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Figure 2 AB
Figure 2 CD
Seeking smoother plating deposits? It may be all in the waves. Our studies have shown that superimposition of a small sinusoidal potential wave (smooth, repetitive oscillation) onto a potentiostatic bias can lead to more level electrodeposits in finishing.
In principle—at least in the investigated case of an Au cyano complex bath—a relatively simple modification of the current supply mode can give rise to plating-quality results that are traditionally achieved with the use of additives that are generally environmentally unfriendly and complex to manage.
It is worth noting that the electrical control we are proposing is utterly different from pulse plating, from both the instrumental and theoretical viewpoints. As far as instrumentation is concerned, simply a controlled ripple has to be applied to an otherwise continuous cell voltage. Concerning theory, while pulse plating essentially relies on the generation of a pulsating concentration double layer, our approach rests on a theory we have been recently developing: explaining roughness development in metal plating on the basis of the dynamic coupling of surface morphology and composition, of which a review of this work can be found in .
Owing to the peculiarities of this dynamic—specifically the interaction between the frequency of a forcing added to the source term for morphology and the different intrinsic timescales of the model—morphological stabilization can be achieved because the controlled potential perturbation counteracts the tendency of roughness to diverge.
The rationale for our idea of adding an electrochemical forcing term is rooted in the evolution of the electrodeposit surface profile obtained as the solution of a balance equation. In the relevant experimental case, the ligand was released during the plating process when it was coupled to a balance equation for an adsorbate. In the morphological balance equation, the flow terms account for adatom surface diffusion, contributing to the build-up of morphology, while the source terms include deposition and corrosion, or desorption, of the relevant material.
Of course, the underlying physics is atomistic, but a continuous model such as ours is acceptable for the description of plating profile dynamics if specific conditions on length and timescales are defined (for details, see the Appendix of ). Under the realistic hypotheses discussed in , the model given in Equation (1) has been shown in a series of recent works of ours (among which [3, 4] stress mathematical aspects and [5, 6] experimental ones) to express a notably varied phenomenology, able to capture the key aspects of roughness formation in electroplating.
The focus in  has been to pinpoint the bearing of a small-signal applied potential on roughness and Turing pattern development.
The equation for the morphological dynamics in the presence of external sinusoidal forcing
is given by:
Here h(x,y,t) represents the shape of the electrodeposit, x and y are the space coordinates and is the surface diffusion coefficient of adatoms. In the source term S*, q(x,y,t) is the surface coverage with adsorbates. The parameters a and b are positive and weight the two terms in S*, respectively accounting for: (i) localization of the electroplating process and (ii) effects of adsorption on the plating rate.
The presence of adsorbable species causes q to develop at the cathode surface, depending on the nature of the adsorbable species and of the surface active sites. The surface coverage dynamics can be classically described in terms of a material balance with a source term containing positive and negative contributions related to adsorption and desorption:
is the surface diffusion coefficient of the additive and
is the electrochemical source term given by:
represent the electrochemical adsorption and desorption rate constants, respectively, where A, A1, a, a1, b, b1 are positive parameters. By coupling equations (1) and (2) one obtains the full model.
Computational and Experimental Study of the Smoothing Effects of Frequency
In order to assess mathematically the smoothing capability of the forcing term, we studied its effectiveness in suppressing Turing patterns. In two dimensions, the typical patterns for Turing systems have been shown to be spots, representing outgrowth features such as projecting ridges and dendrite precursors. In our study, we considered the forcing term with a fixed amplitude and variable frequencyw. The numerical results obtained for steady-state conditions—depicted in Figure 1—show that spots tend to disappear in an intermediate range of frequencies, thus proving the smoothing effect.
In order to assess the effects of frequency on the morphology of electrodeposits, we used a neutral 10 mM KAu(CN)2 solution. In the absence of additives, this bath yields poor-quality, rough electrodeposits. In order to emphasise morphological factors, we plated at a high cathodic bias (working vs. reference electrode: -1.6V vs. Ag/AgCl). A sinusoid of amplitude 10 mV was superimposed on the bias and the frequency was varied in the range 0¸100 kHz. A selection of SEM micrographs is reported in Figures 1 and 2, in combination with the results of our computations.
Electrodeposition experiments were carried out for 30 and 120 minutes (Figures 1 and 2, respectively), in order to emphasise levelling power. From the comparison of numerical and experimental results reported in Figure 1, it can be concluded that there exists an intermediate frequency range (in this case at ca. 1 kHz) giving rise to smoothing, while high-frequencies essentially yield the same results at DC plating. If electrodeposition is prolonged to 120 minutes, severe outgrowth of dendrites is observed (Figure 2). Nevertheless, the comparison of deposits obtained at DC (panel A) and 0.5 kHz (panel B) reveals a remarkable dendrite-suppressing activity of the superimposed frequency.
In addition to the impact of frequency on dendrite dimensions, the images processed by an edge-detection technique (panels C and D) also highlight a major bearing on dendrite density and spatial distribution; in particular the surface density of outgrowth sites is reduced by a factor of ca. 2.5 by applying the small-signal sinusoidal perturbation at the appropriate frequency.
Benedetto Bozzini and Ivonne Sgura are professors at the Università del Salento in Lecce, Italy; Deborah Lacitignola is a professor at Università di Cassino in Cassino, Italy. You can contact the group at firstname.lastname@example.org.
 Benedetto Bozzini, Deborah Lacitignola, Ivonne Sgura. “Frequency as the greenest additive for metal plating: mathematical and experimental study of forcing voltage effects on electrochemical growth dynamics.” International Journal of Electrochemical Science 6 (2011) 4553-4571.
 Benedetto Bozzini, Deborah Lacitignola, Ivonne Sgura. “Morphological Spatial Patterns in a Reaction Diffusion Model for Metal Growth.” Mathematical Biosciences and Engineering 7 (2010) 237-258.
 Benedetto Bozzini, Deborah Lacitignola, Ivonne Sgura. “Travelling Waves in a Reaction-Diffusion Model for Electrodeposition.” Mathematics and Computers in Simulation 81 (2011) 1027-1044.
 Benedetto Bozzini, Ivonne Sgura, Deborah Lacitignola, Claudio Mele, Mariapia Marchitto, Antonio Ciliberto. “Prediction of Morphological Properties of Smart-Coatings for Cr Replacement, Based on mathematical Modelling.” Advanced Materials Research 138 (2010) 93-106.
 Benedetto Bozzini, Lucia D’Urzo, Deborah Lacitignola, Claudio Mele, Ivonne Sgura, Elisabetta Tondo. “An investigation into the dynamics of Au electrodeposition based on the analysis of SERS spectral time series.” Transactions of the Institute of Metal Finishing 87 (2009) 193-200.
 Benedetto Bozzini, Lucia D'Urzo, Luca Gregoratti, Abderrahmane Tadjeddine. “Study of Surface Compositional Waves in Electrodeposited Au-Cu Alloys by Synchrotron-Based High Lateral-Resolution Photoemission Spectroscopy.” Journal of the Electrochemical Society 155 (2008) F165-F168.