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Anomalous scaling of iron thin film electrodeposited in a magnetic field
Journal of
Electroanalytical Chemistry Journal of Electroanalytical Chemistry 587 (2006) 93–98 www.elsevier.com/locate/jelechem
Anomalous scaling of iron thin film electrodeposited in a magnetic field H. Matsushima a, Y. Fukunaka a b
b,*
, Y. Ito b, A. Bund a, W. Plieth
a
Institute of Physical Chemistry and Electrochemistry, Dresden University of Technology, Mommsenstrasse 13, D-01062 Dresden, Germany Graduate School of Energy Science, Department of Energy Science and Technology, Kyoto University, Sakyo-ku, Kyoto 606-8501, Japan Received 4 February 2005; received in revised form 5 September 2005; accepted 16 October 2005 Available online 5 December 2005
Abstract Iron thin films were electrodeposited on a copper substrate in FeSO4 aqueous solution under a magnetic field (0–5 T) at 298 K. The surface morphology was observed by the atomic force microscopy (AFM). It was drastically changed from an angular to a wavy shape by superimposing the magnetic field. Moreover, rectangular shaped precipitates were aligned along the magnetic field. The grain size decreased with increasing in magnetic field intensity, B. The AFM image was characterized by the anomalous scaling method in order to quantitatively analyze the magnetic field effect on surface roughness. The roughness exponent, a, and the growth exponent, b, decreased as B increased. The variation of scaling parameters with B may be utilized to improve the surface morphology evolution and the transition of the crystal growth induced by the magnetohydrodynamic convection can be phenomenologically discussed. 2005 Elsevier B.V. All rights reserved. Keywords: Magnetic field; MHD; Iron electrodeposition; AFM; Scaling; Surface morphology
1. Introduction Electrodeposition process is frequently playing an important role in the microelectronics film formation technology as seen in Damasciene process developed by IBM. Electrochemical processing can be principally applied to induce the giant magnetoresistance (GMR) effect by alternatively depositing nonmagnetic and magnetic thin film layers of only some nanometer thickness [1,2]. However, it is not yet widely employed for the preparation of magnetic multilayers, because the electrochemically grown multilayers do not exhibit so high performance as by plasma processing. Palasantzas et al. [3] reported that the roughness on thin film surfaces/interfaces causes the poor performance induced by the physical characteristics such as magnetic and electronic transport properties. There is unfortunately a considerable lack of understanding how to control the microscopic growth process of electrocrystallization in comparison with the film technology based on the vacuum pro*
Corresponding author. Tel.: +81 75 753 5415; fax: +81 75 753 4719. E-mail address: [email protected] (Y. Fukunaka).
0022-0728/$ - see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.jelechem.2005.10.025
cessing. The shape evolution analysis may provide a good start to compare the microscopic growth process in electrolytic processing with that in vacuum processing. The present paper starts to discuss the scaling analysis on the electrodeposited Fe film, in order to further develop the advanced electrochemical processing in film formation technology. Superimposing an external magnetic field offers many possibilities to influence the electrodeposition process and thus to control the microstructure of the thin film interface [4–6]. Our previous papers [7,8] described the morphology of electrodeposited iron film strongly depended on both the magnetic field intensity and the direction. Furthermore, it was found that the texture evolution was controlled by a magnetic field [9]. That is, biaxial texture structure evolved in the presence of magnetic field while uniaxial texture was formed without such a magnetic field. The present paper focuses the effect of magnetic field on the surface morphological variations by applying the scaling analysis technique. 2. Experimental The electrodeposition apparatus has been already described as well as the experimental procedure in our
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H. Matsushima et al. / Journal of Electroanalytical Chemistry 587 (2006) 93–98
previous paper [7]. Thus, only several important points are mentioned here. The cathode was made of a sheet of copper (10 · 10 · 0.2 mm, Cu 99.99%, Nilaco Corp.). The anode was a sheet of pure iron (10 · 10 · 0.2 mm, Fe 99.99%, Nilaco Corp.). The polycrystalline copper substrate was mechanically polished by an emery paper and buffed with linen cloth containing alumina suspension (0.3 lm). Then, it was electropolished in 70-wt% phosphoric acid solution for an hour at the terminal voltage of 1.0 V before supplying it to the electrodeposition. An electrolyte was FeSO4 (0.9 mol L1) aqueous solution. The value of pH was adjusted to 1.5 with H2SO4 solution. The electrolyte temperature was maintained at 298 K. Iron electrodeposition was galvanostatically conducted until the amount of the electrical charge reached 5– 100 C cm2. A uniform magnetic field was superimposed parallel to the electrode planes. The magnetic field was generated by a helium free superconducting magnet (HF5-100VHF, Sumitomo Heavy Industries). The surface morphology was observed by AFM (SPI 3800, Seiko Instruments). The AFM images were acquired with a contact mode. The image scans were taken with a resolution of 512 · 512 pixels. 3. Results Galvanostatic electrodeposition was conducted at 10 mA cm2. Iron film was electrodeposited in the magnetic field intensities, B = 0, 0.5, 1, 3, and 5 T, respectively. AFM images of the surface morphology obtained at various magnetic fluxes are illustrated in Fig. 1(a)–(e). The amount of electricity was kept at 5 C cm2. The film thickness was estimated to be 800 nm based on the measured iron current efficiency of about 60%. Fig. 1(a) (B = 0 T) illustrates the surface morphology consisted of angular iron grains with the size of about 100 nm. They are randomly precipitated on the substrate, although the image (a) shows several small areas left from the nucleation because of preferential H2 gas evolution. The average surface roughness was measured to be about 60 nm. As the time proceeded, the surface roughness appeared to become significant. Comparing the surface morphology electrodeposited under a conventional electrochemical deposition condition (B = 0 T), the superposition of magnetic field introduces another degree of freedom to the heterogeneous surface reaction field to induce the drastic differences in surface morphology. A striking morphological variation appears Fig. 1(b). The superimposition of 0.5 T introduces a morphology which rectangular precipitates with about 100 nm long lateral faces are considerably aligned along a direction. That is, the bottom shape of each precipitate was rectangular where all the long lateral faces were arranged uniquely in a magnetic field direction. Much smaller precipitates appear on the surface of lateral plane. The alignment direction should be controllable. With further increased B, the rectangular shape starts to change to a roundish shape. The images shown in
Fig. 1(b)–(e) consisted of wavy grains. The individual grains appeared to become smaller and more roundish as B increased. The surface morphology became smoother. The reduction of grains size by B has been also reported in other metal electrodeposition like copper [10] and nickel [11]. 4. Discussion Fig. 1 clearly illustrates that the superimposition of magnetic field drives the alignment of rectangular precipitates along the magnetic flux field. This is the unique characteristic caused by the superimposition of magnetic field to electrodeposited iron film morphology. Unfortunately, the prediction on this magnetic field alignment is far behind the quantitative discussion at the present moment. Therefore, another aspect of smooth surface morphology caused by magnetic field is now focused. 4.1. Anomalous scaling theory The surface microstructure must be quantitatively described in order to understand the magnetic field effects on the electrodeposition process. The scaling analysis of surface evolution has been usually studied through the dynamic scaling theory, Family–Vicsek model [12]. The analysis is based on the surface width, W(l, t), known as the root mean square height of the surface which is defined as follows: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 W ðl; tÞ ¼ hðh hhiÞ i; ð1Þ where h, l and t are the surface height, the size of measured region and the deposition time, respectively. The averaged surface width is fitted to a normal scaling relation t W ðl; tÞ ¼ la f a=b ; ð2Þ l where a and b are defined as the roughness and growth exponent, respectively. The scaling function f(x) is constant for x 1, and varies as xb for x 1. The normal scaling has been employed to study the effect of additives on quasi-two dimensional growth of the nucleation [13– 17]. The fitted values are compared with the predictions of theoretical models to assess the surface growth mechanism. Schwarzacher et al. [18,19], on the other hand, proposed a different kind of anomalous dynamic scaling. They introduced W(l, t) having a power law dependence on t even for small l. Anomalous scaling is thus represented by the following expression [19]: t W ðl; tÞ ¼ lH tbloc f z ; ð3Þ l where H is the Hurst exponent, and z (=H/b) is the dynamic exponent.
H. Matsushima et al. / Journal of Electroanalytical Chemistry 587 (2006) 93–98
95
Fig. 1. AFM images of the iron films electrodeposited from FeSO4 solution with the passage of 5 C cm2 at 10 mA cm2 in the magnetic fields of (a) 0 T, (b) 0.5 T, (c) 1 T, (d) 3 T and (e) 5 T.
For a given value of t, the crossover between these two scaling regimes occurs at l = lc, where lc is the critical scaling length. Hence, Eq. (3) is ( lH tbloc for l < lc W ðl; tÞ / ð4Þ tbþbloc for l > lc For a given t, the roughness increased as lH and then saturated at a value that is proportional to lac . Moreover, the roughness exponent, a, is expressed as follows: a ¼ H ð1 þ bloc =bÞ.
ð5Þ
4.2. Parameter determination A quantitative methodology for surface analysis is provided by a scaling method of electrodeposited iron film surface. W(l, t) were measured at several times in the magnetic field of 0 and 5 T. They are illustrated in Figs 2 and 3, respectively. Log W increased linearly with log l for small l, and saturated for large l, which was consistent with Eq. (4) independently of a magnetic field. In order to calculate the Hurst exponent, H (the gradient of the plot for small l), saturated width, Wsat (the value of W for large l) and critical scaling length, lc (the crossover between the two
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H. Matsushima et al. / Journal of Electroanalytical Chemistry 587 (2006) 93–98 10 2
Wloc(t) / nm
W(l , t) / nm
102
100 C cm-2
10 50 C cm-2
0T 0.5 T 1T 3T 5T
10
10 C cm-2 5 C cm-2
1
10 2
10
10 3
1
10 4
10 3
l / nm Fig. 2. Surface width, W(l, t), of the iron films measured over regions of size l at several times in no magnetic field (d: 5 C cm2, j: 10 C cm2, m: 50 C cm2, ·: 100 C cm2).
W(l , t) / nm
100 C cm-2 50 C cm-2 10 C cm-2 5 C cm-2
1 10
Fig. 4. Local surface width, Wloc(t), for iron films electrodeposited at different deposition time, t, with and without B (d: 0 T, n: 0.5 T, j: 1 T, e: 3 T, .: 5 T, scaling length l = 100 nm).
(50 C cm2) to 1.0 · 104 s (100 C cm2). The relationship between Wloc(t) and t could be expressed by a liner equation whose gradient is equivalent to bloc as shown in Eq. (4) (at l < lc). Fig. 5 shows the saturated surface width, Wsat(t), at the scale size l = 104 nm as the function of t. Similarly to Fig. 4, a good liner dependence between Wsat(t) and t is demonstrated. The gradient of the fitted line is equal to b + bloc as shown in Eq. (4) (at l > lc). The parameter of growth exponent, b, is calculated by subtracting bloc from the gradient value in Fig. 5.
10 2
10
10 4
t/s
10 2
10 3
4.3. Effect of magnetic field on scaling factors
10 4
l / nm Fig. 3. Surface width, W(l, t), of the iron films measured over regions of size l at several times in a magnetic field of 5 T (d: 5 C cm2, j: 10 C cm2, m: 50 C cm2, ·: 100 C cm2).
In order to investigate the magnetic field effect on scaling factors, the dependences of scaling parameters on B are summarized. Fig. 6 is a plot of roughness exponent, a, vs. B for the iron-electrodeposited film. The error bar
regimes), the following function was used to fit the data [19]:
0T 0.5 T 1T
ð6Þ
It is clearly seen that measured data can be described more reasonably by Eq. (6). H was found to be constant for all electrodeposition times. It remarkably decreases by the magnetic field. For example, it is 0.45 for 0 T and 0.16 for 5 T. Figs. 2 and 3 demonstrate a characteristic of anomalous scaling in which the persistent time increases of the roughness even for small scales (1st line in Eq. (4)). In order to obtain the local growth exponent, bloc, the local surface width, Wloc(t), was measured at a scale size well below the critical length. Fig. 4 shows the Wloc(t) for the iron films electrodeposited as the function of deposition time, t, under B. In the present case, the scale size was fixed at 102 nm and the electrodeposition time was varied from 5.0 · 102 s (5 C cm2), 1.0 · 103 s (10 C cm2), 5.0 · 103 s
3T 5T
Wsat( t) / nm
W ðlÞ ¼ W sat f1 exp½ðl=lc ÞH .
10 2
10
1
10 3
10 4
t/s Fig. 5. Saturated surface width, Wsat(l,t), for iron films electrodeposited at different deposition time, t, with and without B (d: 0 T, n: 0.5 T, j: 1 T, e: 3 T, .: 5 T, scaling length l > lc).
H. Matsushima et al. / Journal of Electroanalytical Chemistry 587 (2006) 93–98
α
0.8 0.6 0.4 0.2 0 0
1
2
3
4
5
B/T Fig. 6. Plots of the roughness exponent, a, against B for the iron films electrodeposited on copper substrate.
indicates the standard deviation of a for each iron film prepared at different deposition time. Metals electrodeposited onto a foreign substrate surfaces in the additive free solutions typically exhibit a value between 0.7 and 1.0, for example, Cu = 0.8–0.9 [17,19], Ag = 0.7 [20], Ni = 0.9 [21] and NiP = 1.0 [22]. The present value of a = 0.35–1.1 is in the range of these parameters. It is interesting to know that the anomalous scaling can be applied to analyze the surface evolution phenomena even for the iron film, although the superimposition of magnetic field introduces another complexity like grain shape variation in iron electrodeposition mechanism. Many theoretical studies have modeled the various growth processes and quantitatively calculated the surface texture evolution phenomena. According to their papers, a is an important factor to clarify the shape evolution mode combining the surface diffusion and the step growth mechanism [17]. The effect of additives to the surface morphology of electrodeposited film has been focused. The model considers that the adsorbed additives on substrate may hinder the surface diffusion of atoms to introduce a smoother surface. The numerical simulation predicts a slower surface diffusion rate to result in smaller parameter of a. Fig. 6 clearly shows that the parameter of a considerably decreases from 1.1 in 0 T to 0.35 in 5 T. Comparing the present experimental results with the work by Illinois group [17], the superimposition of magnetic field introduces a phenomenologically similar effect of addition of additives, expect for the appearance of precipitates arranged in magnetic field direction demonstrated in Fig. 1(b)–(e). The shape evolution or surface roughness factor may be governed by the competition between the surface diffusion rate primarily determined by the electrochemical processing parameters like the current density and the step growth rate by the adsorbed additive. The enhanced ionic mass transfer rate by MHD convection significantly drives the surface diffusion of additives molecules as well as atom. This MHD convection essentially results in enhancing the
0.5
0.5
β loc
0.4 0.3
0.4 0.3
β
β loc
1.0
mass transfer rate of adsorbed additives to the step or kink site on the growing crystal. The growth mode changes from surface diffusion to step growth mode. The present experimental result suggests that the iron deposition mechanism might be significantly influenced by the alignment caused by the magnetic field as demonstrated in Fig. 1(b). Moreover, the surface pH may be different from the bulk electrolyte under MHD condition to result in the transition of surface shape evolution mode. The deviation of surface pH value may introduce a drastic change of electrocrystallization mechanism. Furthermore, the effect of localized magnetic field gradient may result in a unique crystallographic orientation, because iron metal is a very significant magnetic susceptibility. These aspects must be further examined especially to emphasize the pH value on the cathode surface combining MHD convection. The relationship between growth exponent, b, and local growth exponent, bloc, vs. B for the iron film is demonstrated in Fig. 7. The typical value of b for the metal electrodeposits without additives has been reported to be around 0.25, which agrees well with the present value. In this experiments, b slightly decreases from 0.31 to 0.27 with increasing in the magnetic flux density. It suggests that the surface morphology obtained in the magnetic field does not roughen as quickly as that in no magnetic field. That is, the rate of roughening is surely depressed by superimposing the magnetic field. On the other hand, bloc linearly decreases from 0.44 in 0 T to 0.29 in 5 T. Castro et al. [23] reports that more compact films are produced for larger electric field, resulting in anomalous scaling properties being replaced by Family– Vicsek scaling [12]. As well as our experiments, the film surface looks compact for larger B and the anomalous scaling may disappear. This may be related to the observation that roughening rate is slower for larger B values. Fig. 8 shows a plot of the critical length, lc, vs. B for the iron film deposited through the charge passage of 5 C cm2. A variation of lc means a change in the lateral
β
1.2
97
0.2
0.2
0.1
0.1
0
0
1
2
3
4
5
0
B/T Fig. 7. Plots of growth exponent, b, and local growth exponent, bloc, against B for the iron films electrodeposited at 10 mA cm2.
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H. Matsushima et al. / Journal of Electroanalytical Chemistry 587 (2006) 93–98
to be the enhancement of the ionic mass transfer caused by MHD convection. The anomalous scaling analysis is a good technique to quantitatively describe one of magnetic field effects on the surface morphology of electrodeposits.
10 3
lc / nm
Acknowledgments
10 2 0
1
2
3
4
5
This study was partly supported by 21st COE Program (Establishment of COE on Sustainable-Energy System) and the Ministry of Education, Science and Culture (Grant-in-Aid for Exploration Research No. 15360402), for which the authors are granted. H. Matsushima expresses his gratitude for Alexander von Humboldt Foundation in Germany.
B/T Fig. 8. Plots of critical length, lc, against B for the iron films electrodeposited with the passage of 5 C cm2 at 10 mA cm2.
size of precipitates, because lc is the critical length scale over which the roughness levels are cut off. The figure evidently demonstrates that the value of lc is remarkably depressed by the magnetic field superimposition. The reduction of lc is explained by the morphological variations as shown in Fig. 1, where the shape of precipitates changes and the grain size decreases under the magnetic field. In the electrodeposition process, the competition between nucleation and growth process determines the granularity and roughness of the surface morphology as well as the crystalline microstructure. Anomalous scaling technique provides a good method to phenomenologically describe this process. MHD field further influences this competition especially for the iron deposits. That is, the concentration profiles of both H+ and Fe2+ ions are significantly changed, which determines the hydroxide generation and concentration overpotential [24–27]. It may result in the transition of growth mode of electrodeposited iron film. 5. Conclusions The evolution of the surface morphology of iron thin films electrodeposited in a magnetic field (0–5 T) was investigated by applying the anomalous scaling analysis for AFM images. The superimposition of a magnetic field introduced (1) a significant alignment of precipitates as well as (2) a smooth surface roughness due to smaller precipitates. The former may be understood from the transition of electrocrystallization mechanism probably caused by the surface pH value in such a magnetic field gradient. The anomalous scaling is introduced to quantitatively analyze the surface morphology evolution phenomena. The roughness exponent, a, decreased from 1.1 to 0.35 as B increased. The growth exponent, b, slightly decreased from 0.31 to 0.27 by the magnetic field superimposition. The variation of the scaling factors might be attributed
References [1] T. Osaka, Electrochim. Acta 45 (2000) 3311. [2] W. Schwarzacher, D.S. Lashmore, IEEE Trans. Magn. 32 (1996) 3133. [3] G. Palasantzas, J.T.D. Hosson, J. Barnas, Surf. Sci. 507–510 (2002) 541. [4] M. Uhlemann, A. Gebert, M. Herrich, A. Krause, A. Cziraki, L. Schultz, Electrochim. Acta 48 (2003) 3005. [5] T.Z. Fahidy, Prog. Surf. Sci. 68 (2001) 155. [6] O. Devos, A. Olivier, J.P. Chopart, O. Aaboubi, G. Maurin, J. Electrochem. Soc. 145 (1998) 401. [7] H. Matsushima, T. Nohira, Y. Ito, Electrochem. Solid State Lett. 7 (2004) C81. [8] H. Matsushima, T. Nohira, Y. Ito, J. Solid State Electrochem. 8 (2004) 195. [9] H. Matsushima, T. Nohira, I. Mogi, Y. Ito, Surf. Coat. Tech. 179 (2004) 245. [10] A. Chiba, T. Ogawa, T. Yamashita, Surf. Coat. Tech. 34 (1998) 455. [11] A. Chiba, K. Kitamura, T. Ogawa, Surf. Coat. Tech. 27 (1986) 83. [12] F. Family, T. Vicsek, J. Phys. A 18 (1985) L75. [13] A. Wu, D.P. Barkey, J. Electrochem. Soc. 150 (2003) C553. [14] T.Y.B. Leung, M. Kang, B.F. Corry, A.A. Gewirth, J. Electrochem. Soc. 147 (2000) 3326. [15] L. Vazquez, R.C. Salvarezza, A.J. Arvia, Phys. Rev. Lett. 79 (1997) 709. [16] A. Iwamoto, T. Yoshinobu, H. Iwasaki, Phys. Rev. Lett. 72 (1994) 4025. [17] W.U. Schmidt, R.C. Alkire, A.A. Gewirth, J. Electrochem. Soc. 143 (1996) 3122. [18] S. Huo, W. Schwarzacher, Phys. Rev. Lett. 86 (2001) 256. [19] R. Cecchini, J.J. Mallett, W. Schwarzacher, Electrochem. Solid State Lett. 6 (2003) C103. [20] D.G. Foster, Y. Shapir, J. Jorne, J. Electrochem. Soc. 150 (2003) C375. [21] M. Saitou, W. Oshikawa, M. Mori, A. Makabe, J. Electrochem. Soc. 148 (2001) C780. [22] A. Kurowski, J.W. Schultze, G. Staikov, Electrochem. Commun. 4 (2002) 565. [23] M. Castro, R. Cuerno, A. Sanchez, F. Dominguez-Adame, Phys. Rev. E 62 (2000) 161. [24] Y. Fukunaka, H. Doi, Y. Kondo, J. Electrochem. Soc. 137 (1990) 88. [25] A. Bund, S. Koehler, H.H. Kuehnlein, W. Plieth, Electrochim. Acta 49 (2003) 147. [26] A. Bund, A. Ispas, J. Electroanal. Chem. 575 (2005) 221. [27] C.O. Reilly, G. Hinds, J.M.D. Coey, J. Electrochem. Soc. 148 (2001) C674.
Electroanalytical Chemistry Journal of Electroanalytical Chemistry 587 (2006) 93–98 www.elsevier.com/locate/jelechem
Anomalous scaling of iron thin film electrodeposited in a magnetic field H. Matsushima a, Y. Fukunaka a b
b,*
, Y. Ito b, A. Bund a, W. Plieth
a
Institute of Physical Chemistry and Electrochemistry, Dresden University of Technology, Mommsenstrasse 13, D-01062 Dresden, Germany Graduate School of Energy Science, Department of Energy Science and Technology, Kyoto University, Sakyo-ku, Kyoto 606-8501, Japan Received 4 February 2005; received in revised form 5 September 2005; accepted 16 October 2005 Available online 5 December 2005
Abstract Iron thin films were electrodeposited on a copper substrate in FeSO4 aqueous solution under a magnetic field (0–5 T) at 298 K. The surface morphology was observed by the atomic force microscopy (AFM). It was drastically changed from an angular to a wavy shape by superimposing the magnetic field. Moreover, rectangular shaped precipitates were aligned along the magnetic field. The grain size decreased with increasing in magnetic field intensity, B. The AFM image was characterized by the anomalous scaling method in order to quantitatively analyze the magnetic field effect on surface roughness. The roughness exponent, a, and the growth exponent, b, decreased as B increased. The variation of scaling parameters with B may be utilized to improve the surface morphology evolution and the transition of the crystal growth induced by the magnetohydrodynamic convection can be phenomenologically discussed. 2005 Elsevier B.V. All rights reserved. Keywords: Magnetic field; MHD; Iron electrodeposition; AFM; Scaling; Surface morphology
1. Introduction Electrodeposition process is frequently playing an important role in the microelectronics film formation technology as seen in Damasciene process developed by IBM. Electrochemical processing can be principally applied to induce the giant magnetoresistance (GMR) effect by alternatively depositing nonmagnetic and magnetic thin film layers of only some nanometer thickness [1,2]. However, it is not yet widely employed for the preparation of magnetic multilayers, because the electrochemically grown multilayers do not exhibit so high performance as by plasma processing. Palasantzas et al. [3] reported that the roughness on thin film surfaces/interfaces causes the poor performance induced by the physical characteristics such as magnetic and electronic transport properties. There is unfortunately a considerable lack of understanding how to control the microscopic growth process of electrocrystallization in comparison with the film technology based on the vacuum pro*
Corresponding author. Tel.: +81 75 753 5415; fax: +81 75 753 4719. E-mail address: [email protected] (Y. Fukunaka).
0022-0728/$ - see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.jelechem.2005.10.025
cessing. The shape evolution analysis may provide a good start to compare the microscopic growth process in electrolytic processing with that in vacuum processing. The present paper starts to discuss the scaling analysis on the electrodeposited Fe film, in order to further develop the advanced electrochemical processing in film formation technology. Superimposing an external magnetic field offers many possibilities to influence the electrodeposition process and thus to control the microstructure of the thin film interface [4–6]. Our previous papers [7,8] described the morphology of electrodeposited iron film strongly depended on both the magnetic field intensity and the direction. Furthermore, it was found that the texture evolution was controlled by a magnetic field [9]. That is, biaxial texture structure evolved in the presence of magnetic field while uniaxial texture was formed without such a magnetic field. The present paper focuses the effect of magnetic field on the surface morphological variations by applying the scaling analysis technique. 2. Experimental The electrodeposition apparatus has been already described as well as the experimental procedure in our
94
H. Matsushima et al. / Journal of Electroanalytical Chemistry 587 (2006) 93–98
previous paper [7]. Thus, only several important points are mentioned here. The cathode was made of a sheet of copper (10 · 10 · 0.2 mm, Cu 99.99%, Nilaco Corp.). The anode was a sheet of pure iron (10 · 10 · 0.2 mm, Fe 99.99%, Nilaco Corp.). The polycrystalline copper substrate was mechanically polished by an emery paper and buffed with linen cloth containing alumina suspension (0.3 lm). Then, it was electropolished in 70-wt% phosphoric acid solution for an hour at the terminal voltage of 1.0 V before supplying it to the electrodeposition. An electrolyte was FeSO4 (0.9 mol L1) aqueous solution. The value of pH was adjusted to 1.5 with H2SO4 solution. The electrolyte temperature was maintained at 298 K. Iron electrodeposition was galvanostatically conducted until the amount of the electrical charge reached 5– 100 C cm2. A uniform magnetic field was superimposed parallel to the electrode planes. The magnetic field was generated by a helium free superconducting magnet (HF5-100VHF, Sumitomo Heavy Industries). The surface morphology was observed by AFM (SPI 3800, Seiko Instruments). The AFM images were acquired with a contact mode. The image scans were taken with a resolution of 512 · 512 pixels. 3. Results Galvanostatic electrodeposition was conducted at 10 mA cm2. Iron film was electrodeposited in the magnetic field intensities, B = 0, 0.5, 1, 3, and 5 T, respectively. AFM images of the surface morphology obtained at various magnetic fluxes are illustrated in Fig. 1(a)–(e). The amount of electricity was kept at 5 C cm2. The film thickness was estimated to be 800 nm based on the measured iron current efficiency of about 60%. Fig. 1(a) (B = 0 T) illustrates the surface morphology consisted of angular iron grains with the size of about 100 nm. They are randomly precipitated on the substrate, although the image (a) shows several small areas left from the nucleation because of preferential H2 gas evolution. The average surface roughness was measured to be about 60 nm. As the time proceeded, the surface roughness appeared to become significant. Comparing the surface morphology electrodeposited under a conventional electrochemical deposition condition (B = 0 T), the superposition of magnetic field introduces another degree of freedom to the heterogeneous surface reaction field to induce the drastic differences in surface morphology. A striking morphological variation appears Fig. 1(b). The superimposition of 0.5 T introduces a morphology which rectangular precipitates with about 100 nm long lateral faces are considerably aligned along a direction. That is, the bottom shape of each precipitate was rectangular where all the long lateral faces were arranged uniquely in a magnetic field direction. Much smaller precipitates appear on the surface of lateral plane. The alignment direction should be controllable. With further increased B, the rectangular shape starts to change to a roundish shape. The images shown in
Fig. 1(b)–(e) consisted of wavy grains. The individual grains appeared to become smaller and more roundish as B increased. The surface morphology became smoother. The reduction of grains size by B has been also reported in other metal electrodeposition like copper [10] and nickel [11]. 4. Discussion Fig. 1 clearly illustrates that the superimposition of magnetic field drives the alignment of rectangular precipitates along the magnetic flux field. This is the unique characteristic caused by the superimposition of magnetic field to electrodeposited iron film morphology. Unfortunately, the prediction on this magnetic field alignment is far behind the quantitative discussion at the present moment. Therefore, another aspect of smooth surface morphology caused by magnetic field is now focused. 4.1. Anomalous scaling theory The surface microstructure must be quantitatively described in order to understand the magnetic field effects on the electrodeposition process. The scaling analysis of surface evolution has been usually studied through the dynamic scaling theory, Family–Vicsek model [12]. The analysis is based on the surface width, W(l, t), known as the root mean square height of the surface which is defined as follows: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 W ðl; tÞ ¼ hðh hhiÞ i; ð1Þ where h, l and t are the surface height, the size of measured region and the deposition time, respectively. The averaged surface width is fitted to a normal scaling relation t W ðl; tÞ ¼ la f a=b ; ð2Þ l where a and b are defined as the roughness and growth exponent, respectively. The scaling function f(x) is constant for x 1, and varies as xb for x 1. The normal scaling has been employed to study the effect of additives on quasi-two dimensional growth of the nucleation [13– 17]. The fitted values are compared with the predictions of theoretical models to assess the surface growth mechanism. Schwarzacher et al. [18,19], on the other hand, proposed a different kind of anomalous dynamic scaling. They introduced W(l, t) having a power law dependence on t even for small l. Anomalous scaling is thus represented by the following expression [19]: t W ðl; tÞ ¼ lH tbloc f z ; ð3Þ l where H is the Hurst exponent, and z (=H/b) is the dynamic exponent.
H. Matsushima et al. / Journal of Electroanalytical Chemistry 587 (2006) 93–98
95
Fig. 1. AFM images of the iron films electrodeposited from FeSO4 solution with the passage of 5 C cm2 at 10 mA cm2 in the magnetic fields of (a) 0 T, (b) 0.5 T, (c) 1 T, (d) 3 T and (e) 5 T.
For a given value of t, the crossover between these two scaling regimes occurs at l = lc, where lc is the critical scaling length. Hence, Eq. (3) is ( lH tbloc for l < lc W ðl; tÞ / ð4Þ tbþbloc for l > lc For a given t, the roughness increased as lH and then saturated at a value that is proportional to lac . Moreover, the roughness exponent, a, is expressed as follows: a ¼ H ð1 þ bloc =bÞ.
ð5Þ
4.2. Parameter determination A quantitative methodology for surface analysis is provided by a scaling method of electrodeposited iron film surface. W(l, t) were measured at several times in the magnetic field of 0 and 5 T. They are illustrated in Figs 2 and 3, respectively. Log W increased linearly with log l for small l, and saturated for large l, which was consistent with Eq. (4) independently of a magnetic field. In order to calculate the Hurst exponent, H (the gradient of the plot for small l), saturated width, Wsat (the value of W for large l) and critical scaling length, lc (the crossover between the two
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Wloc(t) / nm
W(l , t) / nm
102
100 C cm-2
10 50 C cm-2
0T 0.5 T 1T 3T 5T
10
10 C cm-2 5 C cm-2
1
10 2
10
10 3
1
10 4
10 3
l / nm Fig. 2. Surface width, W(l, t), of the iron films measured over regions of size l at several times in no magnetic field (d: 5 C cm2, j: 10 C cm2, m: 50 C cm2, ·: 100 C cm2).
W(l , t) / nm
100 C cm-2 50 C cm-2 10 C cm-2 5 C cm-2
1 10
Fig. 4. Local surface width, Wloc(t), for iron films electrodeposited at different deposition time, t, with and without B (d: 0 T, n: 0.5 T, j: 1 T, e: 3 T, .: 5 T, scaling length l = 100 nm).
(50 C cm2) to 1.0 · 104 s (100 C cm2). The relationship between Wloc(t) and t could be expressed by a liner equation whose gradient is equivalent to bloc as shown in Eq. (4) (at l < lc). Fig. 5 shows the saturated surface width, Wsat(t), at the scale size l = 104 nm as the function of t. Similarly to Fig. 4, a good liner dependence between Wsat(t) and t is demonstrated. The gradient of the fitted line is equal to b + bloc as shown in Eq. (4) (at l > lc). The parameter of growth exponent, b, is calculated by subtracting bloc from the gradient value in Fig. 5.
10 2
10
10 4
t/s
10 2
10 3
4.3. Effect of magnetic field on scaling factors
10 4
l / nm Fig. 3. Surface width, W(l, t), of the iron films measured over regions of size l at several times in a magnetic field of 5 T (d: 5 C cm2, j: 10 C cm2, m: 50 C cm2, ·: 100 C cm2).
In order to investigate the magnetic field effect on scaling factors, the dependences of scaling parameters on B are summarized. Fig. 6 is a plot of roughness exponent, a, vs. B for the iron-electrodeposited film. The error bar
regimes), the following function was used to fit the data [19]:
0T 0.5 T 1T
ð6Þ
It is clearly seen that measured data can be described more reasonably by Eq. (6). H was found to be constant for all electrodeposition times. It remarkably decreases by the magnetic field. For example, it is 0.45 for 0 T and 0.16 for 5 T. Figs. 2 and 3 demonstrate a characteristic of anomalous scaling in which the persistent time increases of the roughness even for small scales (1st line in Eq. (4)). In order to obtain the local growth exponent, bloc, the local surface width, Wloc(t), was measured at a scale size well below the critical length. Fig. 4 shows the Wloc(t) for the iron films electrodeposited as the function of deposition time, t, under B. In the present case, the scale size was fixed at 102 nm and the electrodeposition time was varied from 5.0 · 102 s (5 C cm2), 1.0 · 103 s (10 C cm2), 5.0 · 103 s
3T 5T
Wsat( t) / nm
W ðlÞ ¼ W sat f1 exp½ðl=lc ÞH .
10 2
10
1
10 3
10 4
t/s Fig. 5. Saturated surface width, Wsat(l,t), for iron films electrodeposited at different deposition time, t, with and without B (d: 0 T, n: 0.5 T, j: 1 T, e: 3 T, .: 5 T, scaling length l > lc).
H. Matsushima et al. / Journal of Electroanalytical Chemistry 587 (2006) 93–98
α
0.8 0.6 0.4 0.2 0 0
1
2
3
4
5
B/T Fig. 6. Plots of the roughness exponent, a, against B for the iron films electrodeposited on copper substrate.
indicates the standard deviation of a for each iron film prepared at different deposition time. Metals electrodeposited onto a foreign substrate surfaces in the additive free solutions typically exhibit a value between 0.7 and 1.0, for example, Cu = 0.8–0.9 [17,19], Ag = 0.7 [20], Ni = 0.9 [21] and NiP = 1.0 [22]. The present value of a = 0.35–1.1 is in the range of these parameters. It is interesting to know that the anomalous scaling can be applied to analyze the surface evolution phenomena even for the iron film, although the superimposition of magnetic field introduces another complexity like grain shape variation in iron electrodeposition mechanism. Many theoretical studies have modeled the various growth processes and quantitatively calculated the surface texture evolution phenomena. According to their papers, a is an important factor to clarify the shape evolution mode combining the surface diffusion and the step growth mechanism [17]. The effect of additives to the surface morphology of electrodeposited film has been focused. The model considers that the adsorbed additives on substrate may hinder the surface diffusion of atoms to introduce a smoother surface. The numerical simulation predicts a slower surface diffusion rate to result in smaller parameter of a. Fig. 6 clearly shows that the parameter of a considerably decreases from 1.1 in 0 T to 0.35 in 5 T. Comparing the present experimental results with the work by Illinois group [17], the superimposition of magnetic field introduces a phenomenologically similar effect of addition of additives, expect for the appearance of precipitates arranged in magnetic field direction demonstrated in Fig. 1(b)–(e). The shape evolution or surface roughness factor may be governed by the competition between the surface diffusion rate primarily determined by the electrochemical processing parameters like the current density and the step growth rate by the adsorbed additive. The enhanced ionic mass transfer rate by MHD convection significantly drives the surface diffusion of additives molecules as well as atom. This MHD convection essentially results in enhancing the
0.5
0.5
β loc
0.4 0.3
0.4 0.3
β
β loc
1.0
mass transfer rate of adsorbed additives to the step or kink site on the growing crystal. The growth mode changes from surface diffusion to step growth mode. The present experimental result suggests that the iron deposition mechanism might be significantly influenced by the alignment caused by the magnetic field as demonstrated in Fig. 1(b). Moreover, the surface pH may be different from the bulk electrolyte under MHD condition to result in the transition of surface shape evolution mode. The deviation of surface pH value may introduce a drastic change of electrocrystallization mechanism. Furthermore, the effect of localized magnetic field gradient may result in a unique crystallographic orientation, because iron metal is a very significant magnetic susceptibility. These aspects must be further examined especially to emphasize the pH value on the cathode surface combining MHD convection. The relationship between growth exponent, b, and local growth exponent, bloc, vs. B for the iron film is demonstrated in Fig. 7. The typical value of b for the metal electrodeposits without additives has been reported to be around 0.25, which agrees well with the present value. In this experiments, b slightly decreases from 0.31 to 0.27 with increasing in the magnetic flux density. It suggests that the surface morphology obtained in the magnetic field does not roughen as quickly as that in no magnetic field. That is, the rate of roughening is surely depressed by superimposing the magnetic field. On the other hand, bloc linearly decreases from 0.44 in 0 T to 0.29 in 5 T. Castro et al. [23] reports that more compact films are produced for larger electric field, resulting in anomalous scaling properties being replaced by Family– Vicsek scaling [12]. As well as our experiments, the film surface looks compact for larger B and the anomalous scaling may disappear. This may be related to the observation that roughening rate is slower for larger B values. Fig. 8 shows a plot of the critical length, lc, vs. B for the iron film deposited through the charge passage of 5 C cm2. A variation of lc means a change in the lateral
β
1.2
97
0.2
0.2
0.1
0.1
0
0
1
2
3
4
5
0
B/T Fig. 7. Plots of growth exponent, b, and local growth exponent, bloc, against B for the iron films electrodeposited at 10 mA cm2.
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to be the enhancement of the ionic mass transfer caused by MHD convection. The anomalous scaling analysis is a good technique to quantitatively describe one of magnetic field effects on the surface morphology of electrodeposits.
10 3
lc / nm
Acknowledgments
10 2 0
1
2
3
4
5
This study was partly supported by 21st COE Program (Establishment of COE on Sustainable-Energy System) and the Ministry of Education, Science and Culture (Grant-in-Aid for Exploration Research No. 15360402), for which the authors are granted. H. Matsushima expresses his gratitude for Alexander von Humboldt Foundation in Germany.
B/T Fig. 8. Plots of critical length, lc, against B for the iron films electrodeposited with the passage of 5 C cm2 at 10 mA cm2.
size of precipitates, because lc is the critical length scale over which the roughness levels are cut off. The figure evidently demonstrates that the value of lc is remarkably depressed by the magnetic field superimposition. The reduction of lc is explained by the morphological variations as shown in Fig. 1, where the shape of precipitates changes and the grain size decreases under the magnetic field. In the electrodeposition process, the competition between nucleation and growth process determines the granularity and roughness of the surface morphology as well as the crystalline microstructure. Anomalous scaling technique provides a good method to phenomenologically describe this process. MHD field further influences this competition especially for the iron deposits. That is, the concentration profiles of both H+ and Fe2+ ions are significantly changed, which determines the hydroxide generation and concentration overpotential [24–27]. It may result in the transition of growth mode of electrodeposited iron film. 5. Conclusions The evolution of the surface morphology of iron thin films electrodeposited in a magnetic field (0–5 T) was investigated by applying the anomalous scaling analysis for AFM images. The superimposition of a magnetic field introduced (1) a significant alignment of precipitates as well as (2) a smooth surface roughness due to smaller precipitates. The former may be understood from the transition of electrocrystallization mechanism probably caused by the surface pH value in such a magnetic field gradient. The anomalous scaling is introduced to quantitatively analyze the surface morphology evolution phenomena. The roughness exponent, a, decreased from 1.1 to 0.35 as B increased. The growth exponent, b, slightly decreased from 0.31 to 0.27 by the magnetic field superimposition. The variation of the scaling factors might be attributed
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