Initial stages of electrodeposition of metal nanowires in nanoporous templates

Electrochimica Acta 53 (2007) 205–212

Initial stages of electrodeposition of metal nanowires in nanoporous templates M. Motoyama a , Y. Fukunaka a,∗ , T. Sakka b , Y.H. Ogata b a

Department of Energy Science and Technology, Kyoto University, Yoshida-honmachi, Sakyo, Kyoto 606-8501, Japan b Institute of Advanced Energy, Kyoto University, Uji, Kyoto 611-0011, Japan Received 28 June 2006; received in revised form 24 April 2007; accepted 25 April 2007 Available online 10 May 2007

Abstract This paper describes the initial stages of electrochemical growth of Cu and Ni nanowires in polycarbonate (PC) track-etched membranes as the template. The diameters of the wires ranged from 50 to 200 nm. A thin Pt–Pd layer (∼30 nm thick) was sputter-deposited onto one side of the membrane and used as the cathode. The layer was not thick enough to seal the pore mouths. Cathodic current in the early stages of both Cu and Ni electrodeposition abruptly decreased after a period proportional to the pore diameter. Growing Cu grains plugged the pore openings causing the current to decrease, while the Ni deposition initially yielded a hollow tube in each pore resulting in a nanostructure transition of the tube to the wire at the growth front and a decrease in the current. © 2007 Elsevier Ltd. All rights reserved. Keywords: Cu; Ni; Electrodeposition; Nanowire; Nanotube; Nanoporous template

Electrochemical processing with using nanoporous templates allows us to prepare metallic nanowire arrays with various controlled dimensions [1–5]. The ability to control the composition along the length of the nanowire is an important feature of the electrochemical method [6,7]. Understanding of the coupling between ionic mass transport phenomena and morphological variation within nanoscopic pores is indispensable to allow a more quantitative control of nanoscale materials formed by the electrochemical method. Especially, the control of nucleation and growth is expected to be widely applicable to the advanced designs and thus necessary [8–12]. Solution phase synthesis of nanoparticles is one example pointing out the importance of the above respect [8–10]. Growth model for electrochemical nucleation and growth were initially developed in the 1980s. Scharifker and Hills proposed the models for a diffusion-limited process, based on analysis of the current transient characteristic in the early stages of electrodeposition [13]. However, the literature reported the results significantly deviating the predictions of the models [14,15], hence the experimental understanding is still important. Furthermore, the models have been developed to

∗

Corresponding author. Tel.: +81 75 753 5415; fax: +81 75 753 4719. E-mail address: [email protected] (Y. Fukunaka).

0013-4686/$ – see front matter © 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.electacta.2007.04.122

understand the nucleation and growth in a semi-infinite space, but it is not applicable to complex structures with small length scales, such as nanoscopic channels [16–19]. A more detailed understanding of nucleation and growth during electrodeposition into nanoscopic pores is critical for designing deposition process for obtaining desired nanostructures. In this paper we report on the initial stages of electrochemical growth of Cu and Ni nanowires. The electrochemical deposition begins at a sputter-deposited Pt–Pd layer (∼30 nm thick) as the cathode on a polycarbonate (PC) membrane template. The present sputtering method entails opening the pore mouths due to much smaller size of the sputtered Pt–Pd particles than the mouth diameter [20]. These pore openings can allow us to electroplate a hollow tube in each pore. Indeed, however, the deposition process of metal only along the pore walls is not sufficiently controlled [21–24] relative to an electroless plating method [19,25]. This study has been conducted with the aim of understanding the electrochemical growth mechanism within nanoscopic pores. Here we show the difference of the initially formed structures between Cu and Ni electrodeposition into the PC membrane template. The stability of the Cu nanotube growth is lost immediately after the beginning of the electrodeposition, while the Ni nanotube growth lasts for longer deposition times. The importance of the deposited grain size will be discussed.

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Fig. 2. Cathodic current transients during Cu and Ni electrodeposition into the PC membrane template with the pores of 200 nm in diameter. The Stages I–IV in this figure are expressed for the Cu deposition. Fig. 1. SEM images of the sputter-deposited Pt–Pd layer on the PC membrane template with the pores of 200 nm in diameter. Scale bar: 1.0 ␮m. (Top) The sputtered side. (Bottom) The Pt–Pd nanotubes liberated from the PC membrane.

1. Experimental Two kinds of electrolyte compositions for Cu and Ni electrodeposition were adjusted as 0.60 mol L−1 CuSO4 , 5 × 10−3 mol L−1 H2 SO4 (pH 1.7) and 1.0 mol L−1 NiSO4 , 0.19 mol L−1 NiCl2 , and 0.62 mol L−1 H3 BO3 (pH 3.4), respectively. The pore diameters of the PC membrane templates were 50, 80 (Nomura Micro Science Co. Ltd.), 100, and 200 nm (Toyo Roshi Kaisha Ltd.). Ion sputter coating of Pt–Pd (Hitachi, E1030) was conducted onto one side of the template to prepare the cathode substrate. The deposited Pt–Pd cathode thickness was roughly 30 nm according to the company’s operational data. Fig. 1(top) shows the Pt–Pd surface on the template membrane with the pores of 200 nm in diameter. It is clearly seen that the pores are not sealed and the original diameter is maintained. This sputtering method entails coating the pore walls near the openings with a thin Pt–Pd layer. The membrane can be dissolved away with a dichloromethane solution, and the liberated Pt–Pd tubes as the cathode are imaged via electron microscopy [see Fig. 1(bottom)]. The height of the nanotubes is roughly 300–500 nm. A conventional three-electrode type cell was employed as used in the previous papers [20,26]. Potentiostatic electrodeposition into the PC templates was carried out in a circular area of 2.0 mm in diameter restricted by silicon rubber insulator. Cu and Ni wires were used as the conventional reference electrodes for Cu and Ni electrodeposition, respectively. Electrode potential, E, is measured against each reference electrode. The template membrane was placed on a platinum sheet as the current collector such that the membrane face with the Pt–Pd layer was down to the collector, and they were pressed to keep a tight contact. 2. Results and discussion Current–time, I–t, transient for electrodeposition of the nanowire arrays in the PC template is divided into four stages

[20,26]. Fig. 2 shows the cathodic current transient during Cu electrodeposition into the PC template with the pores of 200 nm in diameter at E = −0.4 V versus a Cu quasi-reference electrode. The cathodic current drops from 1.2 to 0.25 mA before t = 20 s. We define this period as Stage I. The subsequent stage, Stage II, then extends to about t = 260 s with progress of the Cu electrodeposition process along the length of the pores. A profile of the I–t curve in Stage II is responsible for a pore-size distribution along the length. A cigar-shaped profile characterized by a heavy ion irradiation technique was already described in the previous work [26]. Then, the cathodic current increases to 1 mA at t = 380 s because the effective electrode surface area enlarges with progress of the electrodeposited Cu nanowires emerging from the pores in the lateral direction on the PC membrane surface (Stage III). Finally, an electrodeposited Cu film outside the top surface of the membrane template is further developed in a free electrolyte volume in Stage IV. Cathodic current transient for electrodeposition of Ni nanowires can be also characterized by the four stages [26]. Fig. 2 shows the current transient for the Ni deposition at E = −1.0 V versus a Ni quasi-reference electrode. 2.1. Cu electrodeposition Fig. 3(left) shows the cathodic current transients for electrodeposition of the Cu nanowires with different diameters. Each deposition process was interrupted at t = 1 to 5 s in order to prepare the specimens for SEM observation. In all cases the cathodic current rapidly increases to 1.3–1.5 mA immediately after t = 0 s, and thereafter decreases abruptly. The interruption times were determined by appearance of the above abrupt decrease in the current. The cathodic current starts to decrease earlier as the pore diameter decreases. Fig. 3 apparently resembles a typical current transient behavior associated with nucleation and growth process for potentiostatic electrodeposition [11–15,27–31]. Cathodic current transient in the early stages of potentiostatic electrodeposition is often normalized by the current maximum, Im , and the deposition time at which the instant current maximum, tm , is recorded. According to Scharifker and Hills [13], three-dimensional (3D) diffusion zones numerously formed sur-

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Fig. 3. (Left) Cathodic current transients during the Cu electrodeposition into the PC membrane templates with the pores of a: 50 nm, b: 80 nm, c: 100 nm, and d: 200 nm in diameters. (Right) SEM images of the electrodeposited Cu grains on the sputtered Pt–Pd layer. Scale bar: 200 nm.

rounding the nuclei start to interact to form a planar (2D) diffusion zone parallel to the substrate, and the Im is recorded in the early stages corresponding to a transition from the 3D to the 2D diffusion transport. Cu clusters are nucleated uniformly on the Pt–Pd surface including the edge of the pores (see Fig. 4). The 3D diffusion zones formed surrounding the Cu nuclei prevail into the pores. The transient diffusion field will develop along the pore length

Fig. 4. Schematic illustration of diffusion zones surrounding Cu nuclei prevailing into the pores. The upper direction is the growth direction of the nanowires.

as the several 3D diffusion zones in the internal space of the pores start to interact to turn to the 2D field. A longer deposition time should be consumed for the formation of the 2D diffusion zone in each pore with a larger diameter. The above speculation apparently looks sound. The deposition times at which the instant current maximums were recorded, tm , in Fig. 3 ranged from 1 to 3 s. However, these measured periods are too long to quantitatively support the above speculation for analyzing the relationship between the Im and the tm recorded in the present experiments. That is because the √ Nernst diffusion layer thickness, πDt, reaches to 50–200 nm within deposition times of 2–30 ␮s for diffusivity of Cu2+ ions, D = 5 × 10−6 cm−2 s−1 [32]. Another reason must explain the current transient behavior in Stage I. Fig. 3(right) shows SEM images of the Pt–Pd side observed after the Cu deposition with the current transients shown in Fig. 3(left). The present electrolytic cell design forms a narrow gap between the membrane face with the Pt–Pd layer and the Pt sheet. The electrolyte solution permeate the template membrane resulting in leakage of the electrolyte to the gap, and thereby electric field lines penetrate through the pore openings at the bottom to reach the Pt–Pd surface. Thus, the Cu deposition occurs on the Pt–Pd layer and even on the Pt sheet. With the pores of 50 nm in diameter, numerous Cu particles smaller than 100 nm are deposited (Fig. 3(right) (a)). A particle density of 4 × 109 cm−2 is measured from the SEM image. The Cu particles agglomerate or coalesce along with the progress of the electrodeposition, but more than a half of the Pt–Pd surface still remains uncovered with Cu grains.

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The larger pore size requires a longer deposition time to cause the current to start to decrease abruptly. The Cu grains reach the sizes of 50 to 200 nm. The bare Pt–Pd surface is partially seen, and the pores are not covered perfectly. There is no observable morphological difference between (b): 80 nm and (c): 100 nm. With the pores of (d): 200 nm, the electrodeposited Cu gains cover all over the Pt–Pd surface. Almost all the grains are larger than 100 nm. Several dark valleys or deep caldera left among the Cu particles are created due to the pore openings, although they are completely covered with the Cu grains. Averaged sizes of the Cu grains are approximately 50, 80, 80, and 150 nm corresponding to the SEM images of (a), (b), (c), and (d), respectively. The comparison between Fig. 3(left) and (right) suggests that the abrupt decrease in the cathodic current is associated with the plugging process of the pore openings with the Cu grains. That is, the cathodic current starts to decrease once the size of the Cu grains reaches to the pore mouth diameter. Thus, the observed tm is not explained by the diffusion-limited growth as described above, but corresponds to a moment at which the pore opening is plugged with the growing grains occluding current path to the Pt–Pd layer as well as to the Pt sheet (see Fig. 5). The Cu electrodeposition takes place on the Pt–Pd surface and the Pt sheet, but it does only inside the pores once the pore mouths are covered up with the Cu grains. That induces the abrupt decrease in the cathodic current in Stage I. An amount of electricity consumed by the above grain growth process is estimated by the following Avrami equation [33].     Vex 2 2 f = 1 − exp − = 1 − exp − πNr (1) V0 3 where f is fractional of transformation, Vex is extended volume of nuclei, V0 [=1 (cm2 ) × r] is an entire volume to be transformed, N is the nucleus density, and r is the nucleus radius. The hemispherical nuclei are assumed in Eq. (1). It is questionable if the above equation can be applied to the Pt–Pd surface with a number of the pores. However, these pores occupy a fractional area less than 0.09. Such a small fractional number may make possible a first-order approximation that the Pt–Pd surface is assumed as the uniform surface for the above calculation. A limited number

Fig. 5. Schematic illustration of the pore opening plugged with Cu grains.

Table 1 Comparison between the calculated amount of electricity, Qc , and the measured amount of electricity, Qm 2r (nm)

Qc (C cm−2 )

Qm (C cm−2 )

50 80 100 200

3.4 × 10−3 1.4 × 10−2 2.6 × 10−2 1.5 × 10−1

(a) 1.3 × 10−2 (b) 5.5 × 10−2 (c) 5.6 × 10−2 (d) 1.6 × 10−1

Hemispherical nuclei with a diameter of 2r and the nucleus density of N = 4 × 109 cm−2 are assumed.

of the nuclei may be introduced around the edge of the pores, but such contribution is neglected here. The calculated amount of electricity, Qc , and 2r are listed in Table 1. The right end column shows the amount of electricity, Qm , recorded by the time when the cathodic current starts to abruptly decrease in Fig. 3(left). Such deposition times of (a) to (d) correspond to 0.3, 1.3, 1.3, and 3.0 s, respectively. The Qc agrees with the Qm with the pores of 200 nm. However, the smaller the pore diameter, the larger the deviation of the Qc from the Qm . An extra amount of Cu, which is not taken into account for the calculation, was deposited on the Pt sheet, and the Qm is suspected to become less constant with the smaller pores. These situations support that Table 1 reasonably provides the presumption that the abrupt decrease in the current is induced as the growing grains start to cover up the pores at the bottom. 2.2. Ni electrodeposition Fig. 6(left) shows the cathodic current transients for the electrodeposition of the Ni nanowires with different diameters. After the cathodic current quickly increases after starting the electrodeposition, it shows about 1.5 mA with a slower decrease over a certain period proportional to the pore diameter. Then, a large decrease in the current is measured abruptly. The period of time to keep the slower decrease in the current is longer as the pore diameter increases. Those current transient behaviors are similar to the case of the Cu electrodeposition in the several respects. SEM images of the Pt–Pd side are shown in Fig. 6(right). The images of (a), (b), (c), and (d) correspond to morphologies of the Ni grains formed through the electrodeposition process of (a)–(d) in Fig. 6(left), respectively. The morphologies observed in these images are clearly different from those of the Cu deposition. The case of (a): 50 nm shows the abrupt decrease in the current at t = 3 s. The Ni deposition on the Pt–Pd surface uniformly and densely forms the 30–50-nm-sized grains to cover almost all the Pt–Pd area with a Ni thin film. In the cases of the larger diameters: (b)–(d), the period of time to keep the slower decrease in the current is longer. The Ni film growth on the Pt–Pd side further progresses as observed in the images of (b)–(d). The individual grains are recognized at (a) t = 3 s, but the observable boundaries disappear over 10 s. Some cracks are introduced in the film by enlarging pits near the pores. The cracks are developed more deeply to connect with each other as the pore size increases. It is probably due to the residual stress generated in the Ni film covering the vicinity of the pores. The dense Ni mor-

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Fig. 6. (Left) Cathodic current transients during the Ni electrodeposition into the PC membrane templates with the pores of a: 50 nm, b: 80 nm, c: 100 nm, and d: 200 nm in diameters. (Right) SEM images of the electrodeposited Ni grains on the sputtered Pt–Pd layer. Scale bar: 200 nm.

phology composed of the much finer grains contrasts with the coarser grains observed in the case of the Cu deposition. The cathodic current transient of (d): 200 nm in Fig. 6(left) is again shown in Fig. 7(left). It was interrupted at the end of Stage I at t = 32 s. The Ni films electrodeposited over three different deposition times, which are indicated by dotted line segments of a to c, were prepared for SEM observation. The SEM images of the Pt–Pd side are shown in Fig. 7(right). The image (b) in

Fig. 7 is exactly the same as Fig. 6(d). The pore mouth diameter decreases to about 100 nm at (a) t = 7 s. The progress of the Ni film growth makes the pores narrower after the deposition times of (b) 15 s and (c) 32 s. There is no essential difference between both morphologies except for the development of the cracks in (c). These images suggest that the deposition process to decrease the mouth diameter is limited and the residual stress generated near the pores is saturated with the development of the cracks.

Fig. 7. (Left) Cathodic current transient during the Ni electrodeposition into the PC membrane template with the pores of 200 nm in diameter. Dotted line segments of a to c correspond to t = 7, 15, and 32 s, respectively. (Right) SEM images of the electrodeposited Ni grains on the sputtered Pt–Pd layer. Scale bar: 200 nm.

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Fig. 9. Schematic illustration of the pore plugging at the growth front of a Ni hollow tube.

Fig. 8. SEM images of Ni nanostructures formed at the deposition times of (a)–(c) in Fig. 7. Scale bar: 200 nm.

While the Ni film grows on the Pt–Pd side, progress of the deposition also occurs in each pore. The resulting structure was observed after the template membrane was dissolved in dichloromethane (see Fig. 8). The images with the same alphabet: (a) to (c) in Figs. 7 and 8 were from the same specimen. Hollow tubes with wall thicknesses of 20–40 nm are clearly observed at (a) t = 7 s. This image indicates the proof of the deposition of nickel only along the pore walls from the edge of the Pt–Pd tubes as the cathode. The Ni tube walls become thicker gradually. The wall thickness shows roughly 50 nm at (b) t = 15 s. Finally, the top surface no longer shows a hollow cross-section at (c) t = 32 s. The abrupt decrease in the cathodic current is associated with the nanostructure transition from the tube to the wire occurring on its top. The current path through each pore to the Pt–Pd layer and the Pt sheet under the template is blocked at the top of the growing nanostructure (see Fig. 9), while the same situation occurs at the pore openings at the bottom in the case of the Cu deposition. The hollow cross-section formed in Stage I is not filled with nickel even after the Ni deposition yields the wires in Stage II. Fig. 10(top) shows the side views of the Ni nanostructures observed in Fig. 8(a)–(c). The height is plotted versus the deposition time in Fig. 10 (bottom). When a linear regression line is applied to the height variation with time, the slope and the intercept at t = 0 s are estimated as 0.030 ␮m s−1 and 0.46 ␮m, respectively. The slope is slightly smaller than the averaged growth rate of 0.043 ␮m s−1 , estimated from Fig. 2, over the

Fig. 10. (top) SEM images of the side views of the electrodeposited Ni nanostructures. (bottom) Variations of the height and the wall thickness of a nanotube as functions of time. Solid circle and blank circle indicate the height and the wall thickness, respectively.

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whole 10 ␮m-length. The intercept is close to the height of the Pt–Pd nanotubes presented in Fig. 1(bottom). This good agreement supported that the electrochemical deposition process of the nanotubes begins at the top of the Pt–Pd nanotubes. The observed wall thickness is also plotted versus time in Fig. 10(bottom). A linear time-dependence of the tube wall thickness is also obtained. The soundness of this linearity is supported by Fig. 6(left) where the induction time of the abrupt decrease in the cathodic current is proportional to the pore diameter. The tube wall thickness at t = 32 s is approximated as 100 nm. The slope and the intercept of the regression line of the tube wall thickness versus time are roughly 0.003 ␮m s−1 and 0.01 ␮m, respectively. The rate of the growth along the length is about 10 times faster than that of the tube wall thickening. As a result, a hollow Ni tube is obtained in each pore before the current starts to decrease abruptly. The maximum length of the Ni nanotubes with a 200 nm outer diameter was about 1 ␮m at pH 3.4 and E = −1.0 V. The electrochemical growth process of the Ni nanowires has been examined carefully. It is considerably different from that of the Cu nanowires. The key feature of the electrochemical deposition process of the Ni nanotubes is that the fineness of the Ni grains can form the nanotube walls in the early stages. Therefore, it is deduced that metallic nanotubes cannot be fabricated by electrodeposition if the growing grains readily become comparable to an employed pore size. Davis and Podlaha successfully produced Cu nanotubes with also the PC template having the pores partially covered with the sputter-deposited cathode layer [24]. The outer diameters and the tube wall thickness were reported as 800 and 200–300 nm, respectively. Their electrolyte composition is slightly different from ours, but it is expected that many coarser grains of 200 nm in size were deposited in the pores with a much larger diameter than ours. Thus, the above mechanism does not interfere with their results. The grain size relative to the pore size is therefore essential to designing the nanostructure formed in each pore. According to classification of metals by Winand [34,35], Cu and Ni are categorized into different groups i.e., intermediate metals with moderate melting points (Au, Cu, Ag) and inert metals with high melting points (Fe, Ni, Co, Pt, Cr, Mn), respectively. As the melting point is lower, smoothness of the film is more difficult to obtain due to high surface diffusion coefficient for adatoms. In general, the grain size is proportional directly to the linear growth rate of nuclei and inversely to the nucleation rate [36–38]. If the surface diffusion coefficient for adatoms is large enough, they diffuse to increase the island rather than form a new nucleus. Cluster coalescence phenomena such as Ostwald ripening and cluster migration also increase the grain size. An understanding of diffusion of adatoms or clusters on the cathode surface adjacent to the membrane walls, which may play a role similar to surfactant additives, as well as the growth kinetics of metal islands [39] can lead to control of the grain size. Interestingly, H2 evolution can sustain deposition of metal only on the pore walls [24,25]. Simulations are required to optimize a grain size distribution for desired structures, including contribution from ionic mass transfer accompanied with H2 evolution.

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A control of surface diffusion of adatoms or clusters at an interface of three phase of electrolyte/gas/metal or PC/electrolyte/metal is one of the ultimate aims in materials processing for nanostructured devices. Tailored interface promises a better performance of the devices and new applications. 3. Conclusions Cu and Ni nanowires were electrodeposited into the PC membrane templates containing the cylindrical pores with diameters of 50 to 200 nm. The sputter-deposited Pt–Pd layer as the cathode was so thin that the pores at the bottom were opened to pathways for the electrolyte. The abrupt decrease in the cathodic current in Stage I during the Cu deposition was correlated with the progress of the Cu grain growth with the careful observation. It was found that the cathodic current abruptly decreased when the pores on the Pt–Pd side are plugged with the coarse Cu grains, and the nanowires were then grown. On the other hand, a similar abrupt decrease in the Ni deposition current was associated with a nanostructure transition from the tube to the wire occurring at the growth front. The growth rate of the tubes along the length was one order faster than that for the wall thickening. The important combination of the nanoporous template with a size distribution of metal grains must be emphasized when the nanostructured interface is designed. Acknowledgments Part of this work was supported by financial aides from the 21st Century COE Program and the Ministry of Education, Science and Culture (Giant-in-Aid for Exploration Research No. 15360402), for which the authors are granted. References [1] C.R. Martin, Science 266 (1994) 1961. [2] C. Ji, P.C. Searson, Electrochem. Solid-State Lett. 81 (2002) 4437. [3] Y. Wu, G. Cheng, K. Katsov, S.W. Sides, J. Wang, J. Tang, G.H. Frederickson, M. Moskovits, G.D. Stucky, Nat. Mater. 3 (2004) 816. [4] L. Sun, Y. Hao, C.-L. Chien, P.C. Searson, IBM J. Res. Dev. 49 (2005) 79. [5] F. Li, J. He, W.L. Zhou, J.B. Wiley, J. Am. Chem. Soc. 125 (2003) 16166. [6] L. Piraux, J.M. George, J.F. Despres, C. Leroy, E. Ferain, R. Legras, K. Ounadjela, A. Fert, Appl. Phys. Lett. 65 (1994) 7. [7] C. Ji, G. Oskam, Y. Ding, J.D. Erlebacher, A.J. Wagner, P.C. Searson, J. Electrochem. Soc. 150 (2003) C520. [8] C.B. Murray, D.J. Norris, M.G. Bawendi, J. Am. Chem. Soc. 115 (1993) 8706. [9] X. Peng, M.C. Schlamp, A.V. Kadavanich, A.P. Alivisatos, J. Am. Chem. Soc. 119 (1997) 7019. [10] L. Manna, E.C. Scher, A.P. Alivisatos, J. Am. Chem. Soc. 122 (2000) 12700. [11] R.M. Penner, J. Phys. Chem. B 106 (2002) 3339. [12] M.J. Williamson, R.M. Tromp, P.M. Vereecken, R. Hull, F.M. Ross, Nat. Mater. 2 (2003) 532. [13] B. Scharifker, G. Hills, Electrochim. Acta 28 (1983) 879. [14] D. Grujicic, B.W. Sheldon, E. Chason, A.F. Bower, Appl. Phys. Lett. 81 (2002) 1204. [15] O.E. Kongstein, U. Bertocci, G.R. Stafford, J. Electrochem. Soc. 152 (2005) C116.

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