Investigation of relaxor PLZT thin films as resonant optical waveguides and the temperature dependence of their refractive index

Abstract

Relaxor lead lanthanum zirconate titanate (PLZT) thin films, with compositions of (7/65/35), (8/65/35), and (9/65/35), have been investigated as optical waveguides. Resonant structures were observed in the reflected light beam that passes through these thin films after coupling with a laser-inscribed azo polymer surface relief diffraction grating. The temperature was then varied on the PLZT thin films between -20 and 70 degrees C, and a shift in the above resonance peaks was observed that is due to a change in the refractive index of the samples. The temperature dependence of the refractive index of the tested PLZT thin films was subsequently plotted and was found to decrease linearly with an increase in temperature at different rates for all the thin-film compositions tested.

Full text

Investigation of relaxor PLZT thin films as resonant
optical waveguides and the temperature
dependence of their refractive index
Ribal Georges Sabat* and Paul Rochon
Department of Physics, Royal Military College of Canada, P.O. Box 17000, Station Forces, Kingston,
Ontario K7K 7B4, Canada
*Corresponding author: sabat@rmc.ca
Received 27 January 2009; revised 1 April 2009; accepted 3 April 2009;
posted 9 April 2009 (Doc. ID 106876); published 4 May 2009
Relaxor lead lanthanum zirconate titanate (PLZT) thin films, with compositions of (7=65=35), (8=65=35),
and (9=65=35), have been investigated as optical waveguides. Resonant structures were observed in the
reflected light beam that passes through these thin films after coupling with a laser-inscribed azo poly-
mer surface relief diffraction grating. The temperature was then varied on the PLZT thin films between
−20 and 70 °C, and a shift in the above resonance peaks was observed that is due to a change in the
refractive index of the samples. The temperature dependence of the refractive index of the tested PLZT
thin films was subsequently plotted and was found to decrease linearly with an increase in temperature
at different rates for all the thin-film compositions tested. © 2009 Optical Society of America
OCIS codes: 310.2785, 310.3840, 310.5448, 310.6860.
1. Introduction
Perovskite ferroelectric lead lanthanum zirconate ti-
tanate (PLZT) thin films are usually identified by
their atomic composition such as (La=Zr=Ti), where
La is the percentage of lead atoms that have been re-
placed by lanthanum in the perovskite structure A-
sites, and Zr and Ti are the respective percentage of
zirconium and titanium atoms in the B-sites. In gen-
eral, PLZT ceramics with compositions of ða=65=
35Þ, where 7<a<12, are known as relaxor ferro-
electrics because they exhibit a frequency relaxation
in their thermal dielectric response near their Curie
transition temperature. Relaxor PLZT thin films are
prime candidates for applications in integrated op-
tics, such as light waveguides and modulators, be-
cause they possess excellent transparency in the
visible and the IR, a relatively high index of refrac-
tion and dielectric permittivity, large electro-optic
coefficients, and a fairly slim ferroelectric hysteresis
around room temperature.
PLZT thin films were first RF sputtered and char-
acterized by Ishida et al. [1,2] in 1977, and they were
first investigated as light waveguides by Kawaguchi
et al. [3] in 1984. After improving the fabrication pro-
cess of such films, they were successfully used as
light modulators [4] and other optical applications [5]
ensued in the 1990s. More recently, further advances
have been made on the fabrication methods of good
quality PLZT thin films, and their characteristics as
light modulators have been improved [6,7]. There
has also been an increased interest in gaining a bet-
ter understanding of the physical material properties
of PLZT thin films, particularly the influence of the
substrate orientation on their electro-optic response
[8] as well as their nonlinear optical behavior [9]. In
general, relaxor PLZT bulk ceramics are known to
undergo a thermally or electrically dependent ferro-
electric–paraelectric phase transition just below
room temperature [10]. Reports on the temperature
dependence of other ferroelectric materials have in-
dicated that there is a change in the sign of the
temperature coefficient of the refractive index of
both SbSI [11]andPb
1−xGexTe [12] around their
0003-6935/09/142649-06$15.00/0
© 2009 Optical Society of America
10 May 2009 / Vol. 48, No. 14 / APPLIED OPTICS 2649

transition temperature between the ferroelectric and
the paraelectric phases. Even the application of a
large dc bias on ferroelectric Ba0:5Sr0:5Nb2O6thin
films proved to change the sign of the thermal coeffi-
cient of the refractive index compared to a zero field
condition [13]. These results indicate that the varia-
tion of the refractive index with temperature in ferro-
electric materials can be affected by the phase in
which they are in.
We used azo polymer surface relief diffraction grat-
ings to couple a laser beam into relaxor PLZT thin-
film waveguides. After varying the temperature of
the samples, a shift was then observed in the reso-
nance peaks of the reflected light that is due to a
change in the refractive index of the films, and the
temperature coefficients of their refractive index
were subsequently found.
2. Experiment
Relaxor PLZT thin films, prepared with the chemical
solution deposition method, were acquired from
Inostek (Gyeonggi-do, South Korea). These films,
with compositions of ð7=65=35Þand ð8=65=35Þ, were
grown on Si wafers and had a thickness of 500 nm;
composition ð9=65=35Þfilms were grown on c-cut
h0001isapphire substrates and had a thickness of
1500 nm. All the films had a 150 nm Pt bottom elec-
trode. A 3% solution of an azo polymer compound,
poly (MEA-co-DR1M) 2:8 [14], dissolved in dichloro-
methane, was prepared and spin coated with a thick-
ness of 450 nm on top of the PLZT thin films. This
polymer has a refractive index of 1.659. Here we take
advantage of the fact that surface relief diffraction
gratings can be written on azo polymers using an in-
terference pattern generated by a laser [15].
The spacing of the diffraction gratings written on
azo polymers can easily be modified by changing the
interference pattern. A 1 min exposure to the writing
laser usually yields gratings with a depth between
100 and 150 nm. After inscribing the azo polymer
gratings on our PLZT thin films, a separate appara-
tus was used to measure precisely the positive and
negative first-order diffraction angles and an accu-
rate value of the grating spacing was calculated. Sub-
sequently, the light from a spectrometer, with a 1nm
resolution, passed through a mechanical chopper, a
quarter-wave plate, a converging mirror, a polarizer,
and onto the PLZT films, at which point it was re-
flected by the Pt bottom electrode and its intensity
was measured by a photodetector connected to a
lock-in amplifier. The quarter-wave plate was used
to render the laser light circularly polarized, and,
hence, the incident light beam polarization on a
tested sample could easily be chosen by rotating
the polarizer. The PLZT thin films were positioned
on a computer-controlled turntable located inside a
liquid-nitrogen-cooled Delta Design 9023 tempera-
ture chamber with a temperature uncertainty
of 2°C.
3. Results and Discussion
Figure 1is a picture of an azo polymer surface relief
diffraction grating with 750 nm spacing taken with
an atomic force microscope. As illustrated in Fig. 2,
when a light beam in the air is incident at an angle θi
on a diffraction grating located on a PLZT film with a
refractive index of n, the transmitted light will be
concentrated in discrete diffraction orders numbered
as m¼0,1,2, etc., according to the well-known
grating equation
k0nsin θm¼k0sin θiþ2πm
Λ;ð1Þ
where k0is the free-space wavenumber ðk0¼2π=λ0Þ,
and Λis the grating spacing. For clarity, Fig. 2shows
only the first-order forward (positive) and backward
(negative) diffracted beams.
The modal theory of light propagation in slab op-
tical waveguides has been explained in many texts
[16,17]. Since the refractive index of the PLZT film
is higher than that of the azo polymer [9], a diffracted
light beam can be trapped inside the PLZT film if the
longitudinal propagation constant of that particular
diffraction order matches that of a discrete allowed
guided mode in the PLZT film [18]. If one sets κand
βas the x-axis and z-axis components, respectively, of
a discrete guided mode propagating in a thin film, κ
and βmust be (for m¼1)
κ¼k0ncos θ1;ð2Þ
β¼k0nsin θ1¼k0sin θi2π
Λ:ð3Þ
It then follows that
β2þκ2¼k2
0n2:ð4Þ
Several discrete propagation modes, hence different
values of κand β, can be allowed in a particular film
Fig. 1. (Color online) Atomic force microscope picture of a surface
relief diffraction grating with 750 nm spacing.
2650 APPLIED OPTICS / Vol. 48, No. 14 / 10 May 2009

depending on its refractive index and thickness, as
well as the index of the cladding and the substrate
[18]. First we consider light incident on a PLZT film
at normal incidence, θi¼0, as one varies the wave-
length, the 0th-order reflected intensity will have ne-
gative resonance peaks when forward and backward
guided modes are simultaneously excited in the film.
Each mode will have a unique κvalue, but all will
have the same jβj¼2π=Λ. On the other hand, when
θi≠0,κremains the same for each corresponding for-
ward and backward mode, but two different solutions
of βare possible for every mode depending on the
sign of the second term on the right-hand side of
Eq. (3). Therefore, forward and backward resonance
peaks will occur at different wavelengths. Using
Eqs. (3) and (4) it can be shown that, for the same
guided mode, λbackward >λforward. Figure 3shows
three distinct guided modes in a 2 μm PLZT
ð8=65=35Þthin film with Λ¼900 nm and θi¼2°.
In Fig. 3, the higher the θithe greater the separation
between the forward and the backward coupling of
each guided mode.
Since each guided mode has a unique value of κ,by
subtracting Eq. (4) for a forward guided coupling
from a backward guided coupling for the same mode,
we obtain
β2
forward −β2
backward ¼ðk2
0forward −k2
0backwardÞn2:ð5Þ
Hence, by finding the forward and backward cou-
pling wavelength for each mode at various incident
angles, a graph of β2
forward −β2
backward as a function
of k2
0forward −k2
0backward can be plotted and the refrac-
tive index of the film can be calculated. An example
of such a graph is shown in Fig. 4as well as an ap-
proximate value of the refractive index of each tested
PLZT thin-film composition at an average wave-
length. The refractive index of a PLZT ð9=65=35Þthin
film was measured independently with a He–Ne la-
ser ellipsometer at room temperature, and it was
found to be 2:24 0:20, which is in good agreement
with the value found in Fig. 4. The refractive index of
a thin-film PLZT ð8=65=35Þwas also measured using
aZ-scan technique [9] and was found to be approxi-
mately 2.12 at 700 nm, again showing good agree-
ment with the value found in Fig. 4. For a fixed
wavelength of 632:8nm, scanning the incident angle
would also exhibit similar resonance peaks in the
0th-order reflected intensity on the PLZT thin films,
as seen in Fig. 5. A second grating was written in the
azo polymer on each film with a slightly larger spa-
cing. This allowed the identification of each peak as a
forward or backward coupling, since the value of β
must remain unchanged for each resonance peak
at a fixed wavelength. From Eq. (3), if Λincreases,
θiforward must increase and θibackward must decrease.
Now, if the temperature of a PLZT thin film is
varied for an angular intensity scan at a fixed
λ¼632:8nm, we expect a change in its refractive in-
dex n, and, subsequently, a change in both κand βfor
each resonance peak. From Eq. (4) we have
n2
1¼β2
1
k2
0
þκ2
1
k2
0
;ð6Þ
n2
2¼β2
2
k2
0
þκ2
2
k2
0
;ð7Þ
where subscripts 1 and 2 denote the values of n,κ,
and βat a temperature of 20 °C and T, respectively.
Fig. 2. Side view of the tested PLZT samples.
Fig. 3. Normalized intensity as a function of wavelength for
PLZT ð8=65=35Þthin film.
Fig. 4. (Color online) β2
forward −β2
backward as a function of k2
0forward −
k2
0backward for various composition PLZT thin films.
10 May 2009 / Vol. 48, No. 14 / APPLIED OPTICS 2651

Using Eq. (3) and subtracting Eq. (7) from Eq. (6),
we obtain an expression for the refractive-index
change that is due to a temperature variation of
ΔT¼T−20 °C:
Δn¼1
2nave ðsin2θi2−sin2θi1Þ
þ2λ
Λð sin θi2∓sin θi1Þþ λ2
4π2ðκ2
2−κ2
1Þ;ð8Þ
where nave is the average refractive index of the film,
using the values of nave from Fig. 4. As expected,
Fig. 6shows a significant angular shift in the reso-
nance peaks for all the thin-film compositions. After
increasing the temperature on the samples from −20
to 60 °C, forward resonance peaks occurred at smal-
ler incident angles, whereas backward resonance
peaks occurred at larger incident angles. The
temperature range used is well below the glass tran-
sition temperature of the azo polymer (∼130 °C), and
diffraction gratings are known to be stable up to
120 °C. From the data of Fig. 4, we can obtain an ap-
proximate value of κfor every mode, and it can be
readily seen that the last term on the right-hand side
of Eq. (8) is very small compared with the other two.
Hence, Δncan be calculated directly for a corre-
sponding ΔTfrom the angular shift of the resonance
peaks. Figure 7shows that the refractive index of the
various PLZT thin films decreased as a function of
increased temperature ranging from −20 to 70 °C
with minimal hysteresis.
A model of our PLZT thin films was constructed in
the electromagnetic numerical analysis software pro-
gram GSOLVER to simulate the effects of changes in
grating spacing, thickness of the PLZT films and
their index of refraction, for a 0th-order reflectivity
angular scan. The simulation results were closely
matched to the experimental results. For example,
a simulation of Δn¼−0:005 resulted in a shift in
the incident angle for a forward resonance mode from
16:6°to16:2° and for a backward mode from 3:9°to
4:1°, as modeled in GSOLVER. Inputting these an-
gles into Eq. (8) results in Δn¼−0:0042. The effect
of linear thermal expansion was also taken into con-
sideration by modeling its effect on the angular reso-
nance peaks using GSOLVER. Haertling [19] found
that most relaxor PLZT bulk ceramics have an aver-
age linear thermal expansion coefficient of approxi-
mately 3:4×10−6=°C. A much larger hypothetical
change of 0.1% in the PLZT thin-film thickness over
the entire tested temperature range was modeled
and resulted in only negligible changes in the angu-
lar position of the resonances because of the thick-
ness change alone. Therefore, the majority of the
angular shift in the experimental resonance peaks
must come from the refractive-index change alone.
From Fig. 7, the temperature coefficients of the
refractive index of thin-film PLZT ð7=65=35Þ,ð8=
65=35Þ, and ð9=65=35Þwere −ð23:20:2Þ×10−5=°C,
−ð13:30:1Þ×10−5=°C, and −ð10:51:4Þ×10−5=°C,
respectively. These temperature coefficients seem
to increase with an increase in La content and clearly
indicate a strong dependence of the refractive index
on the composition and, hence, their crystalline
phase [20]. The results of Fig. 7also contradict
Fig. 5. (Color online) Measured intensity as a function of incident
angle θiat different grating spacing for thin-film PLZT:
(a) ð7=65=35Þ, (b) ð8=65=35Þ, (c) ð9=65=35Þ.
2652 APPLIED OPTICS / Vol. 48, No. 14 / 10 May 2009

previously reported results that indicate positive
temperature coefficients of the refractive index for
bulk PLZT ð9=65=35Þand ð10=65=35Þ[21,22]. This
inconsistency mirrors that seen in the dielectric mea-
surements of similar composition bulk and thin-film
PLZT samples. For example, bulk PLZT ð9=65=35Þ
was found to have a Curie transition temperature
around 70 °C at 100 kHz [23], whereas PLZT thin
films with the same composition have a Curie tem-
perature around 170 °C at the same frequency [5].
This indicates that, at a set temperature, the crystal
structure of bulk and thin-film PLZT with identical
composition could differ. Even though several studies
Fig. 7. Refractive-index change as a function of temperature for
thin-film PLZT: (a) ð7=65=35Þ, (b) ð8=65=35Þ, (c) ð9=65=35Þ.
Fig. 6. (Color online) Measured intensity as a function of incident
angle θiat different temperatures for thin-film PLZT:
(a) ð7=65=35Þ, (b) ð8=65=35Þ, (c) ð9=65=35Þ.
10 May 2009 / Vol. 48, No. 14 / APPLIED OPTICS 2653

[10,24,25] have concentrated on understanding the
phase transitions of bulk PLZT ceramics in the
range between −125 and 125 °C, the ferroelectric–
paraelectric phase transition in PLZT ceramics in
general is still not fully understood. As mentioned
in Section 1, this phase transition might affect the
temperature coefficient of the refractive index of fer-
roelectric materials in general [11–13]. Therefore,
the difference in the results of thin-film and bulk
PLZT is probably associated with differences in their
phase structure in the tested temperature range.
4. Conclusion
Relaxor thin-film PLZT compositions were investi-
gated as optical waveguides. A light beam was
coupled inside these films by laser-inscribed azo
polymer surface relief diffraction gratings. Relatively
deep resonance peaks were observed in the 0th-order
reflected light from the thin films. After varying the
temperature on the PLZT samples, a shift was ob-
served in the angular position of the guided modes
inside the films that is due to a change in the refrac-
tive index of the PLZT. The temperature coefficients
of the refractive index of all tested compositions were
calculated, and they were found to increase with an
increase in La content. However, a significant differ-
ence was observed between those coefficients of
similar composition PLZT thin films and previously
reported bulk PLZT. This inconsistency was
associated with differences in the temperature-
dependent changes in the crystal lattice structure
between thin-film and bulk PLZT materials, mainly
because of the fabrication process.
References
1. M. Ishida, H. Matsunami, and T. Tanaka, “Preparation and
properties of ferroelectric PLZT thin films by rf sputtering,”
J. Appl. Phys. 48, 951–953 (1977).
2. M. Ishida, H. Matsunami, and T. Tanaka, “Electro-optic effects
of PLZT thin films,”Appl. Phys. Lett. 31, 433–434 (1977).
3. T. Kawaguchi, H. Adachi, K. Setsune, O. Yamazaki, and
K. Wasa, “PLZT thin-film waveguides,”Appl. Opt. 23,
2187–2191 (1984).
4. S. Krishnakumar, V. H. Ozguz, C. Fan, C. Cozzolino,
S. C. Esener, and S. H. Lee, “Deposition and characterization
of thin ferroelectric lead lanthanum zirconate titanate (PLZT)
films on sapphire for spatial light modulators applications,”
IEEE Trans. Ultrason. Ferroelectr. Freq. Control 38, 585–590
(1991).
5. H. Adachi and K. Wasa, “Sputtering preparation of ferroelec-
tric PLZT thin films and their optical applications,”IEEE
Trans. Ultrason. Ferroelectr. Freq. Control 38, 645–655
(1991).
6. F. Wang, K. K. Li, V. Fuflyigin, H. Jiang, J. Zhao, P. Norris, and
D. Goldstein, “Thin ferroelectric interferometer for spatial
light modulations,”Appl. Opt. 37, 7490–7495 (1998).
7. G. H. Jin, Y. K. Zou, V. Fuflyigin, S. W. Liu, Y. L. Lu, J. Zhao,
and M. Cronin-Golomb, “PLZT film waveguide Mach–Zehnder
electrooptic modulator,”J. Lightwave Technol. 18, 807–812
(2000).
8. K. Sato, M. Ishii, K. Kurihara, and M. Kondo, “Crystal orien-
tation dependence of the electro-optic effect in epitaxial
lanthanum-modified lead zirconate titanate films,”Appl.
Phys. Lett. 87, 251927 (2005).
9. W. Leng, C. Yang, J. Zhang, H. Chen, W. Hu, H. Ji, J. Tang,
W. Qin, J. Li, H. Lin, and L. Gao, “Nonlinear optical properties
of the lanthanum-modified lead zirconate titanate ferroelec-
tric thin films using Z-scan technique,”Jpn. J. Appl. Phys.
46,L7–L9 (2007).
10. V. Bobnar, Z. Kutnjak, R. Pirc, and A. Levstik, “Electric-
field-temperature phase diagram of the relaxor ferroelectric
lanthanum-modified lead zirconate titanate,”Phys. Rev. B
60, 6420–6427 (1999).
11. R. Johannes and W. Haas, “Temperature dependence of the
refractive index ncin SbSI through the ferroelectric–paraelec-
tric transition,”Appl. Opt. 6, 1059–1061 (1967).
12. W. Jantsch, “Anomalies of the refractive index and the optical
energy gap of ferroelectric Pb1−xGexTe,”Z. Phys. B 40,
193–198 (1980).
13. V. D. Antsigin, E. G. Kostosov, V. K. Malinovsky, and
L. N. Sterelyukhina, “Electrooptics of thin ferroelectric films,”
Ferroelectrics 38, 761–763 (1981).
14. M.-S Ho, A. Natansohn, and P. Rochon, “Azo polymers for
reversible optical storage. 9. Copolymers containing two
types of azobenzene side groups,”Macromolecules 29,44–49
(1996).
15. P. Rochon, J. Mao, A. Natansohn, and E. Batalla, “Optically
induced high efficiency gratings in azo polymer films,”Polym.
Prepr. Am. Chem. Soc. Div. Polym. Chem. 35, 154–155
(1994).
16. D. Marcuse, Geometrical Optics Treatment of Slab Waveguides
(Academic, 1991), pp. 3–7.
17. C. R. Pollock, Fundamentals of Optoelectronics (Richard
D. Irwin, 1994).
18. R. J. Stockermans and P. L. Rochon, “Narrow-band resonant
grating waveguide filters constructed with azobenzene poly-
mers,”Appl. Opt. 38, 3714–3719 (1999).
19. G. H. Haertling, “Improved hot-pressed electrooptic ceramics
in the ðPb;LaÞðZr;TiÞO3system,”J. Am. Ceram. Soc. 54,
303–309 (1971).
20. G. H. Haertling and C. E. Land, “Hot-pressed
ðPb;LaÞðZr;TiÞO3ferroelectric ceramics for electrooptic appli-
cations,”J. Am. Ceram. Soc. 54,1–11 (1971).
21. R. G. Sabat and P. Rochon, “Interferometric determination of
the temperature dependence of the refractive index of relaxor
PLZT ceramics under DC bias,”Opt. Mater. 10.1016/j.optmat.
2009.02.001 (2009).
22. E. A. Falcão, J. R. D. Pereira, I. A. Santos, A. R. Nunes,
A. N. Medina, A. C. Bento, M. L. Baesso, D. Garcia, and
J. A. Eiras, “Thermo optical properties of transparent PLZT
10=65=35 ceramics,”Ferroelectrics 336, 191–196 (2006).
23. R. G. Sabat, P. Rochon, and B. K. Mukherjee, “Quasistatic di-
electric and strain characterization of transparent relaxor fer-
roelectric lead lanthanum zirconate titanate ceramics,”J.
Appl. Phys. 104, 054115 (2008).
24. Q. Tan and D. Viehland, “ac-field-dependent structure-
property relationships in La-modified lead zirconate titanate:
induced relaxor behavior and domain breakdown in soft ferro-
electrics,”Phys. Rev. B 53, 14103–14111 (1996).
25. V. Bobnar, Z. Kutnjak, R. Pirc, and A. Levstik, “Relaxor freez-
ing and electric-field—induced ferroelectric transition in a
lanthanum lead zirconate titanate ceramics,”Europhys. Lett.
48, 326–331 (1999).
2654 APPLIED OPTICS / Vol. 48, No. 14 / 10 May 2009