Fractal features of CdTe thin films grown by RF magnetron sputtering

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Fractal features of CdTe thin films grown by RF magnetron sputtering Fayegh Hosseinpanahi a,∗ , Davood Raoufi b , Khadijeh Ranjbarghanei c , Bayan Karimi a , Reza Babaei c , Ebrahim Hasani b a b c

Department of Physics, Payame Noor University, P.O. Box 19395-4697, Tehran, Iran Department of Physics, University of Bu Ali Sina, P.O. Box 65174, Hamedan, Iran Department of Physics, Plasma Physics Research Center, Science & Research Branch Islamic Azad University, Tehran, Iran

a r t i c l e

i n f o

Article history: Received 3 June 2015 Received in revised form 3 September 2015 Accepted 4 September 2015 Available online xxx Keywords: Sputtering CdTe Thin films Surface morphology Fractal MFDFA

a b s t r a c t Cadmium telluride (CdTe) thin films were prepared by RF magnetron sputtering on glass substrates at room temperature (RT). The film deposition was performed for 5, 10, and 15 min at power of 30 W with a frequency of 13.56 MHz. The crystal structure of the prepared CdTe thin films was studied by X-ray diffraction (XRD) technique. XRD analyses indicate that the CdTe films are polycrystalline, having zinc blende structure of CdTe irrespective of their deposition time. All CdTe films showed a preferred orientation along (1 1 1) crystalline plane. The surface morphology characterization of the films was studied using atomic force microscopy (AFM). The quantitative AFM characterization shows that the RMS surface roughness of the prepared CdTe thin films increases with increasing the deposition time. The detrended fluctuation analysis (DFA) and also multifractal detrended fluctuation analysis (MFDFA) methods showed that prepared CdTe thin films have multifractal nature. The complexity, roughness of the CdTe thin films and strength of the multifractality increase as deposition time increases. © 2015 Elsevier B.V. All rights reserved.

1. Introduction Cadmium telluride (CdTe) is an II-VI compound with both n- and p-type character. It crystallizes in both the wurtzite and zincblende structures. CdTe is a very interesting semiconductor in the form of thin films with wide band gap (1.5–2.1 eV) as active components of desirable properties for producing photo electrochemical cells, field effect transistors, IR detectors, photodiodes, photo conductors and photovoltaic solar cells [1–6]. Among the most cited applications for CdTe films, the use of CdTe film as an absorbent layer in a CdS/CdTe solar cell can be highlighted, because of its very high absorption coefficient >104 cm−1 which allows 99% absorption of the incident light in a 2 ␮m thick film [7]. CdTe thin films have been grown by a wide variety of techniques such as vacuum deposition [8], molecular beam epitaxy [9], metal-organic chemical vapor deposition [10], closed-space sublimation [11], screen-printing [12], electro deposition [13], and RF magnetron sputtering [7,14]. In solar cells applications, the appropriate characteristics for CdTe films are large crystals and smooth surfaces [15]. Thus, motivated by the need of smooth surfaces of CdTe thin films in solar cells devices, it is exciting to study the surface morphology features of the sputter deposited CdTe thin films.

∗ Corresponding author. E-mail address: [email protected] (F. Hosseinpanahi).

Nowadays, statistical measures of thin film surface roughness have become very popular, because these measures provide complete description of the surface morphology features of thin films [16]. So, in order to describe the surface morphology and complexity of thin films, the concepts from fractal geometry may be used. In contrast to traditional analyses, the fractal and multifractal analyses can be used to extract different types of information from measured textures. This makes fractal analysis widely applicable and very useful in describing complex surface characteristics of thin films and in advancing our understanding of how the geometry of surfaces affects the physical properties of the system [17]. Multifractal detrended fluctuation analysis (MFDFA) technique, due to easy implementation, low computational time and definitely high accuracy is being used in various studies. The spectra gained by multifractal analysis are recently used to characterize the surface roughness and moreover to illustrate the shape of peaks and valleys between rough surfaces. The accuracy of the DFA approach has been investigated by Gu and Zhou [18]. They have studied the landscape of the Yardangs region on Mars and the fracture surface of a foamed polyurethane sample with super critical carbon dioxide. In their work, they have shown that an accurate Hurst exponent estimation can be measured by a proper selection of the detrending function. Liu et al. [19] have used multifractal analysis to study the fracture surfaces of foamed polypropylene/polyethylene blends at different temperatures. Pyrak-Nolte et al. [20] obtained multifractal spectra of the fracture surfaces at different normal stress conditions.

http://dx.doi.org/10.1016/j.apsusc.2015.09.048 0169-4332/© 2015 Elsevier B.V. All rights reserved.

Please cite this article in press as: F. Hosseinpanahi, et al., Fractal features of CdTe thin films grown by RF magnetron sputtering, Appl. Surf. Sci. (2015), http://dx.doi.org/10.1016/j.apsusc.2015.09.048

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Stach et al. [21] have provided a comprehensive description of typically brittle fracture surface morphology by means of multifractal technique. Raoufi et al. [22] applied multifractal analysis to investigate the surface topographies of ITO thin films by using atomic force microscopy (AFM) images. Two important factors in multifractal analysis, the scaling exponent, ˛, and its density function, f (˛), allow a quantitative evolution of the degree of reaction probability distribution in homogeneity. The multifractal behavior of annealed Au/Ge bilayer films have been studied by Chen et al. [23]. They found that the fractal crystallization process in these films can be investigated by the multifractal approach, the singularity spectra f (˛) and the width ˛. The relationship between the heights of f and ˛ in Solid-on-Solid (SOS) growth was studied by Wang et al. [24]. They have shown that this relationship is associated to the average films thickness h as ˛ ∝ h0.9 . In this study, by studying AFM images and multifractal analysis, our particular aspect relates to material characterization improvement of surface roughness of CdTe thin films prepared by RF magnetron sputtering technique on float glass substrates.

where x denotes the averaging over the whole time series. Next we break up xi is divided into two non-overlapping Ns = int[N/s] segments of equal length s for data integrity since N is not always an integer multiple of s [26]. In each segment , we fit the profile by using kth order polynomial function, pk which is called the local trend. We detrend the integrated time series y (i) in each box, and calculate the detrended fluctuation function: Ys (i) = y(i) − pk .

here, pk is the fitting polynomial in segment . Linear, quadratic, cubic, or higher order polynomials can be used in the order of the DFA (k = i, DFA (i)). In this work we used linear polynomials function. For a given s, we calculate square fluctuation Fs2 (, s), which defined as the variance of Ys (i):

The multifractal detrended fluctuation analysis (MFDFA) method permits the detection of intrinsic self-similarity embedded in a seemingly nonstationary time series. To implement the MFDFA [17,25], let us suppose we have a time series, xi of length N and determine integrated time series: y(i) =

i  k=1

[xk − x]

i = 1, . . ., N.

(1)

(3)

i=1

Finally, we calculated the average over all segments to obtain the qth order fluctuation function:



3. Multifractal detrended fluctuation analysis

1 2 Ys [( − 1)s + i] s s

Fs2 = Ys2 (i) =

2. Experimental The cadmium telluride (CdTe) thin films were deposited on glass substrates by RF magnetron sputtering technique at room temperature (RT). Before loading the glass substrates into the chamber, they were ultrasonically cleaned in acetone and methanol for 10 min. Then, they were washed with deionized water, and finally dried with nitrogen gas. A CdTe target (99.99% purity) with a diameter of about 2in was used as the sputtering source. The separation between the target and the substrate was about 70 mm. After the chamber was evacuated to a base pressure below 3.5 × 10−6 Torr, pre-sputtering of 15 min was carried out to clean the target surface. The flow rate of the sputtering gas Ar (Argon, 99.99% purity), which is controlled by a mass flow controller, was set to 140 sccm and the Ar pressure was fixed to 1.5 × 10−2 Torr. The RF power was 30 W with a frequency of 13.56 MHz. The deposition of the thin films was carried out for 5, 10, and 15 min on glass substrates. The crystal structure of the CdTe thin films was studied using X-ray diffraction (Philips Powder Diffractometer type PW 1373 goniometer). The XRD was equipped with a graphite monochromator crystal. The X-ray wavelength was 1.5405 A˚ and the diffraction patterns were recorded over the 2 range 10◦ –70◦ with a step size of 0.06 (2/s). The surface morphology of the thin films was characterized with an atomic force microscope (AFM- Park Scientific Instruments, CP, USA) under ambient conditions. The scan size was 1 × 1 ␮m2 . All the surface images were obtained in the contact mode using silicon nitride tips with approximate tip radius of 10 nm; and the height of the surface relief was recorded at a resolution of 256 pixels × 256 pixels. Specific image analyzer software (WSxM version4) was utilized to study the topographic surface parameters. A variety of scans was acquired at random locations on the film surface. Analyzing the AFM images, the topographic image data were converted into ASCII data.

(2)

Fq (s) =

1  2 q/2 Fs (k) 2Ns 2Ns

1/q (4)

k=1

where, in general, the index variable q can take any real value except zero. When q = 0, we have:



F0 (s) = exp



1  ln[Fs2 (k)] 4Ns 2Ns

.

(5)

k=1

When q = 2, we have:

 F(s) =

1/2

1  2 Fs (k) 2Ns 2Ns

(6)

k=1

The above computation is repeated for box sizes s (different scales) to provide a relationship between F(s) and s. A power law relation between F(s) and s indicates the presence of scaling F(s)∼sH

(7)

where the Hurst exponent (H) has been used for the measured selfsimilarity parameters and investigation of correlations at the longrange dependence in empirical time series. The Hurst exponent was seen to be between 0 and 1. If H = 0.5, indicates that the time series is independent e.g. the process probably be a non-Gaussian; if H < 0.5, means anti-persistence or pure random character of records; and finally if H > 0.5, indicates that the time series is persistence [27]. For long-range power-law correlated data, Fq (s) increases asymptotically with s and follows the power-law: Fq (s)∼sh(q)

(8)

where the exponent h(q) describes the scaling behavior of the q-th order fluctuation function which can be obtained by observing the slope of log-log plot of Fq (s) versus s through the method of least squares. This scaling exponent displays self-similar fractal behavior over a broad range of time scales. The function h(q) describes the scaling behavior of the segments with large fluctuations for q > 0 and small fluctuations for q < 0 [25]. For stationary time series, the exponent h(2) is identical to the well-defined Hurst exponent. Thus we call the exponent h(q) the generalized Hurst exponent. For mono-fractal time series the scaling exponent h(q) is independent of q, whereas for multifractal time series, h(q) varies with q so that it is a nonlinear decreasing function of q.

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Fig. 1. XRD patterns of CdTe thin films deposited at room temperature (RT) and deposition times: (a) 5 min, (b) 10 min and (c) 15 min.

Fig. 2. XRD pattern of CdTe thin film deposited at room temperature (RT) and deposition time 15 min. The bar graphs point to the 2 and intensity values of peaks.

The relation between the two sets of multifractal scaling exponents, the mass exponent (q) and h(q) is as follows:

that the CdTe film surfaces show continuous island growth type with granules which possess different sizes, irregular shapes, and separations. There are patterns seen in the surface morphology which its lateral size slightly grows with increasing time. The AFM micrographs of the films clearly show the evolution of surface feature (rough) with deposition time. The root mean square (RMS) roughness, w is given by:

(q) = qh(q) − 1

(9)

The singularity spectrum f(˛) is a traditional method to characterize a multi-fractal series. This singularity spectrum can be related to (q) via a Legendre transform [25,28] as: ˛=

d(q) dh(q) = h(q) + q dq dq

f (˛) = q(˛ − h(q)) + 1

(10) (11)

4. Result and discussion 4.1. Crystalline structure In order to study the microstructure of the CdTe thin films, the X-ray diffractometer (XRD) measurements were performed. It was found that the film microstructure and orientation were both sensitive to the deposition time. The XRD patterns of CdTe thin films prepared at room temperature (RT) and different deposition time namely, 5 min, 10 min and 15 min are shown in Fig. 1. The changes in the XRD patterns of CdTe films due to the different deposition time can be seen clearly in Fig. 1. All XRD patterns exhibit polycrystalline nature with a preferential orientation along the plane (1 1 1), and all of the peaks are broadened and shifted. This feature indicates the presence of residual strains in the CdTe thin films. Fig. 2 shows XRD pattern of the CdTe film deposited with deposition time of 15 min. The bar graphs point to the 2 and intensity values of peaks. As it can be seen from this figure, the diffraction peaks (2) at 23.74◦ , 39.28◦ , 46.60◦ , 56.86◦ and 62.50◦ are respectively indexed to (1 1 1), (2 2 0), (3 1 1), (4 0 0) and (3 3 1) of zinc blende structure of CdTe. The peaks of the unstrained zinc blende structured CdTe are located at 23.800◦ , 39.356◦ , 46.514◦ , 56.877◦ , 62.523◦ , 71.358◦ , and 76.431◦ , respectively (JCPDS card No. 65-8879). The preferred orientation along the (1 1 1) plane is the close-packing direction of the zinc blende structure, and this type of textured growth has often been observed in polycrystalline CdTe films grown on amorphous substrates [29]. 4.2. Topographical and morphological studies The variations of the surface morphology for different growth times of processed samples by AFM are shown in Fig. 3. It is clear

  N N  1 ¯ 2 w= (hij − h) N2

(12)

i=1 j=1

where, hij is the surface height at the position (i, j), h¯ is the mean surface height, and N is the number of data acquired by each AFM line scan (N = 256 in our case). The RMS surface roughness, w for samples, a, b and c are calculated to be 1.98 nm, 2.09 nm and 2.28 nm, respectively. We see that w of the thin films increased with increasing the growth times. This may be due to the fact that different cluster size is affected by time, so the smaller grains seen in Fig. 3 at lower time tend to form bigger clusters at higher time. As a result, thin films also become rougher with increasing time. Based on theoretical consideration, the scaling exponents under constant flux to the surface and constant growth rate conditions, can be determined by scaling of the experimental results with film thickness, so the interface width (roughness) increases as a power law of time deposition [30,31], w(t)∼t ˇ . In Fig. 4, it is obvious that the CdTe thin film surfaces exhibit a kinetic roughening during growth. The linear relationship between w and t in doublelogarithmic scale indicates that the roughness increases with time deposition according to a power law [32]. The growth exponent ˇ for CdTe thin films is estimated to be about 0.12 ± 0.01. 4.3. Multifractal analysis DFA method is used for the analysis and elimination of trends from data sets. This method [33] has become a widely used technique for the determination of fractal scaling properties. Fig. 5 shows the corresponding fluctuation function F(s) vs. the box size s in log-log scale. Based on Eq. (7), we could obtain the following estimate for the Hurst exponent: H = 0.83 ± 0.02 Since H > 0.5, it is clear that the frequency series show persistence. From the above analysis, we could obtain the critical exponents of the model, Hurst exponent H = 0.83 ± 0.02 and, ˇ = 0.12 ± 0.01, respectively. These particular values do not appear as values

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Fig. 4. RMS roughness (w) as function of deposition time in a log–log scale.

Fig. 5. The log-log plot F(s) versus s obtained from multifractal DFA1 for CdTe thin film at deposition time 15 min. The slope of the curve (dash line) gives H, where H is the Hurst exponent.

Fig. 3. AFM surface image of CdTe thin films grown with different times for (a) 5, (b) 10 and (c) 15 minutes, respectively.

described by any of the classes of continuum growth. Hence, the behavior is the combination of the Mullins diffusion model (ˇ = 0.25) and the Edwards-Wilkinson model (ˇ = 0) [34]. The log–log plot of Fq (s) vs. s for different values of q in the range of −3 < q < 3 is shown in Fig. 6; plots obtained from AFM images of the CdTe thin films. The figure clearly shows that every q has fitted nicely on a straight line which demonstrates the power law behavior between detrended fluctuation function Fq (s) and the scale s, as expressed in Eq. (8). According to Eq. (8), the slopes of the straight lines displayed in Fig. 6, which can be determined by least squares regression of log Fq (s) versus log s for each q, are the scaling exponent h(q). The generalized Hurst exponent as a function of q for −3 < q < 3, has shown in Fig. 7a. The function h(q) in all samples depends on q which is a nonlinear decreasing function of q. Furthermore, the computation of the mass exponent function (also known as multifractal scaling exponent) (q), reveals more about the multifractal characteristics of thin film surfaces under investigation, see Fig. 7b. Using Eq. (9), (q) for different values of q in the range of −3 < q < 3 has been computed. We find that (q) is also a nonlinear function of q. It is vivid that, the nonlinearity behavior of h(q) and (q) prove the multifractal nature of thin film surfaces under investigation.

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Fig. 6. Log Fq (s) as function of log s different values of q (−3 < q < 3) at different deposition time.

5

Fig. 8. The multifractal spectra (f(˛) versus ˛) of the CdTe thin film surfaces at different deposition time.

Table 1 The measures of mutifractal spectra of the CdTe thin film at different time deposition. Sample

Time

˛max

˛min

˛

f(˛max )

f(˛min )

f

Sample a Sample b Sample c

5 min 10 min 15 min

1.03 1.08 1.13

0.59 0.60 0.59

0.44 0.48 0.54

0.54 0.51 0.47

0.83 0.81 0.78

0.29 0.30 0.31

which characterize the least and most singular, respectively, are the singularity strengths related to the region of the sets [19–35]. Furthermore, ˛ = ˛max − ˛min , which is the width of singularity strength, reflects the range of singular exponents, the long-range correlations, and the strength of the multi-fractal behavior. Similarly, f(˛min ), f(˛max ), and f = f(˛min ) − f(˛max ) can also be used to quantitatively characterize the multifractal nature of thin film surfaces under investigation. The values of ˛min , ˛max , ˛, f(˛min ), f(˛max ), and f are summarized in Table 1 for CdTe thin film surfaces of deposition time 5 min, 10 min and 15 min, respectively. According to the Fig. 8 and Table 1, with increasing growth time in CdTe thin film, the singularity spectrum becomes wider i.e. the values of ˛ increase. It means that the surface of CdTe thin film is more irregular and rougher with increasing deposition time. 5. Conclusion

Fig. 7. (a) Scaling exponent h(q) and (b) Mass exponent ␶ (q) as function of q.

We compute two most important characteristics in the description of the multifractal [19]; the singularity strength of ˛ (Eq. (10)) and the singularity spectrum f (˛) (Eq. (11)). The multifractal spectra f(␣) as a function ␣ is plotted in Fig. 8 for three samples with different deposition time. The ˛min and ˛max values of ˛(q)

The CdTe thin films were successfully deposited on glass substrates by RF magnetron sputtering at different deposition time 5, 10 and 15 min, while the RF power and Ar gas flow rate were fixed to be 30 W and 140 sccm, respectively, during the sputtering. The effect of deposition time on the structural and morphological properties of CdTe thin films was investigated by AFM and XRD techniques. Their surface morphologies obtained from AFM images were subjected to fractal and multifractal analysis to investigate their structural properties quantitatively. Statistical parameters, fractal and multifractal analysis have provided a valuable description of the complexity of the surface morphology of the CdTe thin films. Using DFA and MFDFA methods, Hurst exponent was higher than 0.5 (positive correlation), nicely power-low scaling is observed and the nonlinear relationship between h(q) and ␶(q) in the range of −3 ≤ q ≤ 3 confirms the multifractal nature of the films under investigation. Moreover, the width of multifractal spectrum and also strength of multifractality are changed with increasing deposition time.

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