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Surface anisotropy characterization and microstructure of Cu–W thin films at different annealing temperatures
ARTICLE IN PRESS
Physica B 349 (2004) 10–18
Surface anisotropy characterization and microstructure of Cu–W thin films at different annealing temperatures Wang Yuana,b, Bai Xuanyua, Xu Keweia,* a
State-Key Laboratory for Mechanical Behavior of Materials, Xian Jiaotong University, Xian 710049, China b Department of Mechanical Engineering, Lanzhou Railway Institute, Lanzhou 730070, China Received 17 November 2003; received in revised form 12 January 2004; accepted 12 January 2004
Abstract Cu–W films were deposited on Al2O3 substrates by magnetron sputtering and then annealed in Ar gas at different temperatures for an hour. The evolution of surface morphology of the films during deposition and annealing was investigated by mathematical techniques. A strategy integrating discrete wavelet transform and fractal geometry concepts was developed for analyzing the anisotropy of surface structure of Cu–W thin films. The results indicated that the agglomeration of Cu–W thin films occurs primarily during annealing process. Based on the observation of positive correlation between the surface anisotropy and W-like phase transition, the relationship between the evolution of surface morphology of Cu–W thin films and the transition of phase structure was constructed. It was concluded that the changes of phase structures could have a significant impact on the anisotropy behavior of surface structure of Cu–W thin films. r 2004 Elsevier B.V. All rights reserved. PACS: 68.55.J; 81.40.E; 64.70.D Keywords: Cu–W thin films; Surface morphology; Phase structure; Mathematical analysis
1. Introduction It is well known that surface morphology is a vital characteristic of thin films. Because many physical and chemical properties, such as electrical [1], optical [2], tribological properties [3] of thin films are controlled by the surface morphology, detailed knowledge and precise control over the surface and interface integration are of great *Corresponding author. State-Key Laboratory for Mechanical Behavior of Materials, Xian Jiaotong University, Xian 710049, China. Tel.: +86-29-88403018; fax: +86-29-83237910. E-mail addresses: [email protected] (Wang Yuan), [email protected] (Xu Kewei).
importance, particularly for modern electronic devices as the dimension of micro-devices continues to shrink. Thin films are usually nonideal material systems. Ion bombardment during deposition further produces a population of surface defects of nonequilibrium in the thin films [4]. These structural defects create a complex array of internal interface that are directly related to the external surface features. In addition, the morphologies of the anisotropic void and grain boundary within the thin films have long been known to directly affect the film properties [5]. Although surface morphology is controlled by the film microstructure, the relationship between surface morphology and thin
0921-4526/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2004.01.146
ARTICLE IN PRESS Wang Yuan et al. / Physica B 349 (2004) 10–18
film microstructures is not yet fully understood. In fact, few studies have been conducted to quantitatively describe the relationship between surface morphology and film microstructure. Substantial amounts of efforts have been directed to the quantitative description of the morphology of rough surfaces and interfaces of thin films [6, 7]. Because the roughness of thin film surfaces usually exhibits self-affine behavior [8], the surface morphology can be described by the concepts of scaling rule. The fractal dimension can be taken as a possible measure of a structure. However, further studies are needed to characterize the irregular structure of the surfaces. The complex morphology of thin films, especially the anisotropy of the structure, can not be described in detail only with a fractal dimension value. Leamy [9] demonstrated that the electron-scattering patterns can be used to determine the direction of growth morphological anisotropy, but proposed method is complex and involves many steps. A new approach of integrating wavelet transform and fractal geometry to characterize the film morphology is developed in the present paper. This integrative method can be used to describe surface morphology in addition to characterize the anisotropy behavior of surface morphology for thin films. The anisotropy behavior of surface roughening process of the Cu–W thin film with annealing temperature is analyzed by this approach as an example because amorphous immiscible binary transition metals are of particular interests as thin-film coatings on parts for microelectronics [10]. Additionally an interest work to interrelate the fractal dimension and a quantitative characterization of the anisotropy of the structure is also conducted, which would enhance our increased understanding of the correlation between the changes of surface and internal structures of thin films.
2. Experimental 2.1. Film preparation The Cu–W thin films were deposited on polished Al2O3 substrates by radio frequency (RF) magne-
11
tron sputtering system with the tungsten target (99.95%, purity) and the circular Cu sector plates (99.99%, purity and 1 mm thick). The deposition of Cu–W film was conducted in a stainless-steel vacuum chamber which was evacuated by a turbomolecular pump to 6 105 Pa prior to deposition. The Al2O3 substrates were mounted on a specimen holder equipped with a water cooling system, and was rotated at a rate of 5 rpm to achieve uniform film depositing during sputtering. The Al2O3 substrates were cleaned ultrasonically with alcohol before they were placed into vacuum chamber and then cleaned again by applying RF power of 100 W under Ar (purity of 99.999%) for 10 min prior to film deposition. The target was pre-sputtered by Ar ions to remove surface contamination that may have formed during the system vacuuming process. The magnetron sputtering deposition was performed at an RF power of 50 W. Argon gas flow was controlled by a mass flowmeter at a flow rate of 8 sccm and 0.3 Pa. The thickness of deposited thin films was about 550 nm. Pure tungsten and copper films were also prepared individually as controls under the same conditions. Samples annealing was carried out in a thermal annealing furnace with flowing argon atmosphere (purity of 99.999%) for 1 hr. The heating rate was 9 C/min and the annealed samples were slowly cooled to room temperature at a rate less than 1 C/min. The annealing temperature was set to 250 C, 350 C, 500 C, and 800 C for samples of No. 2, 3, 4, and 5, respectively, with sample No. 1 being the as-deposited film (no annealing Table 1).
2.2. Film characterization The elemental concentration of thin films was determined by an X-ray photoelectron spectroscopy (PHI-5702). The compositions of Cu50W50 are as-prepared samples, and are kept nominal in the discussion. After heat treatment, each thin film samples was taken out for immediately ex situ measurements by a scanning electron microscopy (JEOL JSM5600LV). Each sample was measured at least four times at different locations on the surface. A
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Table 1 Fractal dimensions and interplanar spacing of Cu–W thin films at different annealing temperatures Samples number
Interplanar spacing ( b d (A)
Fractal dimensions Detailed subimages
1 2 3 4 5
Amorphous 2.16 2.19 2.23 — a b
Original morphology of thin filmsa
Diagonal
Horizontal
Vertical
Standard deviation
2.4668 2.6975 2.9483 2.7629 2.8543
2.4748 2.6595 2.8469 2.6290 2.6912
2.4809 2.6995 2.8793 2.6656 2.7106
0.00707 0.02254 0.05179 0.06921 0.08910
2.346 2.486 2.762 2.584 2.412
The fractal dimension of original morphology of samples which do not be processed by wavelet transformation. W-like phase.
Regaku D/max-3A X-ray diffractometer with Co-Ka radiation was used for phase analysis.
3. Quantification of surface morphology of thin films In the description of the surface of thin films, surface morphology is usually treated as gray scale images in which the brightness of the image pixels is correlated to surface relief. Two-dimensional signals (i.e. images with two dimension of space x and y and gray levels) representing the relief of the surfaces can be easily established. Construction and analysis of these gray scale images of thin films are, however, not yet fully practiced and investigated. Scanning electron microscopy (SEM) was used in this study to view the topology of the surface of thin films. Image analysis of these micrographs is, therefore, expected to produce accurate profile of the evolution of surface morphology, in addition to provide information on the size distribution and shapes of the morphological features. In this work, thin film surfaces structures were firstly decomposed according to three different directions, namely horizontal, vertical, and diagonal directions, by using wavelet transform method. These three different directional subimages represent different directional information of surface morphology, respectively. Fractal geometry was then applied to the analysis of these
subimages. The computed standard deviation of the fractal dimension values of these subimages was used to describe the anisotropy of the surface morphology of thin films. By this approach a quantitative characterization of the anisotropy of thin films can be achieved. 3.1. Wavelet transform of surface morphology The wavelet transform is considered as a mathematical microscope in an analysis of image signals at various scales. The advantage of wavelet analysis over traditional Fourier methods in analyzing physical situations is that signals with discontinuities and sharp spike, such as rough surfaces of thin films, can be accurately described. Wavelet analysis is applied in the way that the transformation will break up a signal into shifted and scaled versions of the original (or parent) wavelet. The mathematical expression of this transformation is [11] 1 tb ca;b ðtÞ ¼ pffiffiffi c ; a; bAR; aa0; ð1Þ a a where a is a scaling parameter which measures the degree of the scale, and b a translation parameter which determines the time location of the wavelet, and t is the space variable. cðtÞ is the parent wavelet. In practical application involving fast numerical algorithms, the wavelet transform can be
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computed at discrete grid points, thus substantially reduce the amount of computations. Discrete wavelet transform (DWT) appears to have a great potential for analyzing the multi-scale features of rough surfaces because the DWT possesses the properties of good time-frequency localization and flexible multi-resolution [12]. As a matter of fact, the 2D DWT is computed by applying a separable filter-bank to an image [13]: L ði; jÞ ¼ ½H ½H L ði; jÞ; ð2Þ n
x
y
n1 k2;1 k1;2
Dn1 ði; jÞ ¼ ½Hx ½Gy Ln1 k2;1 k1;2 ði; jÞ;
ð3Þ
Dn2 ði; jÞ ¼ ½Gx ½Hy Ln1 k2;1 k1;2 ði; jÞ;
ð4Þ
Dn3 ði; jÞ ¼ ½Gx ½Gy Ln1 k2;1 k1;2 ði; jÞ:
ð5Þ
Here denotes the convolution operator. The k2; 1ðk1; 2Þ represents subsampling along the rows (columns) in a window of an image. L0 is the original image. Hx ; Hy and Gx ; Gy are low- and high-pass filters in the horizontal ðxÞ and vertical ðyÞ directions, respectively. Ln is obtained by lowpass filtering and therefore regarded as the lowresolution image at scale n: The detail subimages Dn1 ; Dn2 ; Dn3 are obtained by high-pass filtering in horizontal, vertical and diagonal direction, respectively, and therefore they contain corresponding directional information at scale n. The original image is thus represented by a set of subimages at multiple scales, fLd ; Dni gi¼1;2;3;n¼1;2;y;d ; where d is the level of wavelet decomposition. In this study, a six-level wavelet decomposition using Daubechies’s 4 wavelet basis was performed on the thin film surface morphology images. It was found during the experiment that a six-level discrete wavelet decomposition is sufficient to extract nearly all the directional information for the surface morphology of a thin film. Further improvement in the quality of the extracted information with the increase of decomposition level is minimal. However, more useful information could be missed if less than a six-level wavelet decomposition was used. The six-level discrete wavelet decomposition process is shown in Fig. 1. Because the objective of this study was the characterization of surface structure anisotropy of thin films, the detail subimages at all scales in
13 L0 L1
D11
L2
D21
L3
D31
L4 L5
D41 D51
D52
D42
D32
D12 D13
D22 D23
D33
D43
D53 D2
L6
D61
D62
D63
D1
D3
Fig. 1. Tree structure of wavelet decomposition and the constructing of detail directional subimages.
the same direction were merged into one process with the directional information of surface structures being highlighted (as shown in Fig. 1). The different directional decomposition results of DWT for sample No. 4 are shown in Fig. 2. 3.2. Fractal analysis The fractal dimension of the surfaces was estimated with Fourier power spectral density (PSD). Fourier transform (FT) is a powerful approach in image analysis. It is a linear integral transformation that establishes a unique correspondence between a complex-valued function (e.g., of time) and a complex-valued function of frequency. In addition, it is virtually insensitive to the noise of up to about 10% of signal (10:1 signal-to-noise ratio) and does not deviate significantly until the noise reaches 25% of signal strength (3:1 signal-tonoise). This feature of FT method suggests that for an elevation of the profiles, the influence of instrument noise which is an order of magnitude smaller than the signal can be ignored [14]. Each resulted subimage is still a 2D image after DWT decomposition, so the 2D PSD method can be applied to calculate its fractal dimension. The fractal dimensions of a set of different directional detail subimages can be calculated from the slope of a log S(k)—log k plot. The relationship between the PSD SðkÞ and the frequency k is given as [15] SðkÞpkb :
ð6Þ
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Fig. 2. Different directional detail subimages after wavelet transform of sample No. 4.
The fractal dimension D is related to the slope b in the log–log plot b D¼4þ : 2
ð7Þ
The 2D PSD of an Nx Ny SEM image can be calculated with a 2D fast FT. The equation is as follows: F ðu; vÞ ¼
N y1 x1 N X X x¼0
Zðx; yÞej2pðux=Nx þvy=Ny Þ ;
y¼0
uAf0; Nx1 g; vAf0; Ny1 g;
ð8Þ
where Zðx; yÞ is gray value of image which corresponds to the height function of a 2D topological surface. u and v are the frequency variables. So the 2D PSD can be calculated by the following equation: SðkÞ ¼ jF ðu; nÞj2 :
ð9Þ
No other processing needs to be performed before this calculation. Fig. 3 shows the relationship between PSD SðkÞ and frequency k of three different directional detail subimages for sample No. 4. The fractal dimension values of original surface morphology of thin films, which do not be
processed by DWT, were calculated by the same methods, and the standard deviation values of the fractal dimension of detail directional subimages at different annealing temperatures were also calculated. The results are listed in Table 1.
4. Results and discussion Changes in the X-ray diffraction patterns of the samples caused by the thermal annealing are shown in Fig. 4. The evolution of Cu–W thin film surface features with annealing temperatures can be seen clearly in Fig. 5. The X-ray diffraction measurements show an amorphous structure for as-deposited Cu–W thin film. The XRD measurements also indicate that as-deposited W thin film is a metastable A15 b-W phase [16], and the (2 1 0) and (2 0 0) (not shown) reflections peaks are clearly observed. The lattice parameters of the crystal structure from XRD patterns were calculated to be 0.506 nm for b-W phase and 0.361 nm for FCC Cu, in good agreement with the readings from the powder diffraction standards cards (JCPDS cards). The Cu–W amorphous thin film (sample No. 1) has a very smooth, featureless surface structure as
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8
Diagonal
15
7
Intensity, a.u.
Cu (111)
6
logS(k)
substrate W-like phase Cu (200)
_ β W (210)
5
4
Sample No.4
3
2
3
1 2 -3.0
-2.5
-2.0
-1.5
-1.0
logk
30
40
50
60
70
80
90
2θ, degree Fig. 4. XRD patterns of Cu–W films with annealing temperatures.
8
Horizontal 7
logS(k)
6
5
4
3
2 -3.0
-2.5
-2.0
-1.5
-1.0
logk
8
Vertical
7
logS(k)
6
5
4
Fig. 5. SEM micrographs showing evolution of Cu–W thin film morphology at different annealing temperatures, (a) as-deposited, (b) 250 C, (c) 350 C, (d) 500 C, (e) 800 C.
3
-3.0
-2.5
-2.0
-1.5
-1.0
logk Fig. 3. Power spectra density SðkÞ versus frequency k of three different directional detail subimages for sample No. 4.
showing in Fig. 5(a). However, the surface structures changed significantly with the increase of annealing temperature. At 250 C, some voids
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are formed in the substrate (Fig. 5(b)), while a BCC phase similar to W also appears at the same time. Broad diffraction lines positioned at Bragg angles higher than those of pure W are observed at this temperature. It is likely that on very surface the adatom mobility is high enough that significant crystallization occurs if conditions meet. Grzeta [17] and Dirks [18] believed that the BCC phase is a metastable BCC W(Cu) phase for vapordeposited Cu–W thin films. With the increase of annealing temperature, the voids grow rapidly into islands. The Cu content of islands on top surface of the thin films determined with an energy dispersive spectroscopy (EDS) is above 80 at%. It is concluded that the segregation of Cu occurs during annealing temperature. These thin films deposited by sputtering have a void concentration much higher than the equilibrium concentration at the annealing temperatures [19,20], suggesting that void nucleation may be easily initiated due to supersaturated excess vacancies. In addition, the segregation of Cu would also raise the vacancy formation. Natasi [21] reported that continued heating to about 350 C resulted in the addition of an FCC Cu signal to the diffraction pattern for Cu–W thin film of similar composition. The FCC Cu lattice parameter, however, remained unchanged with the increasing of annealing temperature. Because the diffraction peaks of Cu and substrate largely overlapped in Fig. 4, the changes of interplanar spacing and diffraction intensity of BCC phase were, therefore, used to represent the trend of thin film phase transition during heat treatment for Cu50W50 thin films. With the further increase of annealing temperature, the size of islands increases while the density decreases. Some smaller islands decay due to surface diffusion and the size of larger islands increases due to the growth of grain. This trend indicates that islands could coalesce and the number of islands decreases with annealing temperature. From a thermodynamic point of view, a giant single island has the least free energy for the system. The coalescence of two isolated island surfaces separated by a minimum distance is the energy decrease because of the elimination of two free surfaces.
The size of islands appears to depend on the annealing temperature. The agglomeration of islands takes place in two distinct stages: the nucleation of voids followed by the growth of islands. This agglomeration of islands has been attributed to a change in the surface structure by surface diffusion [22], which results in the migration of particles between grains and promotes the formation of larger islands at the cost of smaller ones, also helps in the formation of elevated islands instead of purely two-dimensional ones. Ozakan et al. [23] demonstrated that surface roughening of thin films preferentially takes place in the form of ridges or islands aligned along some certain directions, and the surface structures rotate toward other directions by means of annealing. This means that the anisotropy of surface morphology would be changed due to surface diffusion and grain growth. The interplanar spacing d and diffraction intensity of the BCC phase increased with annealing temperature, probably due to the segregation of Cu from the metastable phase of W(Cu). Such transformations are not dependent on long-range chemical ordering and can be easily be achieved by structural relaxation [21]. The growth and coalescence of islands (mainly Cu element) on surface of thin films is not isotropic process with annealing temperature [24], therefore it resulted in the anisotropy degree of surface morphology of thin films to some extent. That is to say, the correlation between phase transition and surface morphology can be established by analyzing the anisotropy of surface structures. The variation of fractal dimension of original surface morphology of thin film with annealing temperature is shown in Fig. 6. These fractal dimensions devotedly describe the evolution of surface morphology of Cu–W thin films. It is clear in Fig. 6 that the values of fractal dimension depend on the roughness of Cu–W thin film surface. The fractal dimension values of rough surface of thin films are bigger than those of smooth surface. Fig. 7 shows the dependence of standard deviation of fractal dimension on diffraction intensity and interplanar spacing of W-like phase. The standard deviation of the fractal dimension values (e.g. the anisotropy of thin films morphology) is approximately linear with
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5. Conclusions
2.75 2.70
Fractal Dimension
2.65 2.60 2.55 2.50 2.45 2.40 2.35 2.30 0
200
400
600
800
Annealing Temperature, °C
Fig. 6. Fractal dimensions of original surface morphology of thin films as a function of annealing temperatures.
800 2.24
600
2.22
500 2.20 400
300
2.18
200
Interplanar Spacing, Å
W-like Phase Diffraction Intensity
700
In this study, the surface morphology evolution and phase structures of Cu–W thin films with annealing temperature were investigated. The results indicate that the agglomeration of Cu–W thin films takes place in two distinct stages: the nucleation of voids followed by the growth of islands. The rough surface morphology of thin films can be described quantitatively by its fractal dimension. An integrated approach using the discrete wavelet transform and fractal geometry concepts is presented for analyzing the anisotropy of surface structure of Cu–W thin films. This approach is found to provide simple and accurate descriptions of the anisotropy of the surface structures of thin films. In addition the relationship between multi-scale property of the surface morphology of Cu–W thin films and phase structure transition is constructed by this integrative technique. A positive correlation between the anisotropy of thin films morphology and W-like phase transition is established. It can be concluded that the trend of surface structure anisotropy of thin films with annealing temperature is sensitive to the variation of phase structures of thin film materials.
2.16 100 0.00
As-deposited 0.01
0.02
0.03
0.04
0.05
0.06
0.07
Acknowledgements
Standard Deviation of Fractal Dimension
Fig. 7. Diffraction intensity, interplanar intensity of W-like phase and standard deviation of fractal dimension of detail subimages.
diffraction intensity and interplanar intensity, while the fractal dimension values of original surface morphology do not provide much useful information about the variation of phase structures of Cu–W thin films. It can be concluded that the variations of anisotropy of surface structure with annealing temperature is sensitive to the variation of phase structures. Thus by using the methods of integrating DWT and fractal dimension, the variations of surface structures anisotropy can be readily detected.
This work has been supported by Key Project of Natural Science Foundation of China (Grant No.59931010).
References [1] G.A. McRae, M.A. Maguire, C.A. Jeffrey, D.A. Guzonas, C.A. Brown, Appl. Surf. Sci. 191 (2002) 94. [2] Ming Qiuzhang, Zai Pinglu, Friedrich Klaus, Tribol. Int. 30 (1997) 87. [3] Jong Chao-An, Chin Tsung Shune, Mater. Chem. Phys. 74 (2002) 201. [4] J. Erlebacher, M.J. Aziz, E. Chason, M.B. Sinclair, J.A. Floro, Phys. Rev. Lett. 82 (1999) 2330. [5] Russell Messier, J. Vac. Sci. Technol. A 4(3) (1986) 490. [6] V.I. Trofimov, Thin Solid Films 428 (2003) 56. [7] T.G. Souza Cruz, M.U. Kleinke, A. Gorenstein, Appl. Phys. Lett. 81 (26) (2002) 4922.
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[8] A.-L. Barabasi, H.E. Stanly, Fractal Concepts in Surface Growth, Cambridge University Press, Cambridge, 1995. [9] H.J. Leamy, A.G. Dirks, J. Appl. Phys. 49 (1978) 3430. [10] M.A. Engelhardt, S.S. Jaswal, D.J. Sellmyer, Phys. Rev. B 44 (23) (1991) 12671. [11] L. Debnath, Wavelet Transforms and Their Applications, Birkhauser, Boston, New York, 2002. [12] J. Raja, B. Muralikrishnan, Shengyu Fu, Precis. Eng. 26 (2002) 222. [13] S.G. Mallat, IEEE Trans. Pattern Anal. Machine Intell. 11 (7) (1989) 6743. [14] R. John, Fractal Surfaces, Plenum Press, New York, London, 1994, pp. 77–156. [15] T. Babadagli, K. Develi, Fractals 9 (2001) 105.
[16] Y.G. Shen, Y.W. Mai, Q.C. Zhang, D.R. McKenzie, W.D. McFall, W.E. McBride, J. Appl. Phys. 87 (1) (2000) 177. [17] B. Grzeta, N. Radic, D. Gracin, T. Doslic, T. Car, J. NonCryst. Solids 170 (1994) 101. [18] A.G. Dirks, J.J. van den Broek, J. Vac. Sci. Technol. A 3 (6) (1985) 2618. [19] D.J. Mapps, N. Mahvan, M.A. Akhter, IEEE Trans. Magn. 24 (1989) 4165. [20] W. Lu, K. Komvopoulos, Appl. Phys. Lett. 76 (2000) 3206. [21] M. Nastasi, F.W. Saris, L.S. Hung, J.W. Mayer, J. Appl. Phys. 58 (8) (1995) 3052. [22] K. Seal, M.A. Nelson, Z. Charles Ying, Phys. Rev. B 67 (2003) 035318. [23] C.S. Ozkan, W.D. Nix, H. Gao, J. Mater. Res. 14 (8) (1999) 3247. [24] M. Zinke-Allmang, Thin Solid Films 346 (1999) 1.
Physica B 349 (2004) 10–18
Surface anisotropy characterization and microstructure of Cu–W thin films at different annealing temperatures Wang Yuana,b, Bai Xuanyua, Xu Keweia,* a
State-Key Laboratory for Mechanical Behavior of Materials, Xian Jiaotong University, Xian 710049, China b Department of Mechanical Engineering, Lanzhou Railway Institute, Lanzhou 730070, China Received 17 November 2003; received in revised form 12 January 2004; accepted 12 January 2004
Abstract Cu–W films were deposited on Al2O3 substrates by magnetron sputtering and then annealed in Ar gas at different temperatures for an hour. The evolution of surface morphology of the films during deposition and annealing was investigated by mathematical techniques. A strategy integrating discrete wavelet transform and fractal geometry concepts was developed for analyzing the anisotropy of surface structure of Cu–W thin films. The results indicated that the agglomeration of Cu–W thin films occurs primarily during annealing process. Based on the observation of positive correlation between the surface anisotropy and W-like phase transition, the relationship between the evolution of surface morphology of Cu–W thin films and the transition of phase structure was constructed. It was concluded that the changes of phase structures could have a significant impact on the anisotropy behavior of surface structure of Cu–W thin films. r 2004 Elsevier B.V. All rights reserved. PACS: 68.55.J; 81.40.E; 64.70.D Keywords: Cu–W thin films; Surface morphology; Phase structure; Mathematical analysis
1. Introduction It is well known that surface morphology is a vital characteristic of thin films. Because many physical and chemical properties, such as electrical [1], optical [2], tribological properties [3] of thin films are controlled by the surface morphology, detailed knowledge and precise control over the surface and interface integration are of great *Corresponding author. State-Key Laboratory for Mechanical Behavior of Materials, Xian Jiaotong University, Xian 710049, China. Tel.: +86-29-88403018; fax: +86-29-83237910. E-mail addresses: [email protected] (Wang Yuan), [email protected] (Xu Kewei).
importance, particularly for modern electronic devices as the dimension of micro-devices continues to shrink. Thin films are usually nonideal material systems. Ion bombardment during deposition further produces a population of surface defects of nonequilibrium in the thin films [4]. These structural defects create a complex array of internal interface that are directly related to the external surface features. In addition, the morphologies of the anisotropic void and grain boundary within the thin films have long been known to directly affect the film properties [5]. Although surface morphology is controlled by the film microstructure, the relationship between surface morphology and thin
0921-4526/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2004.01.146
ARTICLE IN PRESS Wang Yuan et al. / Physica B 349 (2004) 10–18
film microstructures is not yet fully understood. In fact, few studies have been conducted to quantitatively describe the relationship between surface morphology and film microstructure. Substantial amounts of efforts have been directed to the quantitative description of the morphology of rough surfaces and interfaces of thin films [6, 7]. Because the roughness of thin film surfaces usually exhibits self-affine behavior [8], the surface morphology can be described by the concepts of scaling rule. The fractal dimension can be taken as a possible measure of a structure. However, further studies are needed to characterize the irregular structure of the surfaces. The complex morphology of thin films, especially the anisotropy of the structure, can not be described in detail only with a fractal dimension value. Leamy [9] demonstrated that the electron-scattering patterns can be used to determine the direction of growth morphological anisotropy, but proposed method is complex and involves many steps. A new approach of integrating wavelet transform and fractal geometry to characterize the film morphology is developed in the present paper. This integrative method can be used to describe surface morphology in addition to characterize the anisotropy behavior of surface morphology for thin films. The anisotropy behavior of surface roughening process of the Cu–W thin film with annealing temperature is analyzed by this approach as an example because amorphous immiscible binary transition metals are of particular interests as thin-film coatings on parts for microelectronics [10]. Additionally an interest work to interrelate the fractal dimension and a quantitative characterization of the anisotropy of the structure is also conducted, which would enhance our increased understanding of the correlation between the changes of surface and internal structures of thin films.
2. Experimental 2.1. Film preparation The Cu–W thin films were deposited on polished Al2O3 substrates by radio frequency (RF) magne-
11
tron sputtering system with the tungsten target (99.95%, purity) and the circular Cu sector plates (99.99%, purity and 1 mm thick). The deposition of Cu–W film was conducted in a stainless-steel vacuum chamber which was evacuated by a turbomolecular pump to 6 105 Pa prior to deposition. The Al2O3 substrates were mounted on a specimen holder equipped with a water cooling system, and was rotated at a rate of 5 rpm to achieve uniform film depositing during sputtering. The Al2O3 substrates were cleaned ultrasonically with alcohol before they were placed into vacuum chamber and then cleaned again by applying RF power of 100 W under Ar (purity of 99.999%) for 10 min prior to film deposition. The target was pre-sputtered by Ar ions to remove surface contamination that may have formed during the system vacuuming process. The magnetron sputtering deposition was performed at an RF power of 50 W. Argon gas flow was controlled by a mass flowmeter at a flow rate of 8 sccm and 0.3 Pa. The thickness of deposited thin films was about 550 nm. Pure tungsten and copper films were also prepared individually as controls under the same conditions. Samples annealing was carried out in a thermal annealing furnace with flowing argon atmosphere (purity of 99.999%) for 1 hr. The heating rate was 9 C/min and the annealed samples were slowly cooled to room temperature at a rate less than 1 C/min. The annealing temperature was set to 250 C, 350 C, 500 C, and 800 C for samples of No. 2, 3, 4, and 5, respectively, with sample No. 1 being the as-deposited film (no annealing Table 1).
2.2. Film characterization The elemental concentration of thin films was determined by an X-ray photoelectron spectroscopy (PHI-5702). The compositions of Cu50W50 are as-prepared samples, and are kept nominal in the discussion. After heat treatment, each thin film samples was taken out for immediately ex situ measurements by a scanning electron microscopy (JEOL JSM5600LV). Each sample was measured at least four times at different locations on the surface. A
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Table 1 Fractal dimensions and interplanar spacing of Cu–W thin films at different annealing temperatures Samples number
Interplanar spacing ( b d (A)
Fractal dimensions Detailed subimages
1 2 3 4 5
Amorphous 2.16 2.19 2.23 — a b
Original morphology of thin filmsa
Diagonal
Horizontal
Vertical
Standard deviation
2.4668 2.6975 2.9483 2.7629 2.8543
2.4748 2.6595 2.8469 2.6290 2.6912
2.4809 2.6995 2.8793 2.6656 2.7106
0.00707 0.02254 0.05179 0.06921 0.08910
2.346 2.486 2.762 2.584 2.412
The fractal dimension of original morphology of samples which do not be processed by wavelet transformation. W-like phase.
Regaku D/max-3A X-ray diffractometer with Co-Ka radiation was used for phase analysis.
3. Quantification of surface morphology of thin films In the description of the surface of thin films, surface morphology is usually treated as gray scale images in which the brightness of the image pixels is correlated to surface relief. Two-dimensional signals (i.e. images with two dimension of space x and y and gray levels) representing the relief of the surfaces can be easily established. Construction and analysis of these gray scale images of thin films are, however, not yet fully practiced and investigated. Scanning electron microscopy (SEM) was used in this study to view the topology of the surface of thin films. Image analysis of these micrographs is, therefore, expected to produce accurate profile of the evolution of surface morphology, in addition to provide information on the size distribution and shapes of the morphological features. In this work, thin film surfaces structures were firstly decomposed according to three different directions, namely horizontal, vertical, and diagonal directions, by using wavelet transform method. These three different directional subimages represent different directional information of surface morphology, respectively. Fractal geometry was then applied to the analysis of these
subimages. The computed standard deviation of the fractal dimension values of these subimages was used to describe the anisotropy of the surface morphology of thin films. By this approach a quantitative characterization of the anisotropy of thin films can be achieved. 3.1. Wavelet transform of surface morphology The wavelet transform is considered as a mathematical microscope in an analysis of image signals at various scales. The advantage of wavelet analysis over traditional Fourier methods in analyzing physical situations is that signals with discontinuities and sharp spike, such as rough surfaces of thin films, can be accurately described. Wavelet analysis is applied in the way that the transformation will break up a signal into shifted and scaled versions of the original (or parent) wavelet. The mathematical expression of this transformation is [11] 1 tb ca;b ðtÞ ¼ pffiffiffi c ; a; bAR; aa0; ð1Þ a a where a is a scaling parameter which measures the degree of the scale, and b a translation parameter which determines the time location of the wavelet, and t is the space variable. cðtÞ is the parent wavelet. In practical application involving fast numerical algorithms, the wavelet transform can be
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computed at discrete grid points, thus substantially reduce the amount of computations. Discrete wavelet transform (DWT) appears to have a great potential for analyzing the multi-scale features of rough surfaces because the DWT possesses the properties of good time-frequency localization and flexible multi-resolution [12]. As a matter of fact, the 2D DWT is computed by applying a separable filter-bank to an image [13]: L ði; jÞ ¼ ½H ½H L ði; jÞ; ð2Þ n
x
y
n1 k2;1 k1;2
Dn1 ði; jÞ ¼ ½Hx ½Gy Ln1 k2;1 k1;2 ði; jÞ;
ð3Þ
Dn2 ði; jÞ ¼ ½Gx ½Hy Ln1 k2;1 k1;2 ði; jÞ;
ð4Þ
Dn3 ði; jÞ ¼ ½Gx ½Gy Ln1 k2;1 k1;2 ði; jÞ:
ð5Þ
Here denotes the convolution operator. The k2; 1ðk1; 2Þ represents subsampling along the rows (columns) in a window of an image. L0 is the original image. Hx ; Hy and Gx ; Gy are low- and high-pass filters in the horizontal ðxÞ and vertical ðyÞ directions, respectively. Ln is obtained by lowpass filtering and therefore regarded as the lowresolution image at scale n: The detail subimages Dn1 ; Dn2 ; Dn3 are obtained by high-pass filtering in horizontal, vertical and diagonal direction, respectively, and therefore they contain corresponding directional information at scale n. The original image is thus represented by a set of subimages at multiple scales, fLd ; Dni gi¼1;2;3;n¼1;2;y;d ; where d is the level of wavelet decomposition. In this study, a six-level wavelet decomposition using Daubechies’s 4 wavelet basis was performed on the thin film surface morphology images. It was found during the experiment that a six-level discrete wavelet decomposition is sufficient to extract nearly all the directional information for the surface morphology of a thin film. Further improvement in the quality of the extracted information with the increase of decomposition level is minimal. However, more useful information could be missed if less than a six-level wavelet decomposition was used. The six-level discrete wavelet decomposition process is shown in Fig. 1. Because the objective of this study was the characterization of surface structure anisotropy of thin films, the detail subimages at all scales in
13 L0 L1
D11
L2
D21
L3
D31
L4 L5
D41 D51
D52
D42
D32
D12 D13
D22 D23
D33
D43
D53 D2
L6
D61
D62
D63
D1
D3
Fig. 1. Tree structure of wavelet decomposition and the constructing of detail directional subimages.
the same direction were merged into one process with the directional information of surface structures being highlighted (as shown in Fig. 1). The different directional decomposition results of DWT for sample No. 4 are shown in Fig. 2. 3.2. Fractal analysis The fractal dimension of the surfaces was estimated with Fourier power spectral density (PSD). Fourier transform (FT) is a powerful approach in image analysis. It is a linear integral transformation that establishes a unique correspondence between a complex-valued function (e.g., of time) and a complex-valued function of frequency. In addition, it is virtually insensitive to the noise of up to about 10% of signal (10:1 signal-to-noise ratio) and does not deviate significantly until the noise reaches 25% of signal strength (3:1 signal-tonoise). This feature of FT method suggests that for an elevation of the profiles, the influence of instrument noise which is an order of magnitude smaller than the signal can be ignored [14]. Each resulted subimage is still a 2D image after DWT decomposition, so the 2D PSD method can be applied to calculate its fractal dimension. The fractal dimensions of a set of different directional detail subimages can be calculated from the slope of a log S(k)—log k plot. The relationship between the PSD SðkÞ and the frequency k is given as [15] SðkÞpkb :
ð6Þ
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Fig. 2. Different directional detail subimages after wavelet transform of sample No. 4.
The fractal dimension D is related to the slope b in the log–log plot b D¼4þ : 2
ð7Þ
The 2D PSD of an Nx Ny SEM image can be calculated with a 2D fast FT. The equation is as follows: F ðu; vÞ ¼
N y1 x1 N X X x¼0
Zðx; yÞej2pðux=Nx þvy=Ny Þ ;
y¼0
uAf0; Nx1 g; vAf0; Ny1 g;
ð8Þ
where Zðx; yÞ is gray value of image which corresponds to the height function of a 2D topological surface. u and v are the frequency variables. So the 2D PSD can be calculated by the following equation: SðkÞ ¼ jF ðu; nÞj2 :
ð9Þ
No other processing needs to be performed before this calculation. Fig. 3 shows the relationship between PSD SðkÞ and frequency k of three different directional detail subimages for sample No. 4. The fractal dimension values of original surface morphology of thin films, which do not be
processed by DWT, were calculated by the same methods, and the standard deviation values of the fractal dimension of detail directional subimages at different annealing temperatures were also calculated. The results are listed in Table 1.
4. Results and discussion Changes in the X-ray diffraction patterns of the samples caused by the thermal annealing are shown in Fig. 4. The evolution of Cu–W thin film surface features with annealing temperatures can be seen clearly in Fig. 5. The X-ray diffraction measurements show an amorphous structure for as-deposited Cu–W thin film. The XRD measurements also indicate that as-deposited W thin film is a metastable A15 b-W phase [16], and the (2 1 0) and (2 0 0) (not shown) reflections peaks are clearly observed. The lattice parameters of the crystal structure from XRD patterns were calculated to be 0.506 nm for b-W phase and 0.361 nm for FCC Cu, in good agreement with the readings from the powder diffraction standards cards (JCPDS cards). The Cu–W amorphous thin film (sample No. 1) has a very smooth, featureless surface structure as
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8
Diagonal
15
7
Intensity, a.u.
Cu (111)
6
logS(k)
substrate W-like phase Cu (200)
_ β W (210)
5
4
Sample No.4
3
2
3
1 2 -3.0
-2.5
-2.0
-1.5
-1.0
logk
30
40
50
60
70
80
90
2θ, degree Fig. 4. XRD patterns of Cu–W films with annealing temperatures.
8
Horizontal 7
logS(k)
6
5
4
3
2 -3.0
-2.5
-2.0
-1.5
-1.0
logk
8
Vertical
7
logS(k)
6
5
4
Fig. 5. SEM micrographs showing evolution of Cu–W thin film morphology at different annealing temperatures, (a) as-deposited, (b) 250 C, (c) 350 C, (d) 500 C, (e) 800 C.
3
-3.0
-2.5
-2.0
-1.5
-1.0
logk Fig. 3. Power spectra density SðkÞ versus frequency k of three different directional detail subimages for sample No. 4.
showing in Fig. 5(a). However, the surface structures changed significantly with the increase of annealing temperature. At 250 C, some voids
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are formed in the substrate (Fig. 5(b)), while a BCC phase similar to W also appears at the same time. Broad diffraction lines positioned at Bragg angles higher than those of pure W are observed at this temperature. It is likely that on very surface the adatom mobility is high enough that significant crystallization occurs if conditions meet. Grzeta [17] and Dirks [18] believed that the BCC phase is a metastable BCC W(Cu) phase for vapordeposited Cu–W thin films. With the increase of annealing temperature, the voids grow rapidly into islands. The Cu content of islands on top surface of the thin films determined with an energy dispersive spectroscopy (EDS) is above 80 at%. It is concluded that the segregation of Cu occurs during annealing temperature. These thin films deposited by sputtering have a void concentration much higher than the equilibrium concentration at the annealing temperatures [19,20], suggesting that void nucleation may be easily initiated due to supersaturated excess vacancies. In addition, the segregation of Cu would also raise the vacancy formation. Natasi [21] reported that continued heating to about 350 C resulted in the addition of an FCC Cu signal to the diffraction pattern for Cu–W thin film of similar composition. The FCC Cu lattice parameter, however, remained unchanged with the increasing of annealing temperature. Because the diffraction peaks of Cu and substrate largely overlapped in Fig. 4, the changes of interplanar spacing and diffraction intensity of BCC phase were, therefore, used to represent the trend of thin film phase transition during heat treatment for Cu50W50 thin films. With the further increase of annealing temperature, the size of islands increases while the density decreases. Some smaller islands decay due to surface diffusion and the size of larger islands increases due to the growth of grain. This trend indicates that islands could coalesce and the number of islands decreases with annealing temperature. From a thermodynamic point of view, a giant single island has the least free energy for the system. The coalescence of two isolated island surfaces separated by a minimum distance is the energy decrease because of the elimination of two free surfaces.
The size of islands appears to depend on the annealing temperature. The agglomeration of islands takes place in two distinct stages: the nucleation of voids followed by the growth of islands. This agglomeration of islands has been attributed to a change in the surface structure by surface diffusion [22], which results in the migration of particles between grains and promotes the formation of larger islands at the cost of smaller ones, also helps in the formation of elevated islands instead of purely two-dimensional ones. Ozakan et al. [23] demonstrated that surface roughening of thin films preferentially takes place in the form of ridges or islands aligned along some certain directions, and the surface structures rotate toward other directions by means of annealing. This means that the anisotropy of surface morphology would be changed due to surface diffusion and grain growth. The interplanar spacing d and diffraction intensity of the BCC phase increased with annealing temperature, probably due to the segregation of Cu from the metastable phase of W(Cu). Such transformations are not dependent on long-range chemical ordering and can be easily be achieved by structural relaxation [21]. The growth and coalescence of islands (mainly Cu element) on surface of thin films is not isotropic process with annealing temperature [24], therefore it resulted in the anisotropy degree of surface morphology of thin films to some extent. That is to say, the correlation between phase transition and surface morphology can be established by analyzing the anisotropy of surface structures. The variation of fractal dimension of original surface morphology of thin film with annealing temperature is shown in Fig. 6. These fractal dimensions devotedly describe the evolution of surface morphology of Cu–W thin films. It is clear in Fig. 6 that the values of fractal dimension depend on the roughness of Cu–W thin film surface. The fractal dimension values of rough surface of thin films are bigger than those of smooth surface. Fig. 7 shows the dependence of standard deviation of fractal dimension on diffraction intensity and interplanar spacing of W-like phase. The standard deviation of the fractal dimension values (e.g. the anisotropy of thin films morphology) is approximately linear with
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5. Conclusions
2.75 2.70
Fractal Dimension
2.65 2.60 2.55 2.50 2.45 2.40 2.35 2.30 0
200
400
600
800
Annealing Temperature, °C
Fig. 6. Fractal dimensions of original surface morphology of thin films as a function of annealing temperatures.
800 2.24
600
2.22
500 2.20 400
300
2.18
200
Interplanar Spacing, Å
W-like Phase Diffraction Intensity
700
In this study, the surface morphology evolution and phase structures of Cu–W thin films with annealing temperature were investigated. The results indicate that the agglomeration of Cu–W thin films takes place in two distinct stages: the nucleation of voids followed by the growth of islands. The rough surface morphology of thin films can be described quantitatively by its fractal dimension. An integrated approach using the discrete wavelet transform and fractal geometry concepts is presented for analyzing the anisotropy of surface structure of Cu–W thin films. This approach is found to provide simple and accurate descriptions of the anisotropy of the surface structures of thin films. In addition the relationship between multi-scale property of the surface morphology of Cu–W thin films and phase structure transition is constructed by this integrative technique. A positive correlation between the anisotropy of thin films morphology and W-like phase transition is established. It can be concluded that the trend of surface structure anisotropy of thin films with annealing temperature is sensitive to the variation of phase structures of thin film materials.
2.16 100 0.00
As-deposited 0.01
0.02
0.03
0.04
0.05
0.06
0.07
Acknowledgements
Standard Deviation of Fractal Dimension
Fig. 7. Diffraction intensity, interplanar intensity of W-like phase and standard deviation of fractal dimension of detail subimages.
diffraction intensity and interplanar intensity, while the fractal dimension values of original surface morphology do not provide much useful information about the variation of phase structures of Cu–W thin films. It can be concluded that the variations of anisotropy of surface structure with annealing temperature is sensitive to the variation of phase structures. Thus by using the methods of integrating DWT and fractal dimension, the variations of surface structures anisotropy can be readily detected.
This work has been supported by Key Project of Natural Science Foundation of China (Grant No.59931010).
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