- Email: [email protected]
Residual stresses and Raman shift relation in anatase TiO2 thin film
Thin Solid Films 517 (2009) 4372–4378
Contents lists available at ScienceDirect
Thin Solid Films j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / t s f
Residual stresses and Raman shift relation in anatase TiO2 thin film Ibrahim A. Alhomoudi a, G. Newaz b,⁎ a b
Mechanical Technology Dept., Hydraulic and Pneumatic Section, Alahsa College of Technology, P.O. Box 804, Hofuf 31982, Saudi Arabia Mechanical Engineering Dept., Wayne State University, Detroit, Michigan 48202, USA
a r t i c l e
i n f o
Article history: Received 22 March 2008 Received in revised 10 January 2009 Accepted 26 February 2009 Available online 9 March 2009 Keywords: Anatase Titanium dioxide Thin film Sputtering Raman spectroscopy Residual stress Curvature measurements
a b s t r a c t Anatase TiO2 film (100–1000 nm thick) grown on glass, sapphire (0001), and Si (100) substrates by pulsed dc-magnetron reactive sputtering were evaluated for stress and strain analysis using Raman spectroscopy and curvature measurement techniques. The X-ray analysis revealed that films prepared for this study were purely anatase, and the measurements indicate that the film exhibit that (101) is the preferred growth orientation of the crystallites, especially for the film thicker than 100 nm. Curvature measurements and Raman spectroscopy, with 514.5 nm excitation wavelength, phonon line shift were used for stress analysis. A comparison between Raman lineshapes and peak shifts yields information on the strain distribution as a function of film thickness. The measurements of residual stresses for crystalline anatase TiO2 thin film showed that all thin film were under compressive stress. A correlation between Raman shifts and the measured stress from the curvature measurements was established. The behavior of the anatase film on three different substrates shows that the strain in film on glass has a higher value compared to the strain on sapphire and on silicon substrates. The dominant 144 cm− 1 Eg mode in anatase TiO2 clearly shifts to a higher value by 0.45–5.7 cm− 1 depending on the type of substrate and film thickness. The measurement of the full width at half maximum values of 0.59–0.80 (2θ°) for the anatase (101) peaks revealed that these values are greater than anatase powder 0.119 (2θ°) and this exhibits strong crystal anisotropy with thermal expansion. © 2009 Elsevier B.V. All rights reserved.
1. Introduction Anatase TiO2 is most commonly used as a photocatalysis material for optical applications [1–6], gas sensors [7–9] and in solar cells [10,11]. It can decompose some pollutions with photocatalytic action and become important for environmental purification [12,13]; it was also used for ethanol and methanol sensing properties for breath analyses [14]. Many different fabrication techniques have been developed to prepare TiO2 thin film; however, the processing conditions have been found to strongly influence the structural properties of the resulting film. Often the film exhibits strain due to thermal stresses caused by differential thermal expansion between the substrate and the film or by the lattice constant mismatch between the two. Most of these stresses are either compressive or tensile, so they can eventually result in the failure of devices. It has been recognized that residual compressive stresses may cause film delamination from the substrate whereas tensile stress may cause surface cracks in the film [15,16]. The most commonly used methods to measure the residual stresses in film are substrate curvature measurements [17,18], X-ray diffraction (XRD) [19,20] and Raman
⁎ Corresponding author. Tel.: +1 313 577 2970. E-mail address: [email protected] (G. Newaz). 0040-6090/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.tsf.2009.02.141
spectroscopy [21,22]. The XRD and the curvature measurements can be used directly to determine the average stress in film. It is also known that (first order) zone center Raman phonon lines shift to higher/lower frequency under compressive/tensile stress. Extracting the magnitude of residual stress from Raman shifts requires knowledge of the relation between these shifts and the lattice strain [15,18,23]. We studied the relation between the Raman shifts and the average film strain, which was deduced from experimental measurements of substrate curvature induced by stresses resulting from film growth. Thermal effects provide an important contribution to film stress. Strain develops in a growing film because it is constrained during the deposition process. Usually this constraint is the bonding to a substrate. Thermal effects provide important additional contributions to film strain. The corresponding stresses will in turn strain the substrate. This substrate strain generally appears as bending of the substrate. The thermal strain is caused by differential thermal expansion between film and substrate when film is deposited at high temperature and then cooled. This film will be residually compressed when measured at room temperature if αf N αs, with α as the linear expansion coefficient. In this case the substrate shrinks more than the film. The total stress (σtotal) acting in a film is the result of three distinct contributions (Eq. (1)). These stresses are as follow: external stress (σext), which is due to possible external loading; thermally-induced stress (σth), which is due to the mismatch between the thermal expansion coefficients of both substrate and film material;
I.A. Alhomoudi, G. Newaz / Thin Solid Films 517 (2009) 4372–4378
and intrinsic stress (σin), which is related to the particular coating microstructure and the particular growing process itself [24,25]. σ total = σ ext + σ th + σ in
ð1Þ
The isothermal stress–strain relation, ignoring the effect of temperature change, is given by Hooke's law, σ = Eε, where the stress is directly proportional to the strain (an approximation limited to small strains and certain materials) [26]. E is a symmetric matrix of the material stiffness. Anatase film has orthotropic stress–strain relationships [27] that can be simplified as expressed in Eq. (2), where the z-axis is the principal material direction [28,29]. 8 9 2 S11 < e1 = e = 4 S12 : 2 ; γ12 0
S21 S22 0
9 38 0 < σ1 = 5 0 σ : 2; S66 τ 12
ð2Þ
4373
(Geigerflex X-ray Goniometer unit) with Cu source. Vmax = 80 kV, Imax = 150 mA for a Cu rotating anode. JADE XRD pattern processing (MDI) was used to collect and process the data. The Raman spectra were recorded in a backscattering geometry using a Renishaw InVia Raman-microscope system and the 514.5 nm excitation wavelength of an Ar-ion laser, focused on a spot size of the order of ≈ 3 µm. The Raman peak positions were obtained by curve-fitting the lineshaped Gaussians to the spectra shapes of the raw data obtained from the spectrometer. The curvature (deflection) measurement technique was performed using a model 128 intelligent film stress measurement system manufactured by Frontier Semiconductor Measurements (FSM) Inc., and the Stoney formula was used to derive a relation between the curvature of the system and the stress of the thin film [18]. 3. Results and discussions 3.1. X-ray diffraction (XRD)
Where S is a symmetric matrix of material compliances (S =E− 1), S11 = 1 / E1, S12 = − v12 / E1 = − v21 / E2, S22 = 1 / E2 and S66 = 1 / G12 =E12 /2(1 +v12). A Raman spectrum is generated when an intense beam of light, usually generated from a laser, is directed onto a material. A small fraction of this excitation light is scattered inelastically and shifted to a different frequency or wavelength. This change in frequency (Δν) is the frequency of a particular vibrational mode of the crystalline material (First order Raman effect) [30–32]. The three natural phases of titanium dioxide TiO2 are anatase, rutile and brookite. Anatase has six Raman active modes, A1g (515 cm− 1), 2B1g (400 and 519 cm− 1), 3Eg (144, 197 and 640 cm− 1), and rutile has four Raman active modes, A1g (612 cm− 1), B1g (143 cm− 1), B2g (826 cm− 1), Eg (447 cm− 1); both are tetragonal, while brookite is orthorhombic has 36 Raman active modes (9A1g + 9B1g + 9B2g + 9B3g) [15,23,33,34]. In our previous work on anatase TiO2 thin film, we studied the structural and morphological properties of amorphous and crystalline anatase TiO2 thin film [35]. We also studied the operation temperature, film thickness, and substrate effects on the resistance of anatase TiO2 thin film when exposed to CO gas [8]. In this work, our research interest was to study the influence of the anatase film thickness and substrate type, glass, sapphire (0001) and Si (100), for residual stress analysis using Raman spectroscopy and curvature measurement techniques. This information is important in order to understand the film structure, residual stress in the film, and film performance on different substrates. The selection of substrates was because the glass substrate has an amorphous structure and is a widely used material, where Si (100) substrate selection was based on the most commonly used substrate in different devices. However, the sapphire substrate has the closest thermal expansion coefficient (9.03 ×10 − 6/°C− 1) compared to the anatase TiO2 (10.20× 10− 6/°C− 1), as well as it has high chemical durability and is a good insulator since its band gap (8.8 eV) is much wider than the band gap of anatase (3.2 eV), thus improving the stability of the sensor. 2. Experimental setup Anatase TiO2 thin film (100–1000 nm thick) was prepared by magnetron sputtering in reactive argon/oxygen gas atmosphere on glass, sapphire (0001) and Si (100) substrates. The deposition condition was selected from our previous work [35] based on the XRD results of the best crystalline quality in terms of the maximum intensity ratio of the sharp diffraction peak to the broad background. This was carried out with the set of parameters, such as growth pressure (3.0–5.0 mTorr), power (300–500 W), and substrate temperature (25–400 °C). The anatase thin film was studied for stress analysis with X-ray diffraction, the Curvature measurement technique and Raman spectroscopy measurement. Crystalline structure and crystallite size were determined by means of standard θ/2θ XRD scans using a Rigaku-Rotaflex RU2000 diffractometer system
Film was characterized by XRD, which confirmed the anatase TiO2 structure of the film, and it also showed that the anatase film is crystalline material. All the observed sharp peaks could be indexed based on the anatase single-phase structure or assigned to substrate reflections, as indicated in Fig. 1(a), (b), and (c). A high peak at 25.22 (2θ°) and other very small peaks at 37.75 and 47.72 (2θ°) were observed, corresponding to anatase (101), (004) and (200) reflections, respectively. There is no evidence of a rutile phase of TiO2. The experimental peak positions were compared with the standard JCPDS card # 71-1169 [36], and the corresponding miller indices were indexed. The XRD analysis revealed that film prepared for this study was purely anatase, and the measurements indicate that the film exhibit that (101) is the preferred growth orientation of the crystallites, especially for the film thicker than 100 nm. As was observed, the diffraction patterns of the film deposited on the three substrates shown in Fig. 1(a), (b), and (c) contain the intensity ratio of the (101) peaks that are several times higher than other peaks in addition to the line assigned to the substrates. The film deposed on sapphire (0001) and Si (100) substrates also exhibit (004) orientation but very small compared to (101) orientation. Fig. 1(b) shows that the small peak observed at 37.75 (2θ°) appears somewhat higher because it consists of two components that are corresponding to the anatase (004) peak and also to the sapphire substrate peak. The broad background on the data for films on glass corresponds to the substrate, and there is no evidence that the thinner films show an amorphous component. The film on the glass substrate shown in Fig. 1(a) and on the sapphire (0001) substrate shown in Fig. 1(b) are transparent, while those grown on the Si (100) substrate shown in Fig. 1(c) present different colors related to interface effects. 3.2. Raman spectra The anatase TiO2 thin film Raman spectra on glass, sapphire (0001) and Si (100) are shown in Fig. 2(a), (b), and (c), respectively, using a wavelength of, λ = 514.5 nm. From the figures, the frequencies of Raman bands identified as 147.3 (± 2.8) cm− 1 are assigned to the Eg phononic modes represented by v6. The bands as 392.8 (± 4.3) cm− 1 are assigned to the B1g phononic mode (v4). The bands as 515.2 (± 5.3) cm− 1 can be attributed to the A1g phononic mode (v2). The bands as 513.14 (± 7.4) cm− 1 can be attributed to the B1g phononic mode (v3), and the bands as 628.8 (± 10.2) cm− 1 can be attributed to the Eg phononic mode (v1), based on the factor group analysis. These bands agree well with those in previous studies for anatase powder and single crystals [23,33,34,37,38]. From the factor plane analysis it was observed that both A1g (v3) and B1g (v2) modes involve the Ti–O bond stretching normal to the film plane [38]. The Raman spectroscopy results showed that the thinner film (100 nm) is
4374
I.A. Alhomoudi, G. Newaz / Thin Solid Films 517 (2009) 4372–4378
The shifts of the 400 cm− 1 B1g and 640 cm− 1 E1g modes were toward lower wave numbers and decrease with film thickness. As the broad band near ~517 cm− 1 consists of two components that are not well resolved, the 515 cm− 1 A1g and 519 cm− 1 B1g modes, the corresponding shifts indicated in Fig. 3 are unreliable and can be considered only as guesses. For the case of the Si (100) substrate even its location is questionable due to the presence of the strong substrate band. If these shifts were caused by the inhomogeneous strain field induced during the growth caused by lattice mismatches between substrate and anatase, the shifts should generally decrease with
Fig. 1. The X-ray diffraction patterns of five different thicknesses of anatase TiO2 thin film deposited on (a) glass, (b) sapphire (0001), and (c) Si (100) substrates.
a crystalline material, and the intensity of Raman spectrum of the thin film increases with film thickness. The positions of the major peaks are all shifted with respect to the corresponding frequencies in the bulk material. Fig. 3 shows the Raman spectrum mode shifts for anatase TiO2 thin film with different thickness on glass substrate shown in Fig. 3(a), on sapphire (0001) substrate shown in Fig. 3(b) and on Si (100) substrate shown in Fig. 3(c) using the excitation wavelength of λ = 514.5 nm. The dominant 144 cm− 1 Eg mode is shifted towards a higher frequency by an amount that depends on the substrate as well as on the thickness of the film. Similar shifts have been previously reported and have been related to the confinement effects in nano-structured anatase crystallites [39].
Fig. 2. Raman spectra of anatase TiO2 thin film with different thickness as deposited on (a) glass, (b) sapphire (0001), and (c) Si (100) with excitation wave length λ = 514 nm.
I.A. Alhomoudi, G. Newaz / Thin Solid Films 517 (2009) 4372–4378
4375
wave-number modes (400 B1g, 515 A1g, 519 B1g and 640 Eg modes) have similarity in Raman shifts, where the modes reduce their shifting from a lower energy to a higher energy band gap of the thin films on glass, sapphire (0001) and Si (100) substrates as shown in Fig. 3(a), (b), and (c), respectively. Another observation is that the high wavemodes have the same slope of shifting, except for the thin film on the Si (100) substrate. 3.3. Curvature measurements The anatase TiO2 thin film (100–1000 nm) grown on glass, sapphire (0001), and Si (100) substrates have also been used for the curvature measurements of substrates before and after the film deposition, where the residual stresses were then determined. The residual film stress (σ) was calculated by using Stoney's formula (Eq. (3)), which is based on an approximate plate analysis [17],
σ =
2 Esub tsub 6ð1 − vsub Þ tfil
!
1 1 − ðMPaÞ ra rb
ð3Þ
where Esub is the Young's modulus, vsub is the Poisson ratio of the substrate, tsub and tfil are the thickness of the substrate and the film, respectively, and ra and rb are the radii of curvature for substrate with and without film. The following have been used with Eq. (3): for glass, Esub = 627.58 GPa and vsub = 0.2; for sapphire, Esub = 370 GPa and vsub = 0.2; for Si, Esub = 230 GPa and vsub = 0.2 [40–43]. In the curvature measurement, Stoney's equation is justified because the film thickness is less than 5% of the substrate thickness. Fig. 4 shows the stress as a function of the anatase TiO2 film thickness (100– 1000 nm) on glass, sapphire (0001) and Si (100) substrate. These results clearly show that the bi-axial stresses are compressive and decrease with the increasing film thickness. Further, the magnitude of residual stress in the film grown on glass substrate is substantially larger than that on sapphire (0001) or Si (100) substrates. The lower residual stress in film prepared on sapphire (0001) and Si (100) substrates can be explained based on the closeness of the thermal expansion coefficient and the lattice match between the substrate and the anatase film. It is interesting to note that anatase film grown on sapphire (0001) exhibits a stress relaxation over a small thickness range compared with the film grown on Si (100) and glass substrates.
Fig. 3. Raman spectrum shift of anatase TiO2 thin film modes deposited on (a) glass, (b) sapphire (0001), and (c) Si (100) substrate using the excitation wavelength of λ = 514.5 nm.
increasing film thickness and should be smaller for the spectra obtained with the shorter wavelength excitation. Fig. 3 implies that this may indeed be the case. In addition, as shown clearly in Fig. 3(a), (b), and (c) for the 144 cm− 1 Eg line, as the shift increases, so does the line broadening, which according to the interpretation given above indicates as expected that the strain field within the probed volume is rather inhomogeneous, but that this inhomogeneity decreases as the point of probing moves further from the substrate. The four high
Fig. 4. Variation of residual stress with anatase TiO2 film thickness on different substrates.
4376
I.A. Alhomoudi, G. Newaz / Thin Solid Films 517 (2009) 4372–4378
3.4. Residual strain of anatase thin film The strains for the anatase TiO2 thin film on the three different substrates were calculated based on Eq. (2). The elastic constants E1 = 303 GPa, E2 = 115 GPa and G12 = 94 GPa for anatase TiO2 were taken from reference [27], and the Poisson's ratio (vsub) has value as mentioned earlier, where the stress values were obtained from curvature measurements. The stress–strain behavior for anatase TiO2 thin film on the three different substrates are shown in Fig. 5, which shows that the calculated data for the film on the three different substrates fit in a straight line. Also, the strain for the thin film on glass has a higher value compared to the strain on sapphire (0001) and on Si (100). Furthermore, the stiffness (E = 179 GPa) for the thin film was calculated from the slope of the stress–strain curve. 3.5. Measurement of Raman peak shifts Quantitative relationships between bi-axial stress and the shift in the phonon frequencies exist for diamond film [22]. It is known that the Raman peak shift (Δω) is proportional to the magnitude of residual stress in thin film [21,44]. However, no theoretical work describing such relations for tetragonal anatase TiO2 is reported in the literature; thus, no proportionality constant factor between Δω and the residual stress in the thin film is known for anatase. The Raman peak shift was measured with respect to its position in the stress free sample. Assuming that the diamond result is also correct for anatase, we can write the relation namely, σ = IAN · Δω ðMPaÞ
ð4Þ
Where IAN (MPa/cm− 1) is the proportionality constant. The value of this constant can be calculated based on the stresses obtained from curvature experiments, particularly Raman transition, substrate and excitation wavelength. Δω (cm− 1) is the Raman peak shift of the film. The Raman spectra of the anatase TiO2 thin film (100–1000 nm) was measured with 514.5 nm laser excitation, and the thickness dependent shifts of Eg phonon mode were given above. The dominant 144 cm− 1 Eg mode in anatase TiO2 clearly shifted to a higher value by 0.45–5.7 cm− 1 depending on the type of substrate and the film thickness (shown in Fig. 6). It is also shown in Fig. 6 that Δω decreases with increasing film thickness. Maximum shift was seen for the film on the glass substrate indicating a higher bi-axial compressive stress in agreement with the curvature measurements. The shifts of Eg mode clearly show that the bi-axial stress increases along the film depth, being larger at the film/substrate interface.
Fig. 5. Stress–strain behavior for anatase TiO2 thin film on three different substrates.
Fig. 6. Variation of Δω with film thickness for 144 cm− 1 Eg mode of anatase TiO2 thin film on different substrates.
Fig. 7(a), (b), and (c) show a summary of the Raman line shift of 144 cm− 1 Eg mode obtained with 514.5 nm excitation wavelength vs. average residual stress values determined from curvature measurements on the three different substrates, glass, sapphire (0001) and Si (100), respectively. The Raman peak positions were obtained by fitting Gaussians to spectra shapes. The value of the proportionality constant, IAN (MPa/cm− 1), in Eq. (4) was obtained by fitting a straight line as shown in Fig. 7, where the value of IAN was found to be equal to − 937, − 337 and − 391 (MPa/cm− 1) for the anatase film on glass, sapphire (0001) and Si (100) substrates as shown in Fig. 7(a), (b), and (c), respectively. The magnitude of the stress in the film changes depending on the film thickness and substrate. The compressive stresses gradually increase with lower film thickness, which means that the stress gets higher closer to the film and substrate interface. In correlation of the Raman spectroscopy peaks shift with the curvature measurements, Fig. 8 shows the Raman shift vs. strain of the film calculated based on Eq. (2). It shows that the shift increases with the strain. It was also observed that the Raman band 144 cm− 1 broadened with decreasing strain as shown in Fig. 9. The broadening of these peaks shows that there are contributions to the Raman band shift from the anatase growth oriented at all angles to the deformation axis. Anatase growth oriented at 90° to the deformation axis will shift to a higher
Fig. 7. The Raman spectrum shift of 144 cm− 1 Eg mode obtained with 514.5 nm excitation wavelength vs. average residual stress values determined from curvature measurements on glass, sapphire (0001) and Si (100) substrate.
I.A. Alhomoudi, G. Newaz / Thin Solid Films 517 (2009) 4372–4378
4377
Fig. 8. Raman spectrum shift of 144 cm− 1 peak vs. strain for anatase TiO2 thin film on three different substrates.
Fig. 10. The average crystallite sizes of the anatase TiO2 thin film with different film thickness on sapphire (0001) substrate.
wave-number with strain due to Poisson's contraction of the matrix; compression on the anatase thin film will result in positive shift of 144 cm− 1 Raman bands. From XRD analysis, the intensities of the XRD (101) anatase peak were increased and the widths became broader. In general, the full width at half maximum (FWHM) of the XRD peak corresponds to the crystal size of the porous materials. When the width was broader, the crystallites exhibited smaller size. The Scherrer equation (Eq. (5)) was used to determine the average crystal sizes of the TiO2 nanoparticles.
anatase powder (0.395° and 0.119° for film with 30 and 200 nm thick), which is assumed to be strain free [45]. Crystallite size values were determined using the Scherrer equation (Eq. (5)) to fined the average crystal sizes of the anatase TiO2 thin film, assuming that all broadening was due to crystallite size. Our XRD analysis of the anatase TiO2 thin film predicted a crystallite size of 10–13 nm on the glass substrate, 11–13 nm on the Si (100) substrate and 10–12 nm on the sapphire (0001) substrate. A likely explanation for the slightly low value of crystallite size predicted by the XRD analysis resides in the assumption that all peak broadening is due to crystallite size effects. Fig. 10 shows the average crystallite sizes of the anatase TiO2 thin film with different film thickness on sapphire (0001) substrate, and it clearly states that the crystallite size is thickness-dependant. It was reported that polycrystalline ceramic materials revealed that the effect of residual stress among grains caused by thermal expansion anisotropy increases with increasing grain size, where anatase exhibits strong crystal anisotropy with thermal expansion [45–48]. The residual stress evaluated by the above-mentioned techniques is actually a sum of thermal stress and intrinsic stress. Therefore, the nature of the residual stress is determined by the nature and relative magnitude of these two stress components. Considering the effect of the thermal mismatch, we can assume the anatase thin film and substrate behave as a bi-metal plate, where the difference in the thermal expansion coefficients will induce stresses in both the film and the substrate and will lead to the film/substrate bending upon cooling from the deposition temperature to room temperature. In other words, the anatase film and substrate might be lattice matched at the deposition temperature and are cooled to a lower temperature, so thermal strain is produced in the layer since the coefficients of thermal expansion of the anatase film and substrate are not equal. As a result, the anatase film is strained such that the in-plane lattice constant of the anatase is the same as that of the substrate. The strain in this case is homogeneous and is known as the misfit strain. Before the deposition process, great care is taken to ensure the cleanliness of the substrates. Since the deposition temperature of the anatase is around 300 °C, which is less than what is needed to grow thermal oxide (750 °C and 1100 °C), the anatase deposition on the Si substrate is assumed to be clean and free of the native amorphous SiO2 thin layer. The resulting measurement stress of the anatase film on the Si (100) substrate gives more confidence assumptions.
t=
0:9λ β · cosθ
ð5Þ
Where t is the crystallite size, λ is the X-ray wavelength of the incident radiation (Cu Kα = 0.154 nm), β is the broadening of diffraction line measured as half of its maximum intensity (FWHM), and θ is the corresponding diffraction angle for anatase TiO2 (101) reflection. The measurements of the FWHM values of anatase (101) peaks were found to be in the range of 0.59–0.76 (2θ°) on the glass substrate, 0.6–0.74 (2θ°) on the Si (100) and 0.60–0.80 (2θ°) on the sapphire (0001) substrate. These values of the FWHM for anatase thin film on the three different substrates are several times larger than for
4. Conclusions Fig. 9. Peak broadening of 144 cm− 1 peak vs. strain of anatase TiO2 thin films on three different substrates.
X-ray diffraction confirmed the anatase TiO2 structure of the thin film and showed that the anatase film is crystalline material. The XRD
4378
I.A. Alhomoudi, G. Newaz / Thin Solid Films 517 (2009) 4372–4378
data showed that the anatase film, 100 nm thick on the glass, has a broader background that corresponds to the substrate, but there is no evidence that this thinner film has an amorphous component. In contrast, Raman spectroscopy showed that this thin film is crystallite material. Raman spectroscopy measurements using the 514.5 nm excitation wavelength of 144 cm− 1 Eg vibration mode yielded information on the strain distribution as a function of film thickness. Curvature measurement and Raman spectroscopy were used for stress/strain analysis. The measurements of residual stresses for crystalline anatase TiO2 thin film showed that all film are under a compressive stress. The stress/strain behavior for anatase film on three different substrates showed that the strain for the thin film on glass has a higher value compared to the strain on sapphire or on silicon substrates. The bi-axial strain originates from growth on lattice-mismatched substrates and from post-growth cooling. Thin 100 nm anatase film on a glass substrate has the highest compressive stress of about 6000–7000 MPa. Compressive stress in the anatase film on sapphire and silicon are considerably less (1200–2000 MPa). Both curvature measurements and Raman peak shift estimated residual stresses in anatase thin film compare well. Acknowledgments The authors wish to acknowledge the support of the Institute for Manufacturing Research and the Smart Sensors and Integrated Microsystems (SSIM) program at Wayne State University. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12]
A. Weibel, R. Bouchet, P. Knauth, Solid State Ionics 177 (2006) 229. B. Huber, H. Gnaser, C. Ziegler, Surf. Sci. 566–568 (2004) 419. H. Wang, Y. Wu, B. Xu, Appl. Catal., B Environ. 59 (2005) 139. I. Justicia, G. Garcia, G.A. Battiston, R. Gerbasi, F. Ager, M. Guerra, J. Caixach, J.A. Pardo, J. Rivera, A. Figueras, Electrochim. Acta 50 (2005) 4605. S. Tanemura, L. Miao, P. Jin, K. Kaneko, A. Terai, N. Nabatova-Gabain, Appl. Surf. Sci. 212–213 (2003) 654. Y. Sheng, B. Zhou, Y. Liu, X. Zhao, C. Wang, Y. Pan, Z. Wang, Mater. Lett. 60 (2006) 1327. H. Tang, K. Prasad, R. Sanjines, F. Levy, Sens. Actuators, B 26–27 (1995) 71. I.A. Al-Homoudi, J.S. Thakur, R. Naik, G.W. Auner, G. Newaz, Appl. Surf. Sci. 253 (2007) 8607. S.A. Akbar, L.B. Younkman, J. Electrochem. Soc. 144 (1997) 1750. J.N. Hart, R. Cervini, Y.B. Cheng, G.P. Simon, L. Spiccia, Sol. Energy Mater. Sol. Cells 84 (2004) 135. K.D. Rogers, D.W. Lane, J.D. Painter, A. Chapman, Thin Solid Films 466 (2004) 97. S. Ikezawa, F. Mutsuga, T. Kubota, R. Suzuki, K. Baba, S. Koh, T. Koshioka, A. Nishiwaki, K. Kida, Y. Ninomiya, K. Wakita, Vacuum 59 (2000) 514.
[13] S. Ikezawa, H. Homyara, T. Kubota, R. Suzuki, S. Koh, F. Mutuga, T. Yoshioka, A. Nishiwaki, Y. Ninomiya, M. Takahashi, K.K.K. Babaa, T. Hara, T. Famakinwa, Thin Solid Films 386 (2001) 173. [14] C. Garzella, E. Comini, E. Tempesti, C. Frigeri, G. Sberveglieri, Sens. Actuators, B 68 (2000) 189. [15] F. Vaz, L. Rebouta, P. Goudea, J.P. Riviere, E. Schaffer, G. Kleer, M. Bodmann, Thin Solid Films 402 (2002) 195. [16] Q.H. Fan, A. Fernandes, E. Pereira, J. Gracio, Diamond Relat. Mater. 8 (1999) 645. [17] L.B. Freund, S. Suresh, Thin Film Materials: Stress, Defect Formation and Surface Evolution, Cambridge University Press, Cambridge, U.K., 2004. [18] G.G. Stoney, Proc. R. Soc. Lond. Ser. A 82 (1909) 172. [19] B.D. Cullity, S.R. Stock, Elements of X-ray Diffraction, Prentice Hall, USA, 2001. [20] F.R. Lamastra, F. Leonardi, R. Montanari, F. Casadei, T. Valente, G. Gusmano, Surf. Coat. Technol. 200 (2006) 6172. [21] S.J. Fonash, J. Appl. Phys. 44 (1973) 4607. [22] V. Teixeira, Thin Solid Films 392 (2001) 276. [23] D. Bersani, P.P. Lotticia, X. Ding, Appl. Phys. Lett. 72 (1998) 73. [24] A. Rizzo, M. Sagace, U. Galietti, C. Pappalettere, Thin Solid Films 433 (2003) 144. [25] S. Tamulevicius, Vacuum 51 (1998) 127. [26] W.F. Riley, L.D. Sturges, D.H. Morris, Statics and Mechanics of Materials: An Integrated Approach, John Wiley & Sons, 1996. [27] T. Nakamura, T. Ichitsubo, E. Matsubara, A. Muramatsu, N. Sato, H. Takahashi, Acta Mater. 53 (2005) 323. [28] R.F. Gibson, Principles of Composite Material Mechanics, McGraw-Hill, Inc., 1994. [29] R.D. Cook, D.S. Malkus, M.E. Plesha, Concepts and Applications of Finite Element Analysis, John Wiley & Sons Inc., 1989. [30] E. Smith, G. Dent, Modern Raman Spectroscopy: A Practical Approach, John Wiley & Sons, 2005. [31] J.R. Ferraro, Introductory Raman Spectroscopy, Academic Press, 2002. [32] H.A. Szymanski, Raman Spectroscopy: Theory and Practice, Plenum Press, 1967. [33] G. Gu, Y. Li, Y. Tao, Z. He, J. Li, H. Yin, W. Li, Y. Zhaoa, Vacuum 71 (2003) 487. [34] K. Lagarec, S. Desgreniers, Solid State Commun. 94 (1995) 519. [35] I.A. Al-Homoudi, L. Zhang, E.F. McCullen, C. Huang, L. Rimai, R.J. Baird, K.Y. Simon Ng, R. Naik, G.W. Auner, G. Newaz, Solid-State Chemistry of Inorganic Materials V, Boston, U.S.A., Nov. 29–Dec. 3, 2004, Mater. Res. Soc. Symp. Proc., vol. 848, 2005, p. FF3.20.1. [36] JCPDS, Card # 71-1169, International Center for Diffraction Data, Swarthmore, PA. USA, 1988. [37] T. Ohsaka, F. Izumi, Y. Fujiki, J. Raman Spectrosc. 7 (1978) 321. [38] W.X. Xu, S. Zhu, X.C. Fu, Q. Chen, Appl. Surf. Sci. 148 (1999) 253. [39] S. Kelly, F.H. Pollak, M. Tomkiewicz, J. Phys. Chem. B 101 (1997) 2730. [40] A.E. Riad, F.D. Barlow, Thin Film Technology Handbook, McGraw-Hill Professional, 1997. [41] R.C. Buchanan, Ceramic Materials for Electronics: Processing, Properties and Applications, Marcel Dekker, 1991. [42] C. Hornbostel, Construction Materials: Types, Uses, and Applications, John Wiley & Sons, 1978. [43] K. Ihokura, J. Watson, The Stannic Oxide Gas Sensor: Principles and Applications, CRC Press, Inc., 1994. [44] C.H. Hsueha, S. Lee, Composites Part B 34 (2003) 747. [45] K. Katsumata, A. Nakajima, H. Yoshikawa, T. Shiota, N. Yoshida, T. Watanabe, Y. Kameshima, K. Okada, Surf. Sci. 579 (2005) 123. [46] J.A. Kuszyk, R.C. Bradt, J. Am. Ceram. Soc. 56 (1973) 420. [47] J.J. Cleveland, R.C. Bradt, J. Am. Ceram. Soc. 61 (1978) 478. [48] K.V.K. Rao, S.V.N. Naidu, L. Iyengar, J. Am. Ceram. Soc. 53 (1970) 124.
Contents lists available at ScienceDirect
Thin Solid Films j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / t s f
Residual stresses and Raman shift relation in anatase TiO2 thin film Ibrahim A. Alhomoudi a, G. Newaz b,⁎ a b
Mechanical Technology Dept., Hydraulic and Pneumatic Section, Alahsa College of Technology, P.O. Box 804, Hofuf 31982, Saudi Arabia Mechanical Engineering Dept., Wayne State University, Detroit, Michigan 48202, USA
a r t i c l e
i n f o
Article history: Received 22 March 2008 Received in revised 10 January 2009 Accepted 26 February 2009 Available online 9 March 2009 Keywords: Anatase Titanium dioxide Thin film Sputtering Raman spectroscopy Residual stress Curvature measurements
a b s t r a c t Anatase TiO2 film (100–1000 nm thick) grown on glass, sapphire (0001), and Si (100) substrates by pulsed dc-magnetron reactive sputtering were evaluated for stress and strain analysis using Raman spectroscopy and curvature measurement techniques. The X-ray analysis revealed that films prepared for this study were purely anatase, and the measurements indicate that the film exhibit that (101) is the preferred growth orientation of the crystallites, especially for the film thicker than 100 nm. Curvature measurements and Raman spectroscopy, with 514.5 nm excitation wavelength, phonon line shift were used for stress analysis. A comparison between Raman lineshapes and peak shifts yields information on the strain distribution as a function of film thickness. The measurements of residual stresses for crystalline anatase TiO2 thin film showed that all thin film were under compressive stress. A correlation between Raman shifts and the measured stress from the curvature measurements was established. The behavior of the anatase film on three different substrates shows that the strain in film on glass has a higher value compared to the strain on sapphire and on silicon substrates. The dominant 144 cm− 1 Eg mode in anatase TiO2 clearly shifts to a higher value by 0.45–5.7 cm− 1 depending on the type of substrate and film thickness. The measurement of the full width at half maximum values of 0.59–0.80 (2θ°) for the anatase (101) peaks revealed that these values are greater than anatase powder 0.119 (2θ°) and this exhibits strong crystal anisotropy with thermal expansion. © 2009 Elsevier B.V. All rights reserved.
1. Introduction Anatase TiO2 is most commonly used as a photocatalysis material for optical applications [1–6], gas sensors [7–9] and in solar cells [10,11]. It can decompose some pollutions with photocatalytic action and become important for environmental purification [12,13]; it was also used for ethanol and methanol sensing properties for breath analyses [14]. Many different fabrication techniques have been developed to prepare TiO2 thin film; however, the processing conditions have been found to strongly influence the structural properties of the resulting film. Often the film exhibits strain due to thermal stresses caused by differential thermal expansion between the substrate and the film or by the lattice constant mismatch between the two. Most of these stresses are either compressive or tensile, so they can eventually result in the failure of devices. It has been recognized that residual compressive stresses may cause film delamination from the substrate whereas tensile stress may cause surface cracks in the film [15,16]. The most commonly used methods to measure the residual stresses in film are substrate curvature measurements [17,18], X-ray diffraction (XRD) [19,20] and Raman
⁎ Corresponding author. Tel.: +1 313 577 2970. E-mail address: [email protected] (G. Newaz). 0040-6090/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.tsf.2009.02.141
spectroscopy [21,22]. The XRD and the curvature measurements can be used directly to determine the average stress in film. It is also known that (first order) zone center Raman phonon lines shift to higher/lower frequency under compressive/tensile stress. Extracting the magnitude of residual stress from Raman shifts requires knowledge of the relation between these shifts and the lattice strain [15,18,23]. We studied the relation between the Raman shifts and the average film strain, which was deduced from experimental measurements of substrate curvature induced by stresses resulting from film growth. Thermal effects provide an important contribution to film stress. Strain develops in a growing film because it is constrained during the deposition process. Usually this constraint is the bonding to a substrate. Thermal effects provide important additional contributions to film strain. The corresponding stresses will in turn strain the substrate. This substrate strain generally appears as bending of the substrate. The thermal strain is caused by differential thermal expansion between film and substrate when film is deposited at high temperature and then cooled. This film will be residually compressed when measured at room temperature if αf N αs, with α as the linear expansion coefficient. In this case the substrate shrinks more than the film. The total stress (σtotal) acting in a film is the result of three distinct contributions (Eq. (1)). These stresses are as follow: external stress (σext), which is due to possible external loading; thermally-induced stress (σth), which is due to the mismatch between the thermal expansion coefficients of both substrate and film material;
I.A. Alhomoudi, G. Newaz / Thin Solid Films 517 (2009) 4372–4378
and intrinsic stress (σin), which is related to the particular coating microstructure and the particular growing process itself [24,25]. σ total = σ ext + σ th + σ in
ð1Þ
The isothermal stress–strain relation, ignoring the effect of temperature change, is given by Hooke's law, σ = Eε, where the stress is directly proportional to the strain (an approximation limited to small strains and certain materials) [26]. E is a symmetric matrix of the material stiffness. Anatase film has orthotropic stress–strain relationships [27] that can be simplified as expressed in Eq. (2), where the z-axis is the principal material direction [28,29]. 8 9 2 S11 < e1 = e = 4 S12 : 2 ; γ12 0
S21 S22 0
9 38 0 < σ1 = 5 0 σ : 2; S66 τ 12
ð2Þ
4373
(Geigerflex X-ray Goniometer unit) with Cu source. Vmax = 80 kV, Imax = 150 mA for a Cu rotating anode. JADE XRD pattern processing (MDI) was used to collect and process the data. The Raman spectra were recorded in a backscattering geometry using a Renishaw InVia Raman-microscope system and the 514.5 nm excitation wavelength of an Ar-ion laser, focused on a spot size of the order of ≈ 3 µm. The Raman peak positions were obtained by curve-fitting the lineshaped Gaussians to the spectra shapes of the raw data obtained from the spectrometer. The curvature (deflection) measurement technique was performed using a model 128 intelligent film stress measurement system manufactured by Frontier Semiconductor Measurements (FSM) Inc., and the Stoney formula was used to derive a relation between the curvature of the system and the stress of the thin film [18]. 3. Results and discussions 3.1. X-ray diffraction (XRD)
Where S is a symmetric matrix of material compliances (S =E− 1), S11 = 1 / E1, S12 = − v12 / E1 = − v21 / E2, S22 = 1 / E2 and S66 = 1 / G12 =E12 /2(1 +v12). A Raman spectrum is generated when an intense beam of light, usually generated from a laser, is directed onto a material. A small fraction of this excitation light is scattered inelastically and shifted to a different frequency or wavelength. This change in frequency (Δν) is the frequency of a particular vibrational mode of the crystalline material (First order Raman effect) [30–32]. The three natural phases of titanium dioxide TiO2 are anatase, rutile and brookite. Anatase has six Raman active modes, A1g (515 cm− 1), 2B1g (400 and 519 cm− 1), 3Eg (144, 197 and 640 cm− 1), and rutile has four Raman active modes, A1g (612 cm− 1), B1g (143 cm− 1), B2g (826 cm− 1), Eg (447 cm− 1); both are tetragonal, while brookite is orthorhombic has 36 Raman active modes (9A1g + 9B1g + 9B2g + 9B3g) [15,23,33,34]. In our previous work on anatase TiO2 thin film, we studied the structural and morphological properties of amorphous and crystalline anatase TiO2 thin film [35]. We also studied the operation temperature, film thickness, and substrate effects on the resistance of anatase TiO2 thin film when exposed to CO gas [8]. In this work, our research interest was to study the influence of the anatase film thickness and substrate type, glass, sapphire (0001) and Si (100), for residual stress analysis using Raman spectroscopy and curvature measurement techniques. This information is important in order to understand the film structure, residual stress in the film, and film performance on different substrates. The selection of substrates was because the glass substrate has an amorphous structure and is a widely used material, where Si (100) substrate selection was based on the most commonly used substrate in different devices. However, the sapphire substrate has the closest thermal expansion coefficient (9.03 ×10 − 6/°C− 1) compared to the anatase TiO2 (10.20× 10− 6/°C− 1), as well as it has high chemical durability and is a good insulator since its band gap (8.8 eV) is much wider than the band gap of anatase (3.2 eV), thus improving the stability of the sensor. 2. Experimental setup Anatase TiO2 thin film (100–1000 nm thick) was prepared by magnetron sputtering in reactive argon/oxygen gas atmosphere on glass, sapphire (0001) and Si (100) substrates. The deposition condition was selected from our previous work [35] based on the XRD results of the best crystalline quality in terms of the maximum intensity ratio of the sharp diffraction peak to the broad background. This was carried out with the set of parameters, such as growth pressure (3.0–5.0 mTorr), power (300–500 W), and substrate temperature (25–400 °C). The anatase thin film was studied for stress analysis with X-ray diffraction, the Curvature measurement technique and Raman spectroscopy measurement. Crystalline structure and crystallite size were determined by means of standard θ/2θ XRD scans using a Rigaku-Rotaflex RU2000 diffractometer system
Film was characterized by XRD, which confirmed the anatase TiO2 structure of the film, and it also showed that the anatase film is crystalline material. All the observed sharp peaks could be indexed based on the anatase single-phase structure or assigned to substrate reflections, as indicated in Fig. 1(a), (b), and (c). A high peak at 25.22 (2θ°) and other very small peaks at 37.75 and 47.72 (2θ°) were observed, corresponding to anatase (101), (004) and (200) reflections, respectively. There is no evidence of a rutile phase of TiO2. The experimental peak positions were compared with the standard JCPDS card # 71-1169 [36], and the corresponding miller indices were indexed. The XRD analysis revealed that film prepared for this study was purely anatase, and the measurements indicate that the film exhibit that (101) is the preferred growth orientation of the crystallites, especially for the film thicker than 100 nm. As was observed, the diffraction patterns of the film deposited on the three substrates shown in Fig. 1(a), (b), and (c) contain the intensity ratio of the (101) peaks that are several times higher than other peaks in addition to the line assigned to the substrates. The film deposed on sapphire (0001) and Si (100) substrates also exhibit (004) orientation but very small compared to (101) orientation. Fig. 1(b) shows that the small peak observed at 37.75 (2θ°) appears somewhat higher because it consists of two components that are corresponding to the anatase (004) peak and also to the sapphire substrate peak. The broad background on the data for films on glass corresponds to the substrate, and there is no evidence that the thinner films show an amorphous component. The film on the glass substrate shown in Fig. 1(a) and on the sapphire (0001) substrate shown in Fig. 1(b) are transparent, while those grown on the Si (100) substrate shown in Fig. 1(c) present different colors related to interface effects. 3.2. Raman spectra The anatase TiO2 thin film Raman spectra on glass, sapphire (0001) and Si (100) are shown in Fig. 2(a), (b), and (c), respectively, using a wavelength of, λ = 514.5 nm. From the figures, the frequencies of Raman bands identified as 147.3 (± 2.8) cm− 1 are assigned to the Eg phononic modes represented by v6. The bands as 392.8 (± 4.3) cm− 1 are assigned to the B1g phononic mode (v4). The bands as 515.2 (± 5.3) cm− 1 can be attributed to the A1g phononic mode (v2). The bands as 513.14 (± 7.4) cm− 1 can be attributed to the B1g phononic mode (v3), and the bands as 628.8 (± 10.2) cm− 1 can be attributed to the Eg phononic mode (v1), based on the factor group analysis. These bands agree well with those in previous studies for anatase powder and single crystals [23,33,34,37,38]. From the factor plane analysis it was observed that both A1g (v3) and B1g (v2) modes involve the Ti–O bond stretching normal to the film plane [38]. The Raman spectroscopy results showed that the thinner film (100 nm) is
4374
I.A. Alhomoudi, G. Newaz / Thin Solid Films 517 (2009) 4372–4378
The shifts of the 400 cm− 1 B1g and 640 cm− 1 E1g modes were toward lower wave numbers and decrease with film thickness. As the broad band near ~517 cm− 1 consists of two components that are not well resolved, the 515 cm− 1 A1g and 519 cm− 1 B1g modes, the corresponding shifts indicated in Fig. 3 are unreliable and can be considered only as guesses. For the case of the Si (100) substrate even its location is questionable due to the presence of the strong substrate band. If these shifts were caused by the inhomogeneous strain field induced during the growth caused by lattice mismatches between substrate and anatase, the shifts should generally decrease with
Fig. 1. The X-ray diffraction patterns of five different thicknesses of anatase TiO2 thin film deposited on (a) glass, (b) sapphire (0001), and (c) Si (100) substrates.
a crystalline material, and the intensity of Raman spectrum of the thin film increases with film thickness. The positions of the major peaks are all shifted with respect to the corresponding frequencies in the bulk material. Fig. 3 shows the Raman spectrum mode shifts for anatase TiO2 thin film with different thickness on glass substrate shown in Fig. 3(a), on sapphire (0001) substrate shown in Fig. 3(b) and on Si (100) substrate shown in Fig. 3(c) using the excitation wavelength of λ = 514.5 nm. The dominant 144 cm− 1 Eg mode is shifted towards a higher frequency by an amount that depends on the substrate as well as on the thickness of the film. Similar shifts have been previously reported and have been related to the confinement effects in nano-structured anatase crystallites [39].
Fig. 2. Raman spectra of anatase TiO2 thin film with different thickness as deposited on (a) glass, (b) sapphire (0001), and (c) Si (100) with excitation wave length λ = 514 nm.
I.A. Alhomoudi, G. Newaz / Thin Solid Films 517 (2009) 4372–4378
4375
wave-number modes (400 B1g, 515 A1g, 519 B1g and 640 Eg modes) have similarity in Raman shifts, where the modes reduce their shifting from a lower energy to a higher energy band gap of the thin films on glass, sapphire (0001) and Si (100) substrates as shown in Fig. 3(a), (b), and (c), respectively. Another observation is that the high wavemodes have the same slope of shifting, except for the thin film on the Si (100) substrate. 3.3. Curvature measurements The anatase TiO2 thin film (100–1000 nm) grown on glass, sapphire (0001), and Si (100) substrates have also been used for the curvature measurements of substrates before and after the film deposition, where the residual stresses were then determined. The residual film stress (σ) was calculated by using Stoney's formula (Eq. (3)), which is based on an approximate plate analysis [17],
σ =
2 Esub tsub 6ð1 − vsub Þ tfil
!
1 1 − ðMPaÞ ra rb
ð3Þ
where Esub is the Young's modulus, vsub is the Poisson ratio of the substrate, tsub and tfil are the thickness of the substrate and the film, respectively, and ra and rb are the radii of curvature for substrate with and without film. The following have been used with Eq. (3): for glass, Esub = 627.58 GPa and vsub = 0.2; for sapphire, Esub = 370 GPa and vsub = 0.2; for Si, Esub = 230 GPa and vsub = 0.2 [40–43]. In the curvature measurement, Stoney's equation is justified because the film thickness is less than 5% of the substrate thickness. Fig. 4 shows the stress as a function of the anatase TiO2 film thickness (100– 1000 nm) on glass, sapphire (0001) and Si (100) substrate. These results clearly show that the bi-axial stresses are compressive and decrease with the increasing film thickness. Further, the magnitude of residual stress in the film grown on glass substrate is substantially larger than that on sapphire (0001) or Si (100) substrates. The lower residual stress in film prepared on sapphire (0001) and Si (100) substrates can be explained based on the closeness of the thermal expansion coefficient and the lattice match between the substrate and the anatase film. It is interesting to note that anatase film grown on sapphire (0001) exhibits a stress relaxation over a small thickness range compared with the film grown on Si (100) and glass substrates.
Fig. 3. Raman spectrum shift of anatase TiO2 thin film modes deposited on (a) glass, (b) sapphire (0001), and (c) Si (100) substrate using the excitation wavelength of λ = 514.5 nm.
increasing film thickness and should be smaller for the spectra obtained with the shorter wavelength excitation. Fig. 3 implies that this may indeed be the case. In addition, as shown clearly in Fig. 3(a), (b), and (c) for the 144 cm− 1 Eg line, as the shift increases, so does the line broadening, which according to the interpretation given above indicates as expected that the strain field within the probed volume is rather inhomogeneous, but that this inhomogeneity decreases as the point of probing moves further from the substrate. The four high
Fig. 4. Variation of residual stress with anatase TiO2 film thickness on different substrates.
4376
I.A. Alhomoudi, G. Newaz / Thin Solid Films 517 (2009) 4372–4378
3.4. Residual strain of anatase thin film The strains for the anatase TiO2 thin film on the three different substrates were calculated based on Eq. (2). The elastic constants E1 = 303 GPa, E2 = 115 GPa and G12 = 94 GPa for anatase TiO2 were taken from reference [27], and the Poisson's ratio (vsub) has value as mentioned earlier, where the stress values were obtained from curvature measurements. The stress–strain behavior for anatase TiO2 thin film on the three different substrates are shown in Fig. 5, which shows that the calculated data for the film on the three different substrates fit in a straight line. Also, the strain for the thin film on glass has a higher value compared to the strain on sapphire (0001) and on Si (100). Furthermore, the stiffness (E = 179 GPa) for the thin film was calculated from the slope of the stress–strain curve. 3.5. Measurement of Raman peak shifts Quantitative relationships between bi-axial stress and the shift in the phonon frequencies exist for diamond film [22]. It is known that the Raman peak shift (Δω) is proportional to the magnitude of residual stress in thin film [21,44]. However, no theoretical work describing such relations for tetragonal anatase TiO2 is reported in the literature; thus, no proportionality constant factor between Δω and the residual stress in the thin film is known for anatase. The Raman peak shift was measured with respect to its position in the stress free sample. Assuming that the diamond result is also correct for anatase, we can write the relation namely, σ = IAN · Δω ðMPaÞ
ð4Þ
Where IAN (MPa/cm− 1) is the proportionality constant. The value of this constant can be calculated based on the stresses obtained from curvature experiments, particularly Raman transition, substrate and excitation wavelength. Δω (cm− 1) is the Raman peak shift of the film. The Raman spectra of the anatase TiO2 thin film (100–1000 nm) was measured with 514.5 nm laser excitation, and the thickness dependent shifts of Eg phonon mode were given above. The dominant 144 cm− 1 Eg mode in anatase TiO2 clearly shifted to a higher value by 0.45–5.7 cm− 1 depending on the type of substrate and the film thickness (shown in Fig. 6). It is also shown in Fig. 6 that Δω decreases with increasing film thickness. Maximum shift was seen for the film on the glass substrate indicating a higher bi-axial compressive stress in agreement with the curvature measurements. The shifts of Eg mode clearly show that the bi-axial stress increases along the film depth, being larger at the film/substrate interface.
Fig. 5. Stress–strain behavior for anatase TiO2 thin film on three different substrates.
Fig. 6. Variation of Δω with film thickness for 144 cm− 1 Eg mode of anatase TiO2 thin film on different substrates.
Fig. 7(a), (b), and (c) show a summary of the Raman line shift of 144 cm− 1 Eg mode obtained with 514.5 nm excitation wavelength vs. average residual stress values determined from curvature measurements on the three different substrates, glass, sapphire (0001) and Si (100), respectively. The Raman peak positions were obtained by fitting Gaussians to spectra shapes. The value of the proportionality constant, IAN (MPa/cm− 1), in Eq. (4) was obtained by fitting a straight line as shown in Fig. 7, where the value of IAN was found to be equal to − 937, − 337 and − 391 (MPa/cm− 1) for the anatase film on glass, sapphire (0001) and Si (100) substrates as shown in Fig. 7(a), (b), and (c), respectively. The magnitude of the stress in the film changes depending on the film thickness and substrate. The compressive stresses gradually increase with lower film thickness, which means that the stress gets higher closer to the film and substrate interface. In correlation of the Raman spectroscopy peaks shift with the curvature measurements, Fig. 8 shows the Raman shift vs. strain of the film calculated based on Eq. (2). It shows that the shift increases with the strain. It was also observed that the Raman band 144 cm− 1 broadened with decreasing strain as shown in Fig. 9. The broadening of these peaks shows that there are contributions to the Raman band shift from the anatase growth oriented at all angles to the deformation axis. Anatase growth oriented at 90° to the deformation axis will shift to a higher
Fig. 7. The Raman spectrum shift of 144 cm− 1 Eg mode obtained with 514.5 nm excitation wavelength vs. average residual stress values determined from curvature measurements on glass, sapphire (0001) and Si (100) substrate.
I.A. Alhomoudi, G. Newaz / Thin Solid Films 517 (2009) 4372–4378
4377
Fig. 8. Raman spectrum shift of 144 cm− 1 peak vs. strain for anatase TiO2 thin film on three different substrates.
Fig. 10. The average crystallite sizes of the anatase TiO2 thin film with different film thickness on sapphire (0001) substrate.
wave-number with strain due to Poisson's contraction of the matrix; compression on the anatase thin film will result in positive shift of 144 cm− 1 Raman bands. From XRD analysis, the intensities of the XRD (101) anatase peak were increased and the widths became broader. In general, the full width at half maximum (FWHM) of the XRD peak corresponds to the crystal size of the porous materials. When the width was broader, the crystallites exhibited smaller size. The Scherrer equation (Eq. (5)) was used to determine the average crystal sizes of the TiO2 nanoparticles.
anatase powder (0.395° and 0.119° for film with 30 and 200 nm thick), which is assumed to be strain free [45]. Crystallite size values were determined using the Scherrer equation (Eq. (5)) to fined the average crystal sizes of the anatase TiO2 thin film, assuming that all broadening was due to crystallite size. Our XRD analysis of the anatase TiO2 thin film predicted a crystallite size of 10–13 nm on the glass substrate, 11–13 nm on the Si (100) substrate and 10–12 nm on the sapphire (0001) substrate. A likely explanation for the slightly low value of crystallite size predicted by the XRD analysis resides in the assumption that all peak broadening is due to crystallite size effects. Fig. 10 shows the average crystallite sizes of the anatase TiO2 thin film with different film thickness on sapphire (0001) substrate, and it clearly states that the crystallite size is thickness-dependant. It was reported that polycrystalline ceramic materials revealed that the effect of residual stress among grains caused by thermal expansion anisotropy increases with increasing grain size, where anatase exhibits strong crystal anisotropy with thermal expansion [45–48]. The residual stress evaluated by the above-mentioned techniques is actually a sum of thermal stress and intrinsic stress. Therefore, the nature of the residual stress is determined by the nature and relative magnitude of these two stress components. Considering the effect of the thermal mismatch, we can assume the anatase thin film and substrate behave as a bi-metal plate, where the difference in the thermal expansion coefficients will induce stresses in both the film and the substrate and will lead to the film/substrate bending upon cooling from the deposition temperature to room temperature. In other words, the anatase film and substrate might be lattice matched at the deposition temperature and are cooled to a lower temperature, so thermal strain is produced in the layer since the coefficients of thermal expansion of the anatase film and substrate are not equal. As a result, the anatase film is strained such that the in-plane lattice constant of the anatase is the same as that of the substrate. The strain in this case is homogeneous and is known as the misfit strain. Before the deposition process, great care is taken to ensure the cleanliness of the substrates. Since the deposition temperature of the anatase is around 300 °C, which is less than what is needed to grow thermal oxide (750 °C and 1100 °C), the anatase deposition on the Si substrate is assumed to be clean and free of the native amorphous SiO2 thin layer. The resulting measurement stress of the anatase film on the Si (100) substrate gives more confidence assumptions.
t=
0:9λ β · cosθ
ð5Þ
Where t is the crystallite size, λ is the X-ray wavelength of the incident radiation (Cu Kα = 0.154 nm), β is the broadening of diffraction line measured as half of its maximum intensity (FWHM), and θ is the corresponding diffraction angle for anatase TiO2 (101) reflection. The measurements of the FWHM values of anatase (101) peaks were found to be in the range of 0.59–0.76 (2θ°) on the glass substrate, 0.6–0.74 (2θ°) on the Si (100) and 0.60–0.80 (2θ°) on the sapphire (0001) substrate. These values of the FWHM for anatase thin film on the three different substrates are several times larger than for
4. Conclusions Fig. 9. Peak broadening of 144 cm− 1 peak vs. strain of anatase TiO2 thin films on three different substrates.
X-ray diffraction confirmed the anatase TiO2 structure of the thin film and showed that the anatase film is crystalline material. The XRD
4378
I.A. Alhomoudi, G. Newaz / Thin Solid Films 517 (2009) 4372–4378
data showed that the anatase film, 100 nm thick on the glass, has a broader background that corresponds to the substrate, but there is no evidence that this thinner film has an amorphous component. In contrast, Raman spectroscopy showed that this thin film is crystallite material. Raman spectroscopy measurements using the 514.5 nm excitation wavelength of 144 cm− 1 Eg vibration mode yielded information on the strain distribution as a function of film thickness. Curvature measurement and Raman spectroscopy were used for stress/strain analysis. The measurements of residual stresses for crystalline anatase TiO2 thin film showed that all film are under a compressive stress. The stress/strain behavior for anatase film on three different substrates showed that the strain for the thin film on glass has a higher value compared to the strain on sapphire or on silicon substrates. The bi-axial strain originates from growth on lattice-mismatched substrates and from post-growth cooling. Thin 100 nm anatase film on a glass substrate has the highest compressive stress of about 6000–7000 MPa. Compressive stress in the anatase film on sapphire and silicon are considerably less (1200–2000 MPa). Both curvature measurements and Raman peak shift estimated residual stresses in anatase thin film compare well. Acknowledgments The authors wish to acknowledge the support of the Institute for Manufacturing Research and the Smart Sensors and Integrated Microsystems (SSIM) program at Wayne State University. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12]
A. Weibel, R. Bouchet, P. Knauth, Solid State Ionics 177 (2006) 229. B. Huber, H. Gnaser, C. Ziegler, Surf. Sci. 566–568 (2004) 419. H. Wang, Y. Wu, B. Xu, Appl. Catal., B Environ. 59 (2005) 139. I. Justicia, G. Garcia, G.A. Battiston, R. Gerbasi, F. Ager, M. Guerra, J. Caixach, J.A. Pardo, J. Rivera, A. Figueras, Electrochim. Acta 50 (2005) 4605. S. Tanemura, L. Miao, P. Jin, K. Kaneko, A. Terai, N. Nabatova-Gabain, Appl. Surf. Sci. 212–213 (2003) 654. Y. Sheng, B. Zhou, Y. Liu, X. Zhao, C. Wang, Y. Pan, Z. Wang, Mater. Lett. 60 (2006) 1327. H. Tang, K. Prasad, R. Sanjines, F. Levy, Sens. Actuators, B 26–27 (1995) 71. I.A. Al-Homoudi, J.S. Thakur, R. Naik, G.W. Auner, G. Newaz, Appl. Surf. Sci. 253 (2007) 8607. S.A. Akbar, L.B. Younkman, J. Electrochem. Soc. 144 (1997) 1750. J.N. Hart, R. Cervini, Y.B. Cheng, G.P. Simon, L. Spiccia, Sol. Energy Mater. Sol. Cells 84 (2004) 135. K.D. Rogers, D.W. Lane, J.D. Painter, A. Chapman, Thin Solid Films 466 (2004) 97. S. Ikezawa, F. Mutsuga, T. Kubota, R. Suzuki, K. Baba, S. Koh, T. Koshioka, A. Nishiwaki, K. Kida, Y. Ninomiya, K. Wakita, Vacuum 59 (2000) 514.
[13] S. Ikezawa, H. Homyara, T. Kubota, R. Suzuki, S. Koh, F. Mutuga, T. Yoshioka, A. Nishiwaki, Y. Ninomiya, M. Takahashi, K.K.K. Babaa, T. Hara, T. Famakinwa, Thin Solid Films 386 (2001) 173. [14] C. Garzella, E. Comini, E. Tempesti, C. Frigeri, G. Sberveglieri, Sens. Actuators, B 68 (2000) 189. [15] F. Vaz, L. Rebouta, P. Goudea, J.P. Riviere, E. Schaffer, G. Kleer, M. Bodmann, Thin Solid Films 402 (2002) 195. [16] Q.H. Fan, A. Fernandes, E. Pereira, J. Gracio, Diamond Relat. Mater. 8 (1999) 645. [17] L.B. Freund, S. Suresh, Thin Film Materials: Stress, Defect Formation and Surface Evolution, Cambridge University Press, Cambridge, U.K., 2004. [18] G.G. Stoney, Proc. R. Soc. Lond. Ser. A 82 (1909) 172. [19] B.D. Cullity, S.R. Stock, Elements of X-ray Diffraction, Prentice Hall, USA, 2001. [20] F.R. Lamastra, F. Leonardi, R. Montanari, F. Casadei, T. Valente, G. Gusmano, Surf. Coat. Technol. 200 (2006) 6172. [21] S.J. Fonash, J. Appl. Phys. 44 (1973) 4607. [22] V. Teixeira, Thin Solid Films 392 (2001) 276. [23] D. Bersani, P.P. Lotticia, X. Ding, Appl. Phys. Lett. 72 (1998) 73. [24] A. Rizzo, M. Sagace, U. Galietti, C. Pappalettere, Thin Solid Films 433 (2003) 144. [25] S. Tamulevicius, Vacuum 51 (1998) 127. [26] W.F. Riley, L.D. Sturges, D.H. Morris, Statics and Mechanics of Materials: An Integrated Approach, John Wiley & Sons, 1996. [27] T. Nakamura, T. Ichitsubo, E. Matsubara, A. Muramatsu, N. Sato, H. Takahashi, Acta Mater. 53 (2005) 323. [28] R.F. Gibson, Principles of Composite Material Mechanics, McGraw-Hill, Inc., 1994. [29] R.D. Cook, D.S. Malkus, M.E. Plesha, Concepts and Applications of Finite Element Analysis, John Wiley & Sons Inc., 1989. [30] E. Smith, G. Dent, Modern Raman Spectroscopy: A Practical Approach, John Wiley & Sons, 2005. [31] J.R. Ferraro, Introductory Raman Spectroscopy, Academic Press, 2002. [32] H.A. Szymanski, Raman Spectroscopy: Theory and Practice, Plenum Press, 1967. [33] G. Gu, Y. Li, Y. Tao, Z. He, J. Li, H. Yin, W. Li, Y. Zhaoa, Vacuum 71 (2003) 487. [34] K. Lagarec, S. Desgreniers, Solid State Commun. 94 (1995) 519. [35] I.A. Al-Homoudi, L. Zhang, E.F. McCullen, C. Huang, L. Rimai, R.J. Baird, K.Y. Simon Ng, R. Naik, G.W. Auner, G. Newaz, Solid-State Chemistry of Inorganic Materials V, Boston, U.S.A., Nov. 29–Dec. 3, 2004, Mater. Res. Soc. Symp. Proc., vol. 848, 2005, p. FF3.20.1. [36] JCPDS, Card # 71-1169, International Center for Diffraction Data, Swarthmore, PA. USA, 1988. [37] T. Ohsaka, F. Izumi, Y. Fujiki, J. Raman Spectrosc. 7 (1978) 321. [38] W.X. Xu, S. Zhu, X.C. Fu, Q. Chen, Appl. Surf. Sci. 148 (1999) 253. [39] S. Kelly, F.H. Pollak, M. Tomkiewicz, J. Phys. Chem. B 101 (1997) 2730. [40] A.E. Riad, F.D. Barlow, Thin Film Technology Handbook, McGraw-Hill Professional, 1997. [41] R.C. Buchanan, Ceramic Materials for Electronics: Processing, Properties and Applications, Marcel Dekker, 1991. [42] C. Hornbostel, Construction Materials: Types, Uses, and Applications, John Wiley & Sons, 1978. [43] K. Ihokura, J. Watson, The Stannic Oxide Gas Sensor: Principles and Applications, CRC Press, Inc., 1994. [44] C.H. Hsueha, S. Lee, Composites Part B 34 (2003) 747. [45] K. Katsumata, A. Nakajima, H. Yoshikawa, T. Shiota, N. Yoshida, T. Watanabe, Y. Kameshima, K. Okada, Surf. Sci. 579 (2005) 123. [46] J.A. Kuszyk, R.C. Bradt, J. Am. Ceram. Soc. 56 (1973) 420. [47] J.J. Cleveland, R.C. Bradt, J. Am. Ceram. Soc. 61 (1978) 478. [48] K.V.K. Rao, S.V.N. Naidu, L. Iyengar, J. Am. Ceram. Soc. 53 (1970) 124.