NANO LETTERS
Quantifying Electrochemical Nucleation and Growth of Nanoscale Clusters Using Real-Time Kinetic Data
2006 Vol. 6, No. 2 238-242
Aleksandar Radisic,† Philippe M. Vereecken,‡,§ James B. Hannon,‡ Peter C. Searson,*,† and Frances M. Ross*,‡ Department of Materials Science and Engineering, Johns Hopkins UniVersity, Baltimore, Maryland 21218, and IBM T. J. Watson Research Center, Yorktown Heights, New York 10598 Received November 3, 2005; Revised Manuscript Received December 19, 2005
ABSTRACT Electrochemical techniques are used widely for the fabrication of nanostructured materials, yet a quantitative understanding of nucleation and growth remains elusive. Here we probe electrochemical nucleation and growth of individual nanoclusters in real time by combining current− time measurements with simultaneous video imaging. We show discrepancies between the growth kinetics measured for individual nanoclusters and the predictions of models, and we describe a significant revision to conventional models that can explain the results. This improved understanding of nucleation and growth allows a more quantitative approach to the electrochemical fabrication of nanoscale structures.
Electrochemical techniques are essential for many types of nanoscale materials fabrication and processing such as the formation of ultrathin films, materials with nanoscale compositional and structural variations, and porous layers.1-3 Electrochemical deposition can be used, for example, to form arrays of catalyst particles on a patterned surface or grow three-dimensional nanostructures such as wires. Electrochemical deposition processes possess some key attributes that make them well suited for the fabrication of materials with applications in nanotechnology: deposition can be exquisitely site specific yet highly reproducible, and the structure of the clusters deposited can be modified strongly by varying the deposition parameters or the chemistry of the electrolyte solution. When using electrochemical techniques to fabricate nanostructured materials, the details of cluster nucleation and growth naturally become extremely important. In the formation of thin films, for example, the nucleus density determines the thickness at which the film becomes continuous, whereas more complex technological applications may require controlled formation of a single cluster at each point in a patterned array. It is therefore surprising that controversy still remains over the most basic principles of electrochemical nucleation and growth.4 Indeed, growth models,5-11 initially developed in the 1980s, can fail to predict parameters such as nucleus density within several * Corresponding authors. E-mail:
[email protected];
[email protected]. † Johns Hopkins University. ‡ IBM T. J. Watson Research Center. § Present address: Interuniversity MicroElectronics Center, Kapeldreef 75 B-3001, Leuven, Belgium. 10.1021/nl052175i CCC: $33.50 Published on Web 01/17/2006
© 2006 American Chemical Society
orders of magnitude.12-14 Placing nucleation and growth on a quantitative theoretical foundation has thus become a central goal as electrochemical techniques are increasingly applied in nanotechnology. In this Letter we probe the details of electrochemical nucleation and growth of nanoclusters in real time by operating a miniature electrochemical cell within an electron microscope to provide a unique combination of electrochemical and structural information. We examine a well-known system, the deposition of 3D nanoscale copper clusters onto a gold electrode from acidified copper sulfate solution. We show discrepancies between the growth kinetics measured for individual nanoclusters and the predictions of models, and we describe a significant revision to conventional models that can explain the kinetics seen. This improved understanding of the initial stages of electrochemical growth is expected to be widely applicable to electrochemical systems and will allow a more quantitative control of nanoscale materials formed by electrochemical methods. Experiments were carried out by fabricating a threeterminal sealed electrochemical cell that is compatible with the vacuum environment and limited space available in the polepiece of a conventional transmission electron microscope (TEM). Time-resolved imaging in liquids has been achieved recently in the TEM by encapsulating the liquid between membranes,15 but the key to the results presented here is to combine such structural information with electrochemical data obtained simultaneously. Thus, in Figure 1 we show a current-time transient curve for Cu deposition on Au with corresponding video stills. A set of videos and associated
current transients obtained at several different potentials is provided in the Supporting Information. By comparing the images and current transients, unique and detailed information can be obtained. First consider the features, common to many systems, of the current transient in Figure 1a. An initial, very rapid peak (discussed below) is followed by a slower increase in current (i.e., the current becomes more negative) because of nucleation and diffusionlimited growth of 3D clusters. Diffusion fields then develop around each cluster and interact, causing the current to start to decrease and eventually resulting in a transition to planar (1D) diffusion-limited growth. At short times, for a single hemispherical cluster growing by direct attachment (reduction of ions at the island surface) the expected growth law is4,5,16 cluster radius r ) [1 - (Cs/Cb)]1/2[2DliqCbt/Vm]1/2 ) [1 - (Cs/Cb)]1/2t1/2 × 9.23 × 10-5 cm s-1/2
(1)
where Dliq is the diffusion coefficient of ions in the liquid (6.0 × 10-6 cm2 s-1 for copper ions), Cb is the ion concentration in the bulk (here 0.1 M), Cs is the concentration at the island surface, and Vm is the molar volume of the solid (7.1 cm3 mol-1 for copper). At long times, the planar diffusion field leads to16 radius r ∝ t1/6
(2)
We now consider the cluster nucleation rate. Assuming that this depends on the density of unoccupied sites, the number of clusters is given by cluster density N(t) ) N0[1 - exp(-knt)]
(3)
where N0 is the final density and kn is a (first order) nucleation rate constant. Using these approximations, a commonly used analytical solution4,5 is current density I(t) ) zF(Cb - Cs)N0-1[Dliq/πt]1/2[1 exp(-2/3knN0Dliq(8π3(Cb - Cs)Vm)1/2t2)] (4)
Figure 1. (a) Current transient recorded during the deposition of Cu on polycrystalline Au at a potential of -0.07 V using 0.1 M CuSO4‚5H2O with 1 vol % H2SO4. (b) Five images extracted from a video recorded simultaneously with the current transient. The times corresponding to the images are indicated by vertical marks on the current-time curve. The field of view is approximately 1.8 µm × 1.4 µm (2.64 µm2), and the scale bar is 500 nm. Nano Lett., Vol. 6, No. 2, 2006
where z is the valence of copper and F is Faraday’s constant. This equation has the correct behavior at short and long times, and fitting it to the experimental current transient allows Dliq, N0, and kn to be extracted. (A slightly different version of eq 4, not shown here, is used4,5 for the case of large kn.) Before carrying out such a fitting, consider the complementary structural information available from the images in Figure 1b. Two types of analysis are possible. First, we can measure the growth of individual clusters, as in Figure 2a, where the two growth regimes r ∝ t1/2 for short times and r ∝ t1/6 for long times can indeed be seen.17 This is important and direct verification that growth is basically consistent with the diffusion limited model under these conditions. Indeed, 239
Figure 3. (a) Growth rate of an individual cluster recorded at -0.07 V, together with the prediction (solid line) from eq 1. The gradient of the experimental curve matches the t1/2 prediction at short times, but the growth rate is 20 times lower than that expected in this case (so that the volume growth rate is 8000 times too low). The dotted line shows the lowest possible growth rate that may be determined from eq 1, assuming that the surface concentration, Cs, is as high as 0.5Cb. (b) The potential dependence of the island density, N0, recorded from images, compared to the value obtained by fitting the current transient curves with eq 3. In each case the experimental value is around 1000 times lower than that expected.
Figure 2. (a) Radius as a function of time recorded for a single Cu cluster growing at -0.08 V. The growth rate decreases gradually, but two linear regions are indicated with exponents s1 ) 0.47 (short times) and s2 ) 0.11 (longer times). (b) Average values 〈s〉 of the two gradients s1 and s2, obtained by averaging measurements made from an ensemble of clusters at each potential. Clusters grown at -0.05 V do not show two clear growth regimes. The expected values of s1 and s2 are indicated by dashed horizontal lines. (c) Cluster density as a function of time, extracted from image series recorded at different potentials.
the more negative the potential, the more closely the growth of individual clusters follows diffusion-limited predictions (Figure 2b). This is expected from the increased importance of diffusion as the rate-limiting step (compared to “kinetic control”, that is, growth in which the surface reaction is the limiting step) for the faster growth at more negative potentials. Although the growth exponents agree with diffusionlimited predictions, we find that the actual growth rates of individual clusters do not (Figure 3a). For all clusters examined, the radial growth rate is 10-20 times less than that expected from eq 1. Note that there are no unknown 240
parameters in eq 1 apart from Cs, the surface concentration. We do not know Cs directly. But if Cs > 0.5Cb, then growth would be under kinetic rather than diffusion control, which we know is not the case, so any correction factor cannot be r0, and the boundary conditions used are C ) Cs for r ) r0 and C ) Cb for r ) ∞. To derive eq 2, we use the fact that the charge associated with a hemispherical cluster is 2zFπr3/ 3AVm. By comparing this expression with the charge obtained from integration of the Cottrell equation, which gives the limiting current at long times to be zFDc/(πt)1/2 (see ref 4), we obtain r ∝ t1/6. (17) The time at which clusters start to interact, which defines the boundary between “short” and “long” times, is longer than that expected from the island spacing and the diffusion coefficient, in part because the probability of nucleation within the diffusion zone is not zero: Jacobs, J. W. M. J. Electroanal. Chem. 1988, 247, 135. (18) Ji, C.; Oskam, G.; Searson, P. C. Surf. Sci. 2001, 492, 115. (19) Ji, C. X.; Oskam, G.; Searson, P. C. J. Electrochem. Soc. 2001, 148, C746. (20) Hoffmann, P. M.; Radisic, A.; Searson, P. C. J. Electrochem. Soc. 2000, 147, 2576. (21) Fransaer, J. L.; Penner, R. M. J. Phys. Chem. B 1999, 103, 7643. (22) Ho¨lzle, M. H.; Retter, U.; Kolb, D. M. J. Electroanal. Chem. 1994, 371, 101. (23) Giesen, M.; Randler, R.; Baier, S.; Ibach, H.; Kolb, D. M. Electrochim. Acta 1999, 45, 527. (24) Giesen, M.; Dietterle, M.; Stapel, D.; Ibach, H.; Kolb, D. M. Surf. Sci. 1997, 384, 168. (25) Dona, J. M.; Gonzalez-Velasco, J. Surf. Sci. 1992, 274, 205. (26) Gonzalez-Velasco, J. Chem. Phys. Lett. 1999, 313, 7. (27) Gonzalez-Velasco, J. Surf. Sci. 1998, 410, 283. (28) Venables, J. A. Introduction to Surface and Thin Film Processes; Cambridge University Press: Cambridge, U.K., 2000. (29) Budevski, E.; Staikov, G.; Lorentz, W. J. Electrochemical Phase Formation and Growth; VCH: New York, 1996. (30) Pimpinelli, A.; Villain, J. Physics of Crystal Growth; Cambridge University Press: Cambridge, U.K., 1998. (31) Liu, C. L.; Cohen, J. M.; Adams, J. B.; Voter, A. F. Surf. Sci. 1991, 253, 334. (32) Stoltze, P. J. Phys.: Condens. Matter 1994, 6, 9495. (33) Giesen, M. Prog. Surf. Sci. 2001, 68, 1.
NL052175I Nano Lett., Vol. 6, No. 2, 2006
