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Roughness evolution in Ga doped ZnO films deposited by pulsed laser deposition
Thin Solid Films 519 (2011) 5444–5449
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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
Roughness evolution in Ga doped ZnO films deposited by pulsed laser deposition Yun-yan Liu a,b, Chuan-fu Cheng a,⁎, Shan-ying Yang a, Hong-sheng Song c, Gong-xiang Wei b, Cheng-shan Xue a, Yong-zai Wang d a
College of Physics and Electronics, Shandong Normal University, Jinan 250014, PR China School of Science, Shandong University of Technology, Zibo 255049, PR China School of Science, Shandong Jianzhu University, Jinan 250101, PR China d Analysis and Testing Center, Shandong University of Technology, Zibo 255049, PR China b c
a r t i c l e
i n f o
Article history: Received 31 March 2010 Received in revised form 15 February 2011 Accepted 15 February 2011 Available online 24 February 2011 Keywords: Ga doped ZnO Pulsed laser deposition Surface roughness Morphology Fractals Atomic force microscopy
a b s t r a c t We analyze the morphology evolution of the Ga doped ZnO(GZO) films deposited on quartz substrates by a laser deposition system. The surface morphologies of the film samples grown with different times are measured by the atomic force microscope, and they are analyzed quantitatively by using the image data. In the initial stage of the growth time shorter than 8 min, our analysis shows that the GZO surface morphologies are influenced by such factors as the random fluctuations, the smoothening effects in the deposition, the lateral strain and the substrate. The interface width uw(t) and the lateral correlation length ξ(t) at first decrease with deposition time t. For the growth time larger than 8 min, w(t) and ξ(t) increase with time and it indicates the roughening of the surface and the surface morphology exhibits the fractal characteristics. By fitting data of the roughness w(t) versus deposition time t larger than 4 min to the power-law function, we obtain the growth exponent β is 0.3; and by the height–height correlation functions of the samples to that of the self-affine fractal model, we obtain the value of roughness exponent α about 0.84 for all samples with different growth time t. © 2011 Elsevier B.V. All rights reserved.
1. Introduction In thin film growth, the morphologies of growth fronts and their evolutions reflect the microscopic growth dynamics, and they play an important role in determining many physical and chemical properties of thin films [1]. The studies of morphologies of growth fronts are of profound significance for both fundamental researches and practical applications. Recently, considerable attention has been paid to this field [2–7]. ZnO transparent conductive film has the advantages of low cost and no pollution and it is an ideal alternative material to the traditional In2O3:Sn and SnO2 transparent conductive films. Ga doped ZnO (GZO) transparent conductive films have attracted great interest for its high transmittance and excellent electrical properties [8]. However, little work has been done in the studies of the morphological evolutions in the GZO film growth. Under the common conditions, the growth of the thin films is a process of far-from-equilibrium, and the complicated dynamics of the growth leads film morphology to evolve in the rough surface structure of random self-affine fractality [9]. From such fractal structure, described by the surface parameter of roughness exponent α, together with the evolutions of the familiar parameters of roughness w and autocorrelation length ξ, the mechanism governing the thin film growth may be understood. In ⁎ Corresponding author. Tel.: + 86 531 86182614; fax: + 86 531 86182521. E-mail addresses: [email protected] (Y. Liu), [email protected] (C. Cheng). 0040-6090/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.tsf.2011.02.056
this paper, we study the properties of the microstructure and the surface evolution of GZO transparent conductive films deposited by pulsed laser deposition (PLD). The morphologies of the thin film samples prepared with properly increased growth times are measured by atomic force microscope (AFM). By quantitatively analyzing the data of AFM images, we obtain the values and the evolutions of the growth front parameters, which indicates that under our growth conditions, the growth of the GZO films is in accordance with the noise-driven Kuromoto–Sivashinsky (KS) growth model. We give the preliminarily discussion of the growth dynamics. 2. Experimental details The GZO films are deposited on quartz substrates in a pulsed laser deposition system with a KrF excimer laser of wavelength 248 nm, energy 200 mJ per pulse, pulse width 10 ns and repetition rate 5 Hz. A Ga doped ZnO ceramic target with a Ga content of 2.5 at.% is used. The distance between the substrate and the target is fixed at 4 cm. The quartz substrates are cleaned in deionized water for 5 min, and then are ultrasonically cleaned in acetone and alcohol for 20 min and subsequently dried at room temperature before being introduced into the deposition system. The background pressure of the sputtering system is 8 × 10−4 Pa. During the deposition, the oxygen pressure is maintained at 0.5 Pa. Seven thin film samples are grown with sputtering times of 1, 2, 4, 8, 10, 20 and 30 min, respectively, and the deposition rate is about 20 nm/min, which is determined by AFM.
Y. Liu et al. / Thin Solid Films 519 (2011) 5444–5449
Then the thicknesses of the samples are estimated at 20, 40, 80, 160, 200, 300, 400 and 600 nm, respectively. The quartz substrates are not intentionally heated during deposition. The surface topography measurement of the GZO films is carried out by using AFM (Auto Probe CP, Park Scientific Instruments) in contact mode with a UL06 probe. The typical radius and side angle of the tip are approximately 10 nm and 10°, respectively. The scanning area for AFM imaging is 2 μm × 2 μm and the resolution is 256 × 256. 3. Results and discussion Fig. 1 shows the AFM images and the corresponding onedimensional cross-section scans of surface profile of different film samples with deposition time = 1, 4, 8, 10 and 20 min, respectively and the AFM image of the quartz substrate, where H(r) denotes the relative surface height at coordinate r on cross-section line. In Fig. 1, we see that the substrate has obvious random grooves on surface, the influence of those random grooves may also be vaguely seen in the films deposited for 1 min and 4 min. This indicates that GZO surface morphology is influenced by the substrate in the initial stage of the growth. With the increase of time, more and more round grains appear and the surface roughness tends to decrease. It is observed that for the film growth time longer than 8 min, the effect of the substrate is faded away and the average film morphology evolution is representative of the process of deposition. For thicker films deposited for 10, 20 and 30 min, the grains distribute uniformly on the film surface and the surface roughness increases with time, which are distinctly different from the films of the earlier time as seen from Fig. 1. From Fig. 1, the following characteristics can be recognized. First, grains with different scales distributed in certain scale range and the grains possess different separations and irregular shapes. Second, the evolution of the surface roughness is a function of deposition time. This means that the surface morphology exhibits the fractal characteristics and such grain distributions may be described with the self-affine fractal model quantitatively [10]. The height–height correlation function H(r, t) of the surface is suitable and convenient for the description of the statistical evolution of surfaces with self-affine fractal characteristics. H(r, t) is defined as a function of lateral position r and the deposition time t by H(r, t) = b[h(r, t)-h(0, t)]2 N, where h(r, t) and h(0, t) represent, respectively, the relative surface heights at lateral positions r and r = 0 at time t. Here the position with r = 0 may be arbitrarily chosen for uniformly deposited thin film samples. The height–height correlation function H(r, t) of random self-affine fractal surfaces contains at least three important parameters: the vertical correlation length (interface width) w(t), the lateral correlation length ξ(t) and the roughness exponent α. The interface width w(t) describes the surface roughness along the vertical direction during the growth process and it is defined as the root mean square surface height fluctuation (RMS roughness), which will evolve with time in the form of power laws w(t) ∝ t β, where β is the growth exponent. ξ(t) is the lateral correlation length that gives an average measure of the lateral coarsening size at the growth time t, and it is the distance within which the surface variations are correlated. Both w(t) and ξ(t) are statistical descriptions for the global surface morphology. The roughness exponent α is an important parameter to describe the self-affine fractal surface and it describes the local surface roughness. A larger value of α (N0.5) corresponds to a smooth short-range surface, while the small value of α (b0.5) corresponds to a more jagged local surface morphology [1]. Despite the complication of the growth processes, the surface morphology and dynamics of a growing interface exhibit simple dynamic scaling behavior for the far-from-equilibrium thin film growth [3,10], as has been demonstrated in a variety of growth processes such as silver and gold films [11], and the growth of the SnO2 nanocrystals [12]. This dynamic scaling behavior can be
5445
described by the height–height correlation function in the scaling form as given by: ( Hðr; tÞ∝
2α
Cr ; 2W 2 ðtÞ ;
r bb ξðtÞ r NN ξðtÞ
ð1Þ
We note that ξ(t) provides a length scale which distinguishes the short-range and long-range behaviors of the rough surface. With the data of the surface height h(r, t) obtained from an image of the atomic force microscope for the sample of growth time t, the height–height correlation function H(r, t) for this image can be calculated. For the i-th horizontal scan line, the height–height correlation function Hi ðmd;tÞ =
1 Nm ∑ ðh N−m j = 1 i;j
2 + m −hi;j Þ
ð2Þ
where d is the distance between two adjacent pixels of the image, N = 256 is the number of pixels in a scan line, N − m is the number of data points contributing to the calculation of the height–height correlation function corresponding to correlation distance md, and subscript i represents the quantities obtained for the i-th line of the image. Next, the height–height correlation function H(r, t) for the image is averaged over the 256 horizontal lines with the data obtained from Eq. (2) for each line. For the finite 256 × 256 pixels of the AFM image, the maximum of m is set at 100. In order to get good statistical properties, we finally take four AFM images of different regions of each GZO film sample to obtain the averaged height–height correlation function H(r, t), which is used as the height–height correlation function for the sample. Fig. 2 (a) and (b) shows the height–height correlation function versus position r = |r| in the log–log scale for the substrates and GZO film samples deposited with time shorter than 8 min and longer than 8 min, respectively. For the short range (r b b ξ(t)), linear relationship between H(r) and r is observed, corresponding to the proportionality of H(r) to r2α. Then in the logarithmic coordinates, the slope of the linear part in the curve is 2α, and it can be obtained by the linear fit of this part in the H(r)~r curve. At sufficiently large r (r N N ξ(t)), H(r) tends to be a constant 2w2 according to Eq. (1). The obtained values of α and w for all the samples are listed in Table 1. The roughness exponent α is found to be 0.84 ± 0.4. The turning point in the curve determines the lateral correlation length ξ(t). In order to obtain the values of ξ(t), we fit the curve of H(r) at a specific time t by the phenomenological function proposed by Sinha et al. [13]: r 2α 2 HðrÞ = 2w 1 exp½ð Þ ξ
ð3Þ
The values of the fitting parameter ξ(t) are also presented in Table 1. There are two different types of dynamic scaling behaviors in the growth front roughening. In the first type, the short-range behavior of H(r, t) is time-invariant, i.e., the process of growth is stationary, and the H(r, t) vs. t curves are overlapped so the coefficient C in Eq. (1) is time-independent [14]. In the second type, the deposition process is non-stationary and the short-range behavior of H(r, t) vary with time which are characterized by the increase of coefficient C with t. Such phenomenon is induced in the growth by the short-range balance in competition between the random fluctuations of the deposition and the local smoothing effects such as diffusion, with the former effect taking place and roughening the surface in both short and long ranges, and the latter ones appearing only in the short range of the growth front. In the short range i.e., in the distance shorter than the correlation length ξ(t), if the competition between random fluctuations and local smoothing can reach the balance, the local surface morphology is statistically stationary; if the balance is broken down
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Y. Liu et al. / Thin Solid Films 519 (2011) 5444–5449
Fig. 1. AFM images and one-dimensional cross section scan of surface profile of GZO thin films prepared by pulsed laser deposition deposited for 1 min, 4 min, 8 min, 10 min and 20 min and AFM image of quartz substrate.
Y. Liu et al. / Thin Solid Films 519 (2011) 5444–5449
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Fig. 1 (continued).
and the short-range scale growth is usually dominated by surface diffusion, often the Mullins diffusion, the local surface morphology is suggested statistically non-stationary, which has been demonstrated in Ref [15]. It is clear that the growth of GZO films belongs to the second type as shown in Fig. 2. In Fig. 3 we plot curve of the roughness w vs. time t with the data obtained from above calculations in Table 1. It can be seen form Fig. 3 that the relation of w and t can be divided into two stages. When the deposition time is shorter than 8 min, the value of w might be related to the overall influences by the factors of random fluctuations and the diffusion process of the deposited particles, the lateral strain, and the effect of the substrate such as the defects on it might be responsible for the initial surface roughening. The roughness w decreases with time and the surface fluctuations became small which indicates that the presence of surface diffusion smoothens the surface roughness in the early stages of film growth. For the film deposition time longer than 8 min, the dynamics of surface morphology is independent of the initial substrate, as shown in Fig. 1. The roughness w increase with further growth due to the formation of mounds, and it is proportional to t β and the curve is close to the self-affine fractal model in this stage. We fit the data of roughness w versus deposition time t for t N 4 min to the relation of w(t) ∝ (t - t0)β, with t0 the measure of the initial transient growth time in which the dynamic scaling has not occurred, Table 1 Surface parameters α, w(t) and ξ(t) for all the samples.
Fig. 2. The height–height correlation function as a function of position r in the log–log plots for (a) the substrate and the GZO films deposited for time shorter than 8 min and (b) the GZO films deposited for time longer than 8 min.
t (min)
1
2
4
8
10
20
30
α w(t) (μm) ξ(t) (μm)
0.86 0.0049 0.13
0.88 0.0044 0.13
0.81 0.0032 0.14
0.80 0.0017 0.043
0.83 0.0025 0.033
0.83 0.0038 0.039
0.86 0.0057 0.07
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Y. Liu et al. / Thin Solid Films 519 (2011) 5444–5449
Fig. 3. Thin film interface width, w, as a function of the deposition time, t. The solid curve is the best fit of a function of the form w(t)∝(t-to)β, where β = 0.3, t0 = 7.3 min.
and the fit curve is also shown as the solid curve in Fig. 3. The fit result gives β = 0.3, t0 = 7.3 min. This result indicates that for the growth time larger than about 7 min, the competition of all the factors influencing the film growth such as the noise deposition, the diffusion, the desorption and the strain, leads to the growth of the film following the aforementioned dynamic scaling law. Similar behaviors are also obtained by [4,16]. The values of t0 are different for different rough substrates and t0 would be larger for rougher substrates. This result is not consistent with the results obtained in many theoretical calculations [17], in which ideal substrate conditions are applied and are far from the complicated growth conditions in real systems. Fig. 4 gives the curve of the lateral correlation length ξ(t) vs. time t. We see that at first, the lateral correlation length ξ(t) is almost constant and decreases abruptly with the increase of deposition time t from 4 to 8 min. Further increase of time t results in a slow increase in ξ(t). Such phenomenon has also appeared in the depositions of InAs buffer layers and SnO2 film on rough substrates by Gyure et al. [18] and T. Lindström et al. [19], respectively, where the lateral correlation length ξ(t) goes towards larger values in rougher regime. They have found that smoothening occurs in the absence of lateral strain. At some time the film thickness variations will increase, giving rise to defects and strain variations as the surface smoothens. This finally triggers the onset of roughening. According to this point of view, we suggest that at the initial stage, the lateral stress in the GZO films is negligible and the diffusion of the deposition atoms flatten the surface. With the progress of deposition, the surface roughening influenced by the substrate is weakened and the global smoothening process of deposition play a dominating role, which corresponds to the initial fast decrease of lateral correlation length ξ(t) when time t increases from 4 min to 8 min. This is a crucial stage in the film surface evolution and in this stage the dynamic scaling appears. For further deposition, roughness caused by the lateral strain becomes obvious, and the global smoothening and roughening process reach a dynamic
balance. This might be the reason why ξ(t) have slight changes in this stage. While in the later growth stage, more defects and larger strain arise; the global roughening factors may surpass the smoothening ones, and this causes the subsequent global surface roughening and leads to latter slow increase of ξ(t). The growth feature of GZO is in good agreement with the noisedriven KS model [20,21], which can describe the growth process by the non-linear Langevin equation in the form ∂h = γ∇2 h− ∂t κ∇4 h + λ2 j∇hj 2 + η, where η = η(r, t) is a white-noise process, representing the stochastic deposition of atoms. The prefactor κand γ is proportional to the surface Mullins diffusion coefficient and tension coefficient, respectively. Numerical solutions of this equation [22] show that the α takes the values of 0.75–0.85, β the values of 0.22–0.25, and a time-dependent coefficient C for early time. Our GZO film is well consistent with this model. 4. Conclusion Height–height correlation function H(r) can be a good quantitative description of the statistical evolution of the surface. The evolution of GZO surface morphology is analyzed quantitatively with height– height correlation function H(r) obtained from the AFM image data. The roughness exponent α is about the same for all t .We have shown that the evolution can be divided into two stages. At the first stage, both the interface width w(t) and the lateral correlation length ξ(t) decrease with time and the surface fluctuations became small. It might be deduced that the morphology evolution is due to overall influences by the factors of the random fluctuations, the smoothening process of deposition, the lateral strain and the rough substrates. For the second stage, when the deposition time is larger than 8 min, the film is thick enough and the effect of the substrate could be neglected. The film grows in its inherent law and the evolution of GZO surface morphology is suggested to obey the dynamic scaling law and to possess the self-affine fractal characteristics. Both w(t) and ξ(t) increase with time due to the strain induced surface roughening. w(t) evolves with time in the form of power laws w(t) ∝ tβ. By fitting the curves in Fig. 3, the growth exponent β is found to be about 0.3. We suggest the growth process of the GZO film deposited by PLD is quite consistent with the noise driven KS model. The properties of the surface morphologies and their evolutions with the deposition time t may reflect the microscopic growth dynamics of thin films. The correlation of developmental growth morphology with more other deposition parameters would also be important in the study of thin film growth dynamics and is worthy to be investigated in our future work. Acknowledgements The authors acknowledge the support of the National Science Foundation of China under grant no.10874105 and no.10974122, and Shandong Provincial Natural Science Foundation under grant no. ZR2009FZ006. References
Fig. 4. The lateral correlation length ξ(t) as a function of time t.
[1] H.N. Yang, Y.P. Zhao, G.C. Wang, T.M. Lu, Phys. Rev. Lett. 76 (1996) 3774. [2] J.H. Kim, K.W. Chung, J. Appl. Phys. 83 (1998) 5831. [3] H.N. Yang, G.C. Wang, T.M. Lu, Diffraction from Rough Surfaces and Dynamic Growth Fronts, World Scientific, Singapore, 1993. [4] H.J. Qi, L.H. Huang, Z.S. Tang, C.F. Cheng, J.D. Shao, Z.X. Fan, Thin Solid Films 444 (2003) 146. [5] H. Wrzesinska, P. Grabiec, Z. Rymuza, M. Misiak, Microelectron. Eng. 61 (2002) 1009. [6] D.J. Freeland, Y.B. Xu, E.T.M. Kernohan, M. Tselepi, J.A.C. Bland, Thin Solid Films 343 (1999) 210. [7] L.H. Yu, J.H. Xu, S.R. Dong, I. Kojima, Thin Solid Films 516 (2008) 1781. [8] E. Fortunato, A. Goncalves, V. Assuncao, A. Marques, H. Aguas, L. Pereira, et al., Thin Solid Films 442 (2003) 121.
Y. Liu et al. / Thin Solid Films 519 (2011) 5444–5449 [9] Y.P. Zhao, G.C. Wang, T.M. Lu, Characterization of Amorphous and Crystalline Rough Surface: Principles and Applications, Academic Press, New York, 2001. [10] F. Family, Phys. A 168 (1990) 561. [11] R. Chiarello, V. Panella, J. Krim, C. Thompson, Phys. Rev. Lett. 67 (1991) 3408. [12] Z.W. Chen, J.K.L. Lai, C.H. Shek, Appl. Phys. Lett. 88 (2006) 033115. [13] S.K. Sinha, E.B. Sir ota, S. Garoff, Phys. Rev. B 38 (1988) 2297. [14] F. Family, T. Vicsek, Dynamics of Fractal Surfaces, World Scientific, Singapore, 1991. [15] T.M. Lu, H.N. Yang, G.C. Wang, Mater. Res. Soc. Symp. Proc. 367 (1995) 283.
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[16] T. Jiang, N. Hall, A. Ho, S. Morin, Thin Solid Films 471 (2005) 76. [17] H.J. Qi, Y.H. Jin, C.F. Cheng, L.H. Huang, K. Yi, J.D. Shao, Chin. Phys. Lett. 20 (2003) 622. [18] M.F. Gyure, J.J. Zinck, C. Ratsch, D.D. Vvedensky, Phys. Rev. Lett. 81 (1998) 4931. [19] T. Lindström, J. Isidorsson, G.A. Niklasson, Thin Solid Films 401 (2001) 165. [20] Y. Kuramoto, T. Tsuzuki, Prog. Theor. Phys. 55 (1977) 356. [21] G.I. Sivashinsky, Acta Astronaut. 6 (1979) 569. [22] J.T. Drotar, Y.P. Zhao, T.M. Lu, G.C. Wang, Phys. Rev. E 59 (1999) 177.
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
Roughness evolution in Ga doped ZnO films deposited by pulsed laser deposition Yun-yan Liu a,b, Chuan-fu Cheng a,⁎, Shan-ying Yang a, Hong-sheng Song c, Gong-xiang Wei b, Cheng-shan Xue a, Yong-zai Wang d a
College of Physics and Electronics, Shandong Normal University, Jinan 250014, PR China School of Science, Shandong University of Technology, Zibo 255049, PR China School of Science, Shandong Jianzhu University, Jinan 250101, PR China d Analysis and Testing Center, Shandong University of Technology, Zibo 255049, PR China b c
a r t i c l e
i n f o
Article history: Received 31 March 2010 Received in revised form 15 February 2011 Accepted 15 February 2011 Available online 24 February 2011 Keywords: Ga doped ZnO Pulsed laser deposition Surface roughness Morphology Fractals Atomic force microscopy
a b s t r a c t We analyze the morphology evolution of the Ga doped ZnO(GZO) films deposited on quartz substrates by a laser deposition system. The surface morphologies of the film samples grown with different times are measured by the atomic force microscope, and they are analyzed quantitatively by using the image data. In the initial stage of the growth time shorter than 8 min, our analysis shows that the GZO surface morphologies are influenced by such factors as the random fluctuations, the smoothening effects in the deposition, the lateral strain and the substrate. The interface width uw(t) and the lateral correlation length ξ(t) at first decrease with deposition time t. For the growth time larger than 8 min, w(t) and ξ(t) increase with time and it indicates the roughening of the surface and the surface morphology exhibits the fractal characteristics. By fitting data of the roughness w(t) versus deposition time t larger than 4 min to the power-law function, we obtain the growth exponent β is 0.3; and by the height–height correlation functions of the samples to that of the self-affine fractal model, we obtain the value of roughness exponent α about 0.84 for all samples with different growth time t. © 2011 Elsevier B.V. All rights reserved.
1. Introduction In thin film growth, the morphologies of growth fronts and their evolutions reflect the microscopic growth dynamics, and they play an important role in determining many physical and chemical properties of thin films [1]. The studies of morphologies of growth fronts are of profound significance for both fundamental researches and practical applications. Recently, considerable attention has been paid to this field [2–7]. ZnO transparent conductive film has the advantages of low cost and no pollution and it is an ideal alternative material to the traditional In2O3:Sn and SnO2 transparent conductive films. Ga doped ZnO (GZO) transparent conductive films have attracted great interest for its high transmittance and excellent electrical properties [8]. However, little work has been done in the studies of the morphological evolutions in the GZO film growth. Under the common conditions, the growth of the thin films is a process of far-from-equilibrium, and the complicated dynamics of the growth leads film morphology to evolve in the rough surface structure of random self-affine fractality [9]. From such fractal structure, described by the surface parameter of roughness exponent α, together with the evolutions of the familiar parameters of roughness w and autocorrelation length ξ, the mechanism governing the thin film growth may be understood. In ⁎ Corresponding author. Tel.: + 86 531 86182614; fax: + 86 531 86182521. E-mail addresses: [email protected] (Y. Liu), [email protected] (C. Cheng). 0040-6090/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.tsf.2011.02.056
this paper, we study the properties of the microstructure and the surface evolution of GZO transparent conductive films deposited by pulsed laser deposition (PLD). The morphologies of the thin film samples prepared with properly increased growth times are measured by atomic force microscope (AFM). By quantitatively analyzing the data of AFM images, we obtain the values and the evolutions of the growth front parameters, which indicates that under our growth conditions, the growth of the GZO films is in accordance with the noise-driven Kuromoto–Sivashinsky (KS) growth model. We give the preliminarily discussion of the growth dynamics. 2. Experimental details The GZO films are deposited on quartz substrates in a pulsed laser deposition system with a KrF excimer laser of wavelength 248 nm, energy 200 mJ per pulse, pulse width 10 ns and repetition rate 5 Hz. A Ga doped ZnO ceramic target with a Ga content of 2.5 at.% is used. The distance between the substrate and the target is fixed at 4 cm. The quartz substrates are cleaned in deionized water for 5 min, and then are ultrasonically cleaned in acetone and alcohol for 20 min and subsequently dried at room temperature before being introduced into the deposition system. The background pressure of the sputtering system is 8 × 10−4 Pa. During the deposition, the oxygen pressure is maintained at 0.5 Pa. Seven thin film samples are grown with sputtering times of 1, 2, 4, 8, 10, 20 and 30 min, respectively, and the deposition rate is about 20 nm/min, which is determined by AFM.
Y. Liu et al. / Thin Solid Films 519 (2011) 5444–5449
Then the thicknesses of the samples are estimated at 20, 40, 80, 160, 200, 300, 400 and 600 nm, respectively. The quartz substrates are not intentionally heated during deposition. The surface topography measurement of the GZO films is carried out by using AFM (Auto Probe CP, Park Scientific Instruments) in contact mode with a UL06 probe. The typical radius and side angle of the tip are approximately 10 nm and 10°, respectively. The scanning area for AFM imaging is 2 μm × 2 μm and the resolution is 256 × 256. 3. Results and discussion Fig. 1 shows the AFM images and the corresponding onedimensional cross-section scans of surface profile of different film samples with deposition time = 1, 4, 8, 10 and 20 min, respectively and the AFM image of the quartz substrate, where H(r) denotes the relative surface height at coordinate r on cross-section line. In Fig. 1, we see that the substrate has obvious random grooves on surface, the influence of those random grooves may also be vaguely seen in the films deposited for 1 min and 4 min. This indicates that GZO surface morphology is influenced by the substrate in the initial stage of the growth. With the increase of time, more and more round grains appear and the surface roughness tends to decrease. It is observed that for the film growth time longer than 8 min, the effect of the substrate is faded away and the average film morphology evolution is representative of the process of deposition. For thicker films deposited for 10, 20 and 30 min, the grains distribute uniformly on the film surface and the surface roughness increases with time, which are distinctly different from the films of the earlier time as seen from Fig. 1. From Fig. 1, the following characteristics can be recognized. First, grains with different scales distributed in certain scale range and the grains possess different separations and irregular shapes. Second, the evolution of the surface roughness is a function of deposition time. This means that the surface morphology exhibits the fractal characteristics and such grain distributions may be described with the self-affine fractal model quantitatively [10]. The height–height correlation function H(r, t) of the surface is suitable and convenient for the description of the statistical evolution of surfaces with self-affine fractal characteristics. H(r, t) is defined as a function of lateral position r and the deposition time t by H(r, t) = b[h(r, t)-h(0, t)]2 N, where h(r, t) and h(0, t) represent, respectively, the relative surface heights at lateral positions r and r = 0 at time t. Here the position with r = 0 may be arbitrarily chosen for uniformly deposited thin film samples. The height–height correlation function H(r, t) of random self-affine fractal surfaces contains at least three important parameters: the vertical correlation length (interface width) w(t), the lateral correlation length ξ(t) and the roughness exponent α. The interface width w(t) describes the surface roughness along the vertical direction during the growth process and it is defined as the root mean square surface height fluctuation (RMS roughness), which will evolve with time in the form of power laws w(t) ∝ t β, where β is the growth exponent. ξ(t) is the lateral correlation length that gives an average measure of the lateral coarsening size at the growth time t, and it is the distance within which the surface variations are correlated. Both w(t) and ξ(t) are statistical descriptions for the global surface morphology. The roughness exponent α is an important parameter to describe the self-affine fractal surface and it describes the local surface roughness. A larger value of α (N0.5) corresponds to a smooth short-range surface, while the small value of α (b0.5) corresponds to a more jagged local surface morphology [1]. Despite the complication of the growth processes, the surface morphology and dynamics of a growing interface exhibit simple dynamic scaling behavior for the far-from-equilibrium thin film growth [3,10], as has been demonstrated in a variety of growth processes such as silver and gold films [11], and the growth of the SnO2 nanocrystals [12]. This dynamic scaling behavior can be
5445
described by the height–height correlation function in the scaling form as given by: ( Hðr; tÞ∝
2α
Cr ; 2W 2 ðtÞ ;
r bb ξðtÞ r NN ξðtÞ
ð1Þ
We note that ξ(t) provides a length scale which distinguishes the short-range and long-range behaviors of the rough surface. With the data of the surface height h(r, t) obtained from an image of the atomic force microscope for the sample of growth time t, the height–height correlation function H(r, t) for this image can be calculated. For the i-th horizontal scan line, the height–height correlation function Hi ðmd;tÞ =
1 Nm ∑ ðh N−m j = 1 i;j
2 + m −hi;j Þ
ð2Þ
where d is the distance between two adjacent pixels of the image, N = 256 is the number of pixels in a scan line, N − m is the number of data points contributing to the calculation of the height–height correlation function corresponding to correlation distance md, and subscript i represents the quantities obtained for the i-th line of the image. Next, the height–height correlation function H(r, t) for the image is averaged over the 256 horizontal lines with the data obtained from Eq. (2) for each line. For the finite 256 × 256 pixels of the AFM image, the maximum of m is set at 100. In order to get good statistical properties, we finally take four AFM images of different regions of each GZO film sample to obtain the averaged height–height correlation function H(r, t), which is used as the height–height correlation function for the sample. Fig. 2 (a) and (b) shows the height–height correlation function versus position r = |r| in the log–log scale for the substrates and GZO film samples deposited with time shorter than 8 min and longer than 8 min, respectively. For the short range (r b b ξ(t)), linear relationship between H(r) and r is observed, corresponding to the proportionality of H(r) to r2α. Then in the logarithmic coordinates, the slope of the linear part in the curve is 2α, and it can be obtained by the linear fit of this part in the H(r)~r curve. At sufficiently large r (r N N ξ(t)), H(r) tends to be a constant 2w2 according to Eq. (1). The obtained values of α and w for all the samples are listed in Table 1. The roughness exponent α is found to be 0.84 ± 0.4. The turning point in the curve determines the lateral correlation length ξ(t). In order to obtain the values of ξ(t), we fit the curve of H(r) at a specific time t by the phenomenological function proposed by Sinha et al. [13]: r 2α 2 HðrÞ = 2w 1 exp½ð Þ ξ
ð3Þ
The values of the fitting parameter ξ(t) are also presented in Table 1. There are two different types of dynamic scaling behaviors in the growth front roughening. In the first type, the short-range behavior of H(r, t) is time-invariant, i.e., the process of growth is stationary, and the H(r, t) vs. t curves are overlapped so the coefficient C in Eq. (1) is time-independent [14]. In the second type, the deposition process is non-stationary and the short-range behavior of H(r, t) vary with time which are characterized by the increase of coefficient C with t. Such phenomenon is induced in the growth by the short-range balance in competition between the random fluctuations of the deposition and the local smoothing effects such as diffusion, with the former effect taking place and roughening the surface in both short and long ranges, and the latter ones appearing only in the short range of the growth front. In the short range i.e., in the distance shorter than the correlation length ξ(t), if the competition between random fluctuations and local smoothing can reach the balance, the local surface morphology is statistically stationary; if the balance is broken down
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Fig. 1. AFM images and one-dimensional cross section scan of surface profile of GZO thin films prepared by pulsed laser deposition deposited for 1 min, 4 min, 8 min, 10 min and 20 min and AFM image of quartz substrate.
Y. Liu et al. / Thin Solid Films 519 (2011) 5444–5449
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Fig. 1 (continued).
and the short-range scale growth is usually dominated by surface diffusion, often the Mullins diffusion, the local surface morphology is suggested statistically non-stationary, which has been demonstrated in Ref [15]. It is clear that the growth of GZO films belongs to the second type as shown in Fig. 2. In Fig. 3 we plot curve of the roughness w vs. time t with the data obtained from above calculations in Table 1. It can be seen form Fig. 3 that the relation of w and t can be divided into two stages. When the deposition time is shorter than 8 min, the value of w might be related to the overall influences by the factors of random fluctuations and the diffusion process of the deposited particles, the lateral strain, and the effect of the substrate such as the defects on it might be responsible for the initial surface roughening. The roughness w decreases with time and the surface fluctuations became small which indicates that the presence of surface diffusion smoothens the surface roughness in the early stages of film growth. For the film deposition time longer than 8 min, the dynamics of surface morphology is independent of the initial substrate, as shown in Fig. 1. The roughness w increase with further growth due to the formation of mounds, and it is proportional to t β and the curve is close to the self-affine fractal model in this stage. We fit the data of roughness w versus deposition time t for t N 4 min to the relation of w(t) ∝ (t - t0)β, with t0 the measure of the initial transient growth time in which the dynamic scaling has not occurred, Table 1 Surface parameters α, w(t) and ξ(t) for all the samples.
Fig. 2. The height–height correlation function as a function of position r in the log–log plots for (a) the substrate and the GZO films deposited for time shorter than 8 min and (b) the GZO films deposited for time longer than 8 min.
t (min)
1
2
4
8
10
20
30
α w(t) (μm) ξ(t) (μm)
0.86 0.0049 0.13
0.88 0.0044 0.13
0.81 0.0032 0.14
0.80 0.0017 0.043
0.83 0.0025 0.033
0.83 0.0038 0.039
0.86 0.0057 0.07
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Fig. 3. Thin film interface width, w, as a function of the deposition time, t. The solid curve is the best fit of a function of the form w(t)∝(t-to)β, where β = 0.3, t0 = 7.3 min.
and the fit curve is also shown as the solid curve in Fig. 3. The fit result gives β = 0.3, t0 = 7.3 min. This result indicates that for the growth time larger than about 7 min, the competition of all the factors influencing the film growth such as the noise deposition, the diffusion, the desorption and the strain, leads to the growth of the film following the aforementioned dynamic scaling law. Similar behaviors are also obtained by [4,16]. The values of t0 are different for different rough substrates and t0 would be larger for rougher substrates. This result is not consistent with the results obtained in many theoretical calculations [17], in which ideal substrate conditions are applied and are far from the complicated growth conditions in real systems. Fig. 4 gives the curve of the lateral correlation length ξ(t) vs. time t. We see that at first, the lateral correlation length ξ(t) is almost constant and decreases abruptly with the increase of deposition time t from 4 to 8 min. Further increase of time t results in a slow increase in ξ(t). Such phenomenon has also appeared in the depositions of InAs buffer layers and SnO2 film on rough substrates by Gyure et al. [18] and T. Lindström et al. [19], respectively, where the lateral correlation length ξ(t) goes towards larger values in rougher regime. They have found that smoothening occurs in the absence of lateral strain. At some time the film thickness variations will increase, giving rise to defects and strain variations as the surface smoothens. This finally triggers the onset of roughening. According to this point of view, we suggest that at the initial stage, the lateral stress in the GZO films is negligible and the diffusion of the deposition atoms flatten the surface. With the progress of deposition, the surface roughening influenced by the substrate is weakened and the global smoothening process of deposition play a dominating role, which corresponds to the initial fast decrease of lateral correlation length ξ(t) when time t increases from 4 min to 8 min. This is a crucial stage in the film surface evolution and in this stage the dynamic scaling appears. For further deposition, roughness caused by the lateral strain becomes obvious, and the global smoothening and roughening process reach a dynamic
balance. This might be the reason why ξ(t) have slight changes in this stage. While in the later growth stage, more defects and larger strain arise; the global roughening factors may surpass the smoothening ones, and this causes the subsequent global surface roughening and leads to latter slow increase of ξ(t). The growth feature of GZO is in good agreement with the noisedriven KS model [20,21], which can describe the growth process by the non-linear Langevin equation in the form ∂h = γ∇2 h− ∂t κ∇4 h + λ2 j∇hj 2 + η, where η = η(r, t) is a white-noise process, representing the stochastic deposition of atoms. The prefactor κand γ is proportional to the surface Mullins diffusion coefficient and tension coefficient, respectively. Numerical solutions of this equation [22] show that the α takes the values of 0.75–0.85, β the values of 0.22–0.25, and a time-dependent coefficient C for early time. Our GZO film is well consistent with this model. 4. Conclusion Height–height correlation function H(r) can be a good quantitative description of the statistical evolution of the surface. The evolution of GZO surface morphology is analyzed quantitatively with height– height correlation function H(r) obtained from the AFM image data. The roughness exponent α is about the same for all t .We have shown that the evolution can be divided into two stages. At the first stage, both the interface width w(t) and the lateral correlation length ξ(t) decrease with time and the surface fluctuations became small. It might be deduced that the morphology evolution is due to overall influences by the factors of the random fluctuations, the smoothening process of deposition, the lateral strain and the rough substrates. For the second stage, when the deposition time is larger than 8 min, the film is thick enough and the effect of the substrate could be neglected. The film grows in its inherent law and the evolution of GZO surface morphology is suggested to obey the dynamic scaling law and to possess the self-affine fractal characteristics. Both w(t) and ξ(t) increase with time due to the strain induced surface roughening. w(t) evolves with time in the form of power laws w(t) ∝ tβ. By fitting the curves in Fig. 3, the growth exponent β is found to be about 0.3. We suggest the growth process of the GZO film deposited by PLD is quite consistent with the noise driven KS model. The properties of the surface morphologies and their evolutions with the deposition time t may reflect the microscopic growth dynamics of thin films. The correlation of developmental growth morphology with more other deposition parameters would also be important in the study of thin film growth dynamics and is worthy to be investigated in our future work. Acknowledgements The authors acknowledge the support of the National Science Foundation of China under grant no.10874105 and no.10974122, and Shandong Provincial Natural Science Foundation under grant no. ZR2009FZ006. References
Fig. 4. The lateral correlation length ξ(t) as a function of time t.
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