLD films,25 or ceramics.27 The mode

around 455 cm�1 was observed at low temperatures in a

CCTO single crystal. It was tentatively attributed to distorted

TiO6 octahedra probably lying at twin boundaries.12 This

mode appeared in our films at room temperature, indicating

the presence of twin boundaries at these temperatures, prob-

ably generated by the multiple domains of rhombohedrally

distorted LAO.34 Kolev et al. observed that a band around

400 cm�1 could be one of the missing F2g modes.12 The ori-

gin of the remaining features at 220 and 243 cm�1 is

unknown; they are likely defect-activated silent modes or

off-center zone modes with momentum conservation assured

by defects.

As a whole, the Raman spectra of the CCTO films con-

firmed the high crystalline quality of the PLD films along

with their excellent in-plane and out-of-plane orientations.

The peak positions were very close to those observed for a

single crystal, showing a relaxed structure, in agreement

with the x-ray results.

The intrinsic (infrared) and extrinsic (radio-frequency)

dielectric response of our epitaxially grown CCTO thin films

have been investigated from 5 to 375 K. The top panel of

Fig. 2 shows the infrared reflectivity data of the room tem-

perature spectrum of the 320 nm CCTO film on the LAO

substrate (dots), fitted by a Lorentz oscillator model (solid

black line), which takes into account the LAO substrate con-

tribution (gray line) because of the relative transparency of

this thin film.25,35 The red line is the CCTO spectrum decon-

voluted from the substrate. This model assumes a film of

thickness d and a complex refraction index nf, on a semi-

infinite substrate of complex refraction index ns. This

approximation means that reflections from the back surface

of the substrate can be neglected. The quasi-normal inci-

dence infrared reflectivity (R) is given by,

R ¼ r0 þnf t

20rf /

2f

1þ rf r0/2f

�����

�����

2

; (1)

where r0¼ (1 – nf)/(1þ nf), t0¼ 2/(1þ nf), rf¼ (nf – ns)/

(nfþ ns), and /f¼ exp(2 p i nf d/k); k being the wavelength

of the light. The optical properties of the LAO substrate (ns)

are measured separately and R is fitted assuming a model

dielectric function for the film,

e xð Þ ¼ n2f xð Þ ¼ e1 þ

X

j

DejX2j;TO

X2j;TO � x2 � icj;TOx

; (2)

where e1 is the electronic polarization contribution and

Xj,TO is the transverse optical (TO) frequency with damping

cj,TO and dielectric strength Dej for the jth polar phonon

mode.

FIG. 1. (Color online) Polarized micro-Raman spectra for the CaCu3Ti4O12

film (320 nm) onto a LaAlO3 substrate, for four special scattering configura-

tions that allows for separating the symmetries of the first-order modes of

CCTO. Defect modes are indicated by asterisks. The Raman modes of LAO

are also indicated.

074102-3 Rubinger et al. J. Appl. Phys. 110, 074102 (2011)

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The infrared dispersion parameters, phonon wavenum-

bers Xj,TO and dampings cj,TO, in cm�1, and the dielectric

strengths, Dej, obtained from the fits of the 320 nm CCTO

thin film on the LAO substrates at 5 and 300 K, are presented

in Table I. Nine of the eleven predicted Fu modes12 were

observed, with phonon parameters close to those obtained

for single crystals14,36 and ceramics.21,37 The fits also gave

the limit values of the dielectric permittivity, e1¼ 6.32 and

er (¼ e1þRj Dej)¼ 80 for this film (at 300 K), which are

comparable to values found for single crystals,3,36 even

though one mode appearing around 421 cm�1 for the single

crystals was missing in our spectra. It is worth noting that

this mode was also missing in the infrared spectrum of a 300

nm CCTO thin film reported by Litvinchuk et al.25 and that

those authors found quite a high value for er at room temper-

ature (er¼ 148), in contrast to our results. The origin of

this high value for the permittivity is related to the individual

polar phonon behavior, as discussed in the following text.

In order to obtain a better comparison between the

behavior of our observed polar phonon modes and those

reported in the literature, we present in Table II the infrared

(TO) phonon wavenumbers, in cm�1, obtained for our 320

nm and 160 nm CCTO thin films, at low and room tempera-

tures, beside the reported data for single crystals14,36 and

thin films.25 Considering the room temperature results, we

observe that, in general, the modes of our CCTO films are

slightly downshifted (by less than 2 cm�1), in comparison to

the single crystal values of Ref. 14. The only exceptions are

the modes around 250 cm�1 (the bending mode of TiO6)

and 550 cm�1 (the TiO6 stretching mode) that presents a

larger downshift (up to 6 cm�1). The mode at about 250

cm�1 is sensitive to the (TiO6) octahedral tilting, with the

latest one to the Ti displacement inside those octahedra. As a

whole, these results could indicate some influence of a faint

tetragonal distortion because of the CCTO/LAO mismatch

on the atomic displacements, acting like a stretching of the

CCTO lattice. Anyway, the relatively small shifts show that

our films have rather relaxed lattices (in agreement with our

previous Raman data). On the contrary, Litvinchuk et al.25

found an important upshift in the phonon modes below

300 cm�1, followed by an appreciable downshift in the

higher wavenumber phonons, which they attribute to a devia-

tion of the oxygen stoichiometry in their samples, discarding

FIG. 2. (Color online) Top panel: room temperature experimental infrared

spectrum (dots) of CCTO film (320 nm) onto the LAO substrate along with

its adjustment with the Lorentz oscillator model (black line), which takes into

account the LAO substrate contribution (gray line). The CCTO deconvoluted

spectrum is shown by the red line. Bottom panels: the temperature behavior

of adjusted real parts of the dielectric constant (left) and optical conductivity

(right), in the region of the four lowest frequency polar phonons.

TABLE I. Infrared dispersion parameters: TO phonon wavenumbers (Xj,TO)

and dampings (cj,TO) in cm�1, and dielectric strengths (Dej), obtained from

the fittings of the 320 nm CCTO thin film on LAO substrates, at 5 K and

300 K. Two extra modes, likely activated by defects (around 175 cm�1) or

LAO leakage (187 cm�1), are in parentheses.

5 K 300 K

Xj,TO cj,TO Dej Xj,TO cj,TO Dej

117.7 4.78 55.75 121.9 4.17 20.30

136.1 2.75 14.99 140.0 6.72 18.58

159.5 4.79 8.08 160.7 5.61 7.30

(175.0) 7.00 9.00 (173.9) 3.97 3.64

(187.1) 2.72 3.87 (185.4) 2.13 1.20

196.0 2.56 5.32 198.5 6.46 7.67

242.5 6.35 7.18 247.6 8.79 11.11

308.1 2.68 0.46 306.8 5.72 0.53

381.2 5.25 1.62 381.0 19.02 2.37

505.9 11.42 0.70 503.3 16.59 0.67

551.8 10.27 0.33 549.6 19.03 0.45

e1¼ 6.32 er¼ 113.62 e1¼ 6.32 er¼ 80.14

TABLE II. Infrared TO phonon wavenumbers (in cm-1) obtained for the

320 nm and 160 nm CCTO thin films onto LAO substrates, at low and room

temperatures, compared with reported data for single crystals (Refs. 14 and

36) and thin films (Ref. 25).

Single crystals Thin films onto LAO substrates

300 nm 320 nm 160 nm

5 Ka 295 Kb 295 Kc 5 K 300 K 10 K 300 K

119.2 122.3 124 117.7 121.9 117.2 121.6

134.5 140.8 146 136.1 140.0 135.8 139.4

158.1 160.8 164 159.5 160.7 158.9 160.3

– (175.0) (173.9) (178.2) (176.5)

(181) (187.1) (185.4) (187.9 (187.0)

195.1 198.9 205 196.0 198.5 196.3 198.1

250.4 253.9 258 242.5 247.6 247.9 251.1

307.7 307.6 304 308.1 306.8 308.3 307.3

382.9 382.1 378 381.2 381.0 382.0 376.3

421.3 421.0 410 – – – –

506.9 504.2 502 505.9 503.3 506.2 503.3

551.6 552.4 550 551.8 549.6 551.5 549.1

aReference 36.bReference 14.cReference 25.

074102-4 Rubinger et al. J. Appl. Phys. 110, 074102 (2011)

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the influence of the tetragonal distortion. Therefore, we can

conclude that the intrinsic phonon mode behavior of thin

films with the correct stoichiometry is quite close to that of

single crystals.

Before discussing the low temperature results, we remark

that two extra modes were observed around 175 and 185

cm�1. A mode at 181 cm�1 was also observed by Litvinchuk

et al. in their thin films.25 This extra mode is practically at the

same position as the lowest frequency LAO mode of Eu sym-

metry,34 that was indeed considered in the fits. Thus, this

mode can be an artifact of the fitting procedure. Concerning

the 175 cm�1 mode, it is likely a silent mode activated by

defects or by the stresses due to the tetragonal distortion.

Let us now discuss the temperature behavior of the polar

phonon modes of our CCTO thin films. An inspection of

Table II shows that, at low temperatures (5 or 10 K), the pho-

non positions are still very close to those depicted for the

CCTO single crystals. Indeed, the difference remains within

2 cm�1 (except for the mode around 250 cm�1). This con-

firms that our films have well relaxed lattices, close to that of

single crystals. In particular, the softening of the lowest fre-

quency CCTO modes (below 300 cm�1) and the hardening

of the highest frequency ones (above 300 cm�1) at low tem-

peratures is evidenced in our thin films, as it is in the single

crystals.3,36 (Note that the extra modes harden at low temper-

ature). The phonons above 300 cm�1 present a classical

anharmonic behavior, while the five lowest frequency modes

behave differently, as already observed by other authors

studying CCTO single crystals3,36 and ceramics.37 The soft-

ening of these modes has been attributed to the charge redis-

tribution between ions within the unit cell,3,37 although

ferroelectric instability has also been suggested, though not

explored, at their origin.3,38,39 Our low-temperature data has

allowed us to discuss this point in more detail.

The bottom panels of Fig. 2 present the temperature evo-

lution of the adjusted real parts of the dielectric permittivity

(left) and of the optical conductivity (right) for the 320 nm

CCTO film, in the region of the four lowest frequency polar

phonons. These figures show the softening and narrowing of

these modes, besides the increasing of the “static” infrared

permittivity, with decreasing temperature. These results are

completely analogous to those observed for single crystals,

which were initially interpreted as a consequence of a charge

transfer within the unit cell with increasing oxygen effective

charges.3,37 However, the dielectric permittivity limit at lower

wavenumbers is twice as large as the predicted Clausius-

Mosotti value (48.5),40 which is calculated for perfect ionic

crystals (effective charges equal to oxidation states). Thus,

the anomalous phonon softening must have a different origin.

It has been suggested that CCTO could be an incipient

ferroelectric, similarly to Mn-doped CCTO,41 and to the iso-

structural compound Na1/2Bi1/2Cu3Ti4O12 (NBCTO).39,42

The low temperature dielectric properties of incipient ferro-

electrics are influenced by quantum fluctuations, which led to

deviations of the Curie-Weiss law. Barrett43 derived a simple

equation for the permittivity of the incipient ferroelectrics,

er ¼M

ðT1=2Þ cothðT1=2TÞ � T0

þ B; (3)

where T1 is the crossover temperature between classical and

quantum behavior, T0 is the Curie-Weiss temperature, M is a

Curie-Weiss-like constant, and B is a temperature independent

parameter. This latest parameter corresponds to the asymptotic

er value at high temperature, and therefore, it should be close

to the Clausius-Mosotti dielectric constant (which does not

account for the dynamics of the ferroelectric soft mode,

reflected only in the temperature dependent part of Eq (3)).

In Fig. 3 we plot the temperature dependence of the

“static” infrared dielectric permittivity (er) for our CCTO

films, for the samples 160 nm (red squares) and 320 nm thick

(blue circles). The dashed and solid lines correspond to fits

to the Curie-Weiss and to Barrett’s equations, respectively.

We can see that, within the experimental accuracy, our data

fit well with Barrett’s expression (the deviation from Curie-

Weiss is clear), confirming the incipient ferroelectric charac-

ter of the frustrated transition. The fitting parameters for the

320 nm film were 9700 K, 179 K, �74 K, and 55 K, for M,

T1, T0, and B, respectively. Note that B is quite close to the

Clausius-Mosotti value, which is a good indication of the

validity of the fitting. Thus, in order to estimate the uncer-

tainties in the fitting parameters, we fixed the B parameter

(the B uncertainty with all parameters free was 20). Then,

we found for this film: M¼ 9700(1300) K, T1¼ 179(44) K,

T0 ¼�74(41) K, and B¼ 55 K. For the 160 nm film, the

dielectric permittivity was lower by �10 for all tempera-

tures, which yielded the worst fitting parameters. We believe

that the partial transmittance of this thinner film was respon-

sible for a lower reflectivity, decreasing the measured

dielectric permittivity. Therefore, we will not consider the

quantitative results of the fittings of this film.

The previously discussed results indicate that pure CCTO

should be an incipient ferroelectric. The meaning of the B pa-

rameter was already discussed. The Curie-like parameter M is

relatively low compared to that of Mn-doped NBCTO.39 This

can have several origins, such as the B value higher than the

Clausius-Mosotti one, experimental uncertainties, or some

FIG. 3. (Color online) Temperature dependence of the “static” infrared

dielectric permittivity (er) for the CCTO films on the LAO substrate for films

with 160 nm (red squares) and 320 nm (blue circles). The dashed and solid

lines correspond to the fittings to the Curie-Weiss and to Barrett’s equations,

respectively.

074102-5 Rubinger et al. J. Appl. Phys. 110, 074102 (2011)

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influence of Mn doping, however, coupling between the low-

est frequency modes could lower the M parameter, as

explained in the following. Indeed, our T1 parameter means

that the quantum fluctuations in CCTO would start around 180

K and that the zero-point vibrational energy ([1/2]kBT1, where

kB is the Boltzmann constant) would be close to 60 cm�1 (7.5

meV). This would be the freezing value for the soft-mode fre-

quency. However, the lowest measured frequency mode is

about twice as large at low temperatures. This should be a con-

sequence of the large coupling between this mode and the sub-

sequent four modes, which is responsible for reducing the soft

mode behavior, increasing the freezing phonon frequency and

limiting the maxima value of the dielectric permittivity (and

therefore, the M value). Finally, our T0 value (�74 K) is quite

close to that obtained for NBCTO:Mn (�79 K). The negative

sign of T0 means that the centrosymmetric (paraelectric) state

remains stable down to 0 K, i.e., CCTO is a (geometrically)

frustrated ferroelectric, as suggested by Homes et al.3

Since we have obtained some information on the intrinsic

phononic response of our CCTO films, let us now discuss their

dielectric behavior at radio-frequency range. Because of the

semiconducting nature of CCTO, several authors reported a

considerable contribution of the sample/electrode interface

polarization to the measured low-frequency capacitance for dif-

ferent metal contacts.23,28,44–47 In our case, where gold top

electrodes were used, we did not observe any nonlinear features

in the dielectric response of the samples; in the ac-voltage

range used (100 to 1000 mVrms). Our results are in agreement

with other authors who also used Au-top electrodes for study-

ing their thin films.10,29 A possible reason for these different

behaviors can also be related to the doping level of the materi-

als, once Yang et al. had shown that the electrode effects appear

only for samples with surface resistivity below 108 X cm.48

The top panels of Fig. 4 present the frequency depend-

ence of the real dielectric permittivity for CCTO films with

160 and 320 nm thicknesses, for several temperatures

between 175 and 375 K. Once there is no signature of any

relaxation between 1 MHz and microwave frequencies in the

temperature region investigated, we used as the relaxed

value at the MHz region the “static” infrared values meas-

ured in these samples (from the Barrett’s curves of Fig. 3, ex-

trapolated up to 375 K). Figure 4 shows that the dielectric

permittivity changes by more than two orders of magnitude

in the five frequency decades presented. The lowest fre-

quency values (�20 000 at room temperature) and the

relaxational behavior are similar to reported results for single

crystals,1–4,36 ceramics,5,16,19,21,49 and thin films.8,9,11,26,27

However, our results reveal an interesting thickness depend-

ence of the relaxation frequency, which is clearly shown in

the bottom panel of Fig. 4. This figure shows that the drop of

the CDC response to the relaxed (phononic) values for single

crystals (full symbols, from Ref. 3) occurs at lower tempera-

tures than for our thin films (semi-hollow symbols for 320

nm film, hollow for 160 nm film). This thickness dependence

constitutes an important issue in view of technological appli-

cations of thin films, when a high dielectric response would

be required in large temperature-frequency regions. In order

to understand its origin, we need to investigate more thor-

oughly the related semiconducting properties of the films.

In Fig. 5 we present the ac-electrical conductivity of the

320 nm CCTO film, in an Arrhenius plot, showing an acti-

vated conduction mechanism. The curves for different fre-

quencies are straight lines with the same slope, however, the

higher frequency responses present an increasing deviation

at lower temperatures. This deviation is due to the tail of the

optical conductivity from the lowest frequency soft mode,

shown in the upper inset in Fig. 5 (note the increasing of the

optical conductivity at low temperature and its order of mag-

nitude). Therefore, the lowest frequency responses (10 kHz

or lower) have only an extrinsic origin, with the nature of the

charge carriers remaining to be demonstrated. The semicon-

ducting nature of the material is also confirmed by optical

absorption (ellipsometry) measurements presented in the

lower inset of Fig. 5, which shows that the optical edge of

the CCTO films occurs at about 2 eV (16 000 cm�1). The

results for the 160 nm CCTO film (not shown here) are

essentially the same.

In order to investigate the CDC relaxation process and

the related conduction mechanism, impedance arc plots were

obtained at several temperatures, as shown in the top panel of

Fig. 6, for the 320 nm CCTO film. The impedance plots

reveal two slightly depressed arcs, characteristic of hopping

mechanisms that can be attributed to Maxwell-Wagner

FIG. 4. (Color online) Top: frequency dependence of the real dielectric per-

mittivity for CCTO films with 160 nm and 320 nm thicknesses, for tempera-

tures ranging from 175 to 375 K. Bottom: thermal evolutions of the real

dielectric “constant” for a bulk sample (full symbols, from Ref. 3), and

CCTO thin films (semi-hollow symbols for the 320 nm film; hollow symbols

for the 160 nm film), for some parameterized frequencies (squares for 20

Hz, circles for 2 kHz, and down triangles for 200 kHz).

074102-6 Rubinger et al. J. Appl. Phys. 110, 074102 (2011)

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relaxations. The bottom panel of Fig. 6 presents the Arrhenius

dependence of the relaxation times determined for each of the

two arcs seen in the impedance plots. The main arc (higher

frequency) is responsible for the CDC effect of the CCTO

thin film. In the Arrhenius plot the corresponding data are

presented in red circles. The data for a secondary relaxation

appearing at lower frequencies, are presented as blue triangles

in the Arrhenius plot of Fig. 6 (bottom). The activation ener-

gies determined for these processes were 132 6 1 meV and

184 6 5 meV for the higher and lower frequency relaxation

frequencies, respectively. For the thinner film (160 nm) the

corresponding energies were 136 6 1 meV and 202 6 9 meV.

Maxwell-Wagner relaxations require high bulk conduc-

tivity (as shown by our films in Fig. 5) limited by insulating

barriers. The semiconducting nature of CCTO has been well

demonstrated, for materials prepared under different condi-

tions. It has been attributed to cupper deficiency17,28 or oxy-

gen deficiency,5,11,16,26 depending on the processing

conditions. The CDC feature has been shown to depend on

this semiconducting behavior. Indeed, this effect can be sup-

pressed by Mn doping on a Cu site (correcting the cation stoi-

chiometry),17 or enhanced by Co or Ge doping on a Ti site

(increasing the cation nonstoichimetry),6,21 in ceramics. On

the contrary, in thin films and single crystals oxygen loss

seem to be more significant. The suppression (and recovering)

of the CDC effect on annealing under O2 (N2) atmosphere has

been demonstrated.9,11 The activation energies measured for

our thin films, ranging from 100 and 200 meV, are compatible

with the calculated V2þO shallow levels into the bandgap.19,50

There is a broad dispersion between the activation energies

measured by different authors. This can be due to the different

semiconducting nature of their CCTO materials (n or p-type)

and to different barrier layers, which depend on the processing

conditions. In the case of ceramic materials, activation ener-

gies ranging from 400 to 700 meV linked to grain boundaries

were observed in secondary low frequency relaxations (not re-

sponsible for the CDC effect).5,17,19,49 The main relaxation

appearing in single crystals,3,36 ceramics,5,17,19 and thin

films8,27,28 have much lower energy barriers, below 200 meV,

usually ranging from 54 to 75 meV,3,5,17,19,49 which is com-

patible with shallow VþO levels,19,50 or 95 to 200 meV

(V2þO levels),27,28,36 as observed in our thin films.

The existence of two arcs in the impedance plots mean

that two different types of sample heterogeneities are acting

as barriers for the Maxwell-Wagner relaxations. While the

CCTO single crystals present a single relaxation in the radio-

frequency region, ceramics and thin films show two relaxa-

tions. The CDC effect is associated with the main higher fre-

quency relaxation (or the sole relaxation in single crystals).

In ceramic materials the secondary arc is surely associated to

the insulating grain boundaries. The CCTO thin films also

present a grained structure, with sub-micrometer sizes,

depending on the growth conditions.9,11,27 The main differ-

ence with ceramics is that the grains in the films are much

more compact. Thus, it is natural to associate the secondary

relaxation of the CCTO films to this grained structure (with a

lower energy barrier than in ceramics). Concerning the main

relaxation that is responsible for the CDC effect, the same

type of insulating barrier would act in CCTO single crystals,

ceramics, and thin films. The fine multiple twin boundaries

observed in these materials have already been considered

as the insulating barriers acting for the Maxwell-Wagner

relaxation.1,4,12,51 The twin boundaries are a consequence of

the lack of the four-fold symmetry of the parent perovskite

structure.1,3,4 Therefore, we can propose that twin boundaries

and grain boundaries are playing the role of insulating bar-

riers in the case of thin films, and that the CDC mechanism

FIG. 5. (Color online) The reciprocal temperature dependence of the real

part of the ac-electrical conductivity measured for the 320 nm-thick CCTO

sample for frequencies ranging from 100 Hz to 1 MHz. The upper inset

shows the optical conductivity behavior measured for this material close to

the lowest frequency polar phonon; the lower inset shows the optical edge of

this film in the visible region.

FIG. 6. (Color online) Top panel: complex impedance plots (Z00 vs Z0) for

the 320 nm-thick CCTO film, for several temperatures. Bottom panel:

Arrhenius dependencies of the relaxation times determined from the two

arcs of the top panel. The red circles are data for the main higher frequency

relaxation and the blue triangles are for the lower frequency one.

074102-7 Rubinger et al. J. Appl. Phys. 110, 074102 (2011)

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originates from the Maxwell-Wagner relaxations owing to

the semiconducting nature of CCTO (irrespective of the

charge carrier) associated with insulating twin boundaries.

Finally, let us comment that the incipient ferroelectric

character and the CDC effect have a common structural ori-

gin: the lack of a four-fold symmetry forbids the ferroelectric

transition and generates a heavily twinned structure in the

nanometer scale, with insulating twin boundaries.

IV. CONCLUSIONS

High quality CaCu3Ti4O12 thin films epitaxially grown

on LaAlO3 substrates by PLD allowed us to investigate the

dielectric response of this material. The phononic (intrinsic)

response shows an incipient ferroelectric behavior, which is

not responsible for the colossal dielectric behavior of the sys-

tem. The huge radio-frequency dielectric response has an ex-

trinsic origin, due to the semiconducting nature of the bulk

material and to non-intentional doping (oxygen vacancies

being the charge carriers), along with sample heterogeneities

that provide insulating barriers. The system reveals two

relaxations of a Maxwell-Wagner type in this frequency

region, owing to heterogeneities in different length scales:

twin boundaries, responsible for the main relaxation, and

grain boundaries, responsible for a secondary relaxation. The

same type of charge carrier (oxygen vacancies) plays a role

in both relaxations. The film thickness is found to influence

the main relaxation time. The intrinsic (incipient ferroelec-

tricity) and extrinsic (CDC) effects have a common origin:

the absence of a four-fold symmetry of the parent ideal

perovskite structure and the tilted TiO6 octahedra along dif-

ferent directions forbid Ti alignment, and therefore the ferro-

electric phase, and lead to multiple twinning in a fine scale,

giving rise to the Maxwell-Wagner effect responsible for the

CDC response of CCTO.

ACKNOWLEDGMENTS

We thank our colleague, Andre S. Ferlauto for the ellip-

sometric measurements. The Brazilian authors acknowledge

the official agencies CAPES, CNPq, FAPEMIG, and FINEP

for partially funding this work.

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