Abstract
Polycrystalline thin ®lms of Ba0.7Sr0.3TiO3(BST) are deposited on SiO2/Si substrates by radio frequency magnetron sputtering. This
work also examines how the O2atmosphere annealing temperature affects not only the crystalline and morphological properties, but also
the refractive index and the optical band gap energy. The BST ®lms possess the highest dense packing growth and near-bulk optical properties as the O2atmosphere annealing temperature increases. Analysis results indicate that the packing density and the refractive index
of BST ®lms increase as the annealing temperature increases, whereas the optical band gap energies apparently decreased. In addition, the dispersion of the refractive index is analyzed in terms of dispersion parameters using the single oscillator dispersion model of Wemple and DiDomentico. # 1999 Elsevier Science S.A. All rights reserved.
Keywords: BST; Thin ®lm; Annealing; Optical properties
1. Introduction
Ferroelectric thin ®lms of high dielectric material such as Ba1ÿxSrxTiO3 have been widely investigated for their
feasibility in thin ®lm integrated capacitors and storage capacitors in gigabit dynamic random access memory (DRAM) applications [1]. The large electro-optical coef®-cient of this material is also highly promising for optical applications [2]. In addition, the thin ®lms or multilayer systems of BST can be used in nonlinear optical devices such as planar waveguides or optical switches with minimal optical propagation losses. Most optical losses are directly related to the thin ®lm growth process and the ®lm structure that develops [3,4].
Some investigations have focused on the dependence of optical properties and ®lm structure on the deposition parameters of thin ®lms deposited by various methods such as sputtering [5], sol±gel process [6], and pulsed laser deposition [7±10]. The published data on refractive indices and dispersion parameters, as well as on fundamental optical band gap energies, suggest that the optical properties and the crystalline and morphological structures of these perovskite thin ®lm materials are strongly interdependent.
For Ba1ÿxSrxTiO3 thin ®lms, no detailed studies have
elucidated the optical and optoelectronic properties related to the thin ®lm growth process in radio-frequency (RF) magnetron sputtering. Therefore, this work investigates the optical properties of Ba0.7Sr0.3TiO3(BST) thin ®lm as
a function of various oxygen ambient annealing temperature after RF magnetron sputtering deposited. The real and imaginary parts of the complex index of refraction, n (refraction index) and k (extinction coef®cient), were obtained from a Nikon n&k Analyzer 1200. Next, the optical dispersion parameters were determined and explained on the basis of the Wemple single electronic oscillator dispersion model which is frequently used to correlate linear optical dispersion data with the fundamental band gap of thin ®lm materials.
2. Experimental procedure
A ceramic target used to prepare BST thin ®lms on SiO2(100 nm)/Si substrates by RF magnetron sputtering
deposition, having a diameter of 2 in. and a thickness of 1/4 in., was prepared from BaCO3, SrCO3and TiO2powders
(purity 99.99%) using standard solid state reaction process. All BST ®lms were prepared at a ®xed power of 100 W (power density of 4.93 W/cm2) and a constant pressure of
*Corresponding author.
E-mail address: [email protected] (T.-Y. Tseng)
0254-0584/99/$ ± see front matter # 1999 Elsevier Science S.A. All rights reserved. PII: S 0 2 5 4 - 0 5 8 4 ( 9 9 ) 0 0 1 5 7 - 1
30 mTorr while maintaining an argon to oxygen ratio of 8 : 2. The constant substrate temperature of 5008C W as used. The ®lm thickness was about 415 nm. The deposited rate was about 3.4 nm/min. After deposition, the ®lms were heat treated with the rapid thermal anneal (RTA) in O2
ambient at various temperatures from 500 to 7508C for 30 min.
The crystallinity of the ®lms was characterized by X-ray diffraction (XRD, MAC science M18, Japan). To determine the optical constants n and k() and the thickness of the BST ®lms, optical re¯ection spectra were measured in the wavelength range 180±900 nm with Nikon n&k Analyzer 1200. Fig. 1 illustrates a typical re¯ection pattern of BST ®lm, together with the envelopes of the re¯ection extrema of the front surface re¯ection. The re¯ection spectral data were analyzed and ®tted using the BST model built-in Nikon n&k Analyzer 1200. The ®lm thickness can be determined from the wavelength position and the interference order of the re¯ection minima and maxima indicated in Fig. 1. Scanning electron microscopy (SEM, HITACHI Model S-4000, Japan) was also used to measure the ®lm thickness which was compared with the thickness calculated from the re¯ec-tion spectrum.
3. Results and discussion 3.1. Structure
Fig. 2 displays the XRD patterns of ®lms as a function of annealing temperature in O2atmosphere. As the annealing
temperature increased, the peaks in the XRD patterns became more intense and the full-width at half maximum (FWHM) decreased. The average grain size of the ®lms can be estimated from the FWHM using Scherrer's equation [11,12]. The results indicated better crystallinity and an increase in grain size (from 8.8 to 10.8 nm) with an increas-ing annealincreas-ing temperature.
The XRD patterns in Fig. 2 reveal a gradual shift of 2 angles to the high angle side, indicating the shrinkage of
perovskite lattice by increasing the annealing temperature. The lattice constants of the BST ®lms determined from the XRD patterns monotonously decrease from a = 4.038 AÊ in as-deposited ®lm to a = 3.987 AÊ in 7508C annealing ®lm, the ®lms have a larger lattice constant than that of bulk material. This phenomenon is also frequently observed in sputtered BaTiO3 base thin ®lms, indicating
non-equili-brium and highly distorted states within the ®lms [13,14]. 3.2. Optical and optoelectronic properties
Fig. 3 depicts the dispersion of the refractive index spectra as a function of wavelength for BST ®lms annealed at various temperatures in O2 atmosphere for 30 min.
According to Fig. 3, the dispersion curve rises sharply toward shorter wavelengths, displaying the typical shape of a dispersion curve near an electronic interband transition. The strong increase in the refractive index is associated with the fundamental band gap absorption. Fig. 4 presents the measured refractive indices of the ®lms with various anneal-ing temperatures. As for ®lms annealed at high tempera-tures, the refractive indices are higher than as-deposited ®lm and increased from 0.25% (5008C) to 10.7% (7508C). This
Fig. 1. Reflection pattern of a 7508C annealing Ba0.7Sr0.3TiO3film with
reflection envelopes.
Fig. 2. XRD patterns of Ba0.7Sr0.3TiO3 films annealed at various
temperatures.
Fig. 3. Variation of refractive index with wavelength for various annealing temperatures films.
difference may be owing to that annealing under O2
atmo-sphere at an elevated temperature increases ®lm's crystal-linity and packing density. According to Fig. 5, the thickness of as-deposited ®lms reduced after annealing at various temperatures in O2 ambient. The thickness reduced from
0.7% (5008C) to 15% (7508C), possibly resulting in increased packing density for the ®lm with an elevated annealing temperature. The similar phenomenon has been found in other studies [15]. The ®lm thickness values were also veri®ed by SEM observation and were found to agree within 10 nm.
Notably, the packing densities of the ®lm and the bulk material can be calculated from the refractive index data. The packing density (p) is de®ned as the ratio of the average ®lm density (f) and the bulk density (b):
p f
b (1)
The correlation between the packing density and the refractive index can be expressed as [16,17]:
p f b n2 fÿ1 n2 f 2 n2 b 2 n2 bÿ1 (2)
where nf denotes the refractive index of the film, nb the
refractive index of the bulk. By assuming that the bulk value of the refractive index of BST is 2.465 at = 550 nm [8], the packing density in various annealing temperatures is shown in Fig. 6. Fig. 7 illustrates the refractive index ( = 550 nm) versus the packing density for BST films on the basis of the results of Figs. 4 and 6. According to Fig. 7, a small packing density reduces the film's refractive index. The packing density has a markedly increased value (from 0.82 to 0.92) due to a higher annealing temperature. A higher annealing temperature not only increases the mobility of atoms or molecules of the film, but also enhances the formation of large and more closely packed crystals. Hence, an increase in grain size (from 8.8 to 10.8 nm) and a decrease in grain boundary area and voids occur.
Thin oxide ®lms deposited by RF magnetron sputtering generally have a columnar structure with pores at high deposition temperature [8,18,19]. Some of these pores are empty or ®lled with water. Therefore, the relative ®lm density (packing density) is lower than that of the bulk material. In order to understand the growth morphology and relation between the refractive index of the ®lm nfand that
of the bulk nbwhich contain a certain volume part of voids,
Fig. 4. Refractive indices nfof Ba0.7Sr0.3TiO3films annealed at various
temperatures.
Fig. 5. Thickness of Ba0.7Sr0.3TiO3films annealed at various
tempera-tures.
Fig. 6. Packing density of Ba0.7Sr0.3TiO3 films annealed at various
temperatures.
Fig. 7. Refractive index n ( = 550 nm) versus the packing density p of BST thin films.
the effective medium mode of Bragg and Pippard can be used on the basis of the growth morphology of the ®lm [20± 22]. A close-packed columnar grain morphology is given by n2 f n2 bp 2ÿpn2bn2p 2ÿpn2 b pn2p (3)
and a columnar structure of reduced density is given by n2 f 1ÿpn4 p 1 pn2pn2b 1 pn2 p 1ÿpn2b (4)
where npdenotes the refractive index of the voids, which
may be 1 for empty voids or 1.33 in the case of water-filled voids [23±25].
Fig. 8 depicts the dependence of the refractive index nf
( = 550 nm) of two microstructures calculated according to the Bragg±Pippard mode with empty and water-®lled voids. Comparing Fig. 8 with Fig. 7, it reveals that a good ®tting in packing density can be achieved from 0.75 to 0.9 by the mode of close-packed columns with empty voids (line (b) in Fig. 8) and columnar growth with water-®lled voids (line (c) in Fig. 8). In order to distinguish these two modes, the dependence of the dispersion parameters Eoand
Ed on the O2 ambient annealing temperature must be
determined.
The dispersion data of the refractive index can be inter-preted in terms of the individual dipole oscillator mode [26,27], i.e. assuming that the medium contains elastically bound particles capable of vibrating with the same natural frequency of oscillation o. The refractive index as a
func-tion of wavelength, n , can be expressed as : n 2ÿ1 EoEd
E2
oÿ hc=2
(5) where c denotes the light speed, h Plank constant, Eothe
single-oscillator energy and Edthe dispersion energy. The
dispersion data of the refractive index also can be analyzed by using Sellmeir dispersion formula that is given by: n 2ÿ1 So2o
1ÿ o=2
(6) where So is an average oscillator strength and o is an
average oscillator wavelength. Fig. 9 displays the optical dispersion behavior of BST thin films annealed at various temperatures in O2atmosphere, (n2ÿ1)ÿ1versus ÿ2plot,
where Ed, Eo, Soand oare deduced from the slope of the
resulting straight fitting line and from the infinite wave-length intercept, respectively.
The study also determined the dependence of the disper-sion parameters Eoand Ed on the annealing temperature.
Fig. 10(a) and (b) depict the calculated dependence of the Wemple dispersion parameters Eoand Edfor different O2
atmosphere annealing temperatures and packing densities. According to our results, Eodepended only slightly on the
annealing temperature, with a small decrease to about 5.93 eV. On the other hand, the annealing temperature signi®cantly affects the dispersion energy Edin a manner
qualitatively similar to the refractive index n. According to these ®gures, the dispersion energy Ed increases rapidly
with an increasing annealing temperature. The values of Ed
and Eofor the ®lm annealing at 7508C are 22 and 5.85 eV,
respectively, which agrees well with the reported bulk values for BaTiO3 (Ed= 24.0 eV, Eo= 5.63 eV) [26,27]
and SrTiO3(Ed= 23.7 eV, Eo= 5.68 eV) [26,27] and thin
®lm value for Ba0.65Sr0.35TiO3[8]. This manner appears to
be qualitatively similar to the reported result of changes in the dispersion coef®cients Ed and Eo with the relative
packing density. A higher annealing temperature increases the packing density, which correlates with the situation in Fig. 6. The increase in dispersion energy Ed at a higher
annealing temperature may be attributed to the increased packing density. The only slightly dependence of Eoin O2
atmosphere annealing temperature and packing density suggests that the ®lms are most likely composed with empty voids [8].
Fig. 8. Refractive index n ( = 550 nm) versus the packing density p for two microstructures calculated according to the Bragg±Pippard model: (a) close-packed columns with filled voids; (b) close-packed columns with empty voids; (c) columnar growth with filled voids; (d) columnar growth with empty voids.
Fig. 9. The single electronic oscillator model fitting of Ba0.7Sr0.3TiO3
Fig. 11 depicts the average oscillator strength Soand the
ratio of Eo/So as a function of annealing temperature.
According to Fig. 11, Soincreases with an increasing the
annealing temperature while, at the same time, Eo/So
decreases. The values of So, oand Eo/Sowere estimated
to 8.3 1013mÿ2, 209 nm (Fig. 12) and 7.3 10ÿ14eV/m2,
respectively, for the ®lm annealing at 7508C, which closely corresponds to the reported bulk values for BaTiO3
(So= 9.1, 8.4 1013mÿ2, Eo/So= 6.4, 6.6, 7.4 10ÿ14eV/
m2) [9,27,28] and SrTiO
3 (So= 8.9 1013mÿ2, Eo/So=
6.5, 7.4 10ÿ14eV/m2) [9,26,28].
The dispersion energy can be correlated with the coordi-nation with the nearest neighbors and the effective electro-nic charge as recommended in [27] by
ENd
cZeNe (7)
where Ncdenotes the coordination number of the cations to
their nearest-neighbor anions, Zethe valence number of the
anions, Ne the number of valence electrons, and an
empirical factor which is given as 0.26 0.04 eV for most oxides containing a single anion [26,27]. Fig. 12 indicates that the calculated value of increases with an increasing annealing temperature. The observed of the film annealing at 7508C is 0.23 which is close to the bulk BaTiO3( = 0.24,
0.25) and bulk SrTiO3( = 0.25) and correlates well with
many other bulk oxides [26,27].
The optical band gap energy Egap of each ®lm was
deduced from the spectral dependence of the absorption constant by applying the Tauc relation [29]:
EA EÿEgap1=r (8)
where A is a constant, and r = 1/2, 2, 3/2 or 3 for allowed direct, allowed indirect, forbidden direct and forbidden indirect electronic transitions, respectively [30,31]. The absorption constant was determined from each reflec-tion spectrum using a reflecreflec-tion extrema envelope method described in detail elsewhere [32,33]. Once is obtained from the n&k analyzer 1200, can be calculated from the equation:
4 (9)
The E1=r versus E plots were found to give a linear dependence with r = 1/2, as shown in Fig. 13, corresponding to a direct allowed transition. In the higher energy region of
Fig. 10. Changes in the dispersion coefficients Edand Eowith (a) various annealing temperatures; (b) the relative packing density.
Fig. 11. The average oscillator strength and the energy dispersive parameter Eo/Soof Ba0.7Sr0.3TiO3films with various annealing
tempera-tures.
Fig. 12. The empirical factor and the average oscillator wavelength of Ba0.7Sr0.3TiO3films with various annealing temperatures.
the absorption edge, E2varied linearly with E. In the low energy region of the edge, the absorption spectrum deviated from the straight line plot. Notably, the straight line beha-vior of E2 versus. E plot in the high energy range was taken as the prime evidence for a direct allowed electronic transition between the highest occupied state of the valence band and the lowest unoccupied state of the conduction band. The optical band gap was determined by extrapolating the linear portion of the plot to E2 0. Fig. 14 illustrates the optical band gap energies (Egap) for ®lms of different
annealing temperatures. The Egapdecreases from 4.2 to 3.98
with the increasing annealing temperature up to 7508C. Kumar and Mansingh [34] suggested that the decrease in the optical band gap energy value in annealing might be attributed to the lowering of the interatomic spacing, which reduced the polarization and electron±hole interaction cor-rections. The ratios between the optical band gap energies Egapand the experimental Wemple oscillator energies Eoof
the ®lms were determined to be relatively constant factors of 1.47±1.5, which correlates well with most oxides (Eo 1.5Egap) [26,27]. However, the different values have
higher than Egapof polycrystalline sputtered BaTiO3®lms
[35] with 3.68 eV for a mean grain size of 8 nm, to 3.53 eV for a grain size of about 35 nm.
4. Conclusion
Thin ®lms of Ba0.7Sr0.3TiO3(BST) were prepared on the
SiO2/Si substrates with radio frequency magnetron
sputter-ing. This work also examined how the O2 atmosphere
annealing temperature affects the crystalline structure, the grain growth and the optical and optoelectronic properties. According to our results, the packing density, the grain size and the refractive index of the ®lms increased with an increasing annealing temperature. The ®lms exhibit the highest dense packing growth and near-bulk optical proper-ties as the O2atmosphere annealing temperature increases.
The optical band gap energy depends on the grain size and, becomes smaller for ®lms with a larger grain size. The dispersion of the refractive index was also analyzed in terms of the parameters Eo and Ed using the single oscillator
dispersion model of Wemple and DiDomentico. Our experi-mental results about Wemple oscillator energies Eo
(1.49Egap) and the empirical factor 0.23 of the
7508C annealing ®lms closely correspond with most reported data (Eo 1.5Egapand (0.26 0.04) eV).
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