Ohmic-controlled deposition

It is interesting to note that (67c) describes qualitatively the increase of the apparent current density over the value of the limiting diffusion current density after initiation of dendritic growth, since the quantitative treatment of the polarization characteristics in the presence of dendrite growth is simply impossible. This is because dendrites can have a variety of unpredictable structures. In this way, the results of Ibl and Schadegg,59 Diggle et al.,12 and Popov et al.,21 as well as the Ohmic-controlled deposition of tin,57 silver,7 and lead,58 could be explained qualitatively. 

Thus, instead of a limiting diffusion current density plateau, a curve inflection point or a short inclined plateau can be expected on the polarization curve in Ohmic-controlled electrodeposition of metals, as observed in the case of silver electrodeposition from nitrate solutions. The exchange current density of the silver reaction in nitrate electrolytes is sufficiently large to permit Ohmic-controlled deposition as well as dendritic growth at low overpotentials.27 After a linear increase of the deposition current density with increasing overpotential, an exponential increase after the inflection point appears, meaning the elimination of mass-transfer limitations due to the initiation of dendritic growth. 

The exchange current density of the silver reaction in nitrate electrolytes is sufficiently large to permit ohmic-controlled deposition, as well as dendritic growth at low overpotentials [30]. 

Figures 2.12-2.14 show morphologies of lead deposits obtained in the ohmic-controlled deposition (Fig. 2.12), in the transitional zone corresponding to the end of the ohmic-controlled electrodeposition (Fig. 2.13) and to the zone of rapid increase of the current of electrodeposition (Fig. 2.14).

Mass-transport deposition control occurs when the exchange current density P is high and the limiting current density is low. Ohmic resistance can be a cause of nonuniformity if there is an appreciable difference in solution resistance from the bulk of the solution to peaks or to recesses. Distribution of the current density will be such that ip > i. and peaks will receive a larger amount of deposit than will recesses. Distribution of deposit in the triangular groove under conditions of mass transport and ohmic control nonuniform deposition, with ip > is shown in Figure 10.14. 

Under the conditions shown in Figure 10.14, the roughness of the surface increases. Thus, to get leveling of the surface it is necessary to change from diffusion and ohmic control to activation control. Activation control can result in uniform deposition (ip = iy) or in nonuniform deposition (with i. > ip). In nonuniform deposition with... 

Figure 10.14. Distribution of deposit in a triangular profile when 8. > 8p and ir

In the case under consideration, complete Ohmic control of the deposition process can be expected for 70//L > 100 up to a current density about 0.95yh (Fig. 7) and for yo/yh = 10 up to 0.6yh (Fig. 9). It is obvious from Figs. 7-10 that, regardless of the shape of the polarization curve, which depends on the jo/jh ratio and /c, a limiting diffusion current density plateau is present in all cases. 

Obviously, increasing the concentration of the reacting ion and decreasing the concentration of the supporting electrolyte in a simple salt solution stimulates Ohmic control of the deposition process, but a large value of the exchange current density seems to be the most important for it (Figs. 9 and 10). 

The initiation of dendritic growth is followed by an increase of the deposition current density, and the overall current density will be larger than the limiting diffusion current on a flat active electrode. Based on the above discussion, the polarization curve equation in the Ohmic-controlled electrodeposition of metals can be determined now by 9... 

At overpotentials larger than 175 my the current density is considerably larger than the one expected from the linear dependence of current on overpotential. The formation of dendritic deposits (Fig. 16d-f) confirms that the deposition was dominantly under activation control. Thus, the elimination of mass transport limitations in the Ohmic-controlled electrodeposition of metals is due to the initiation of dendritic growth at overpotentials close to that at which complete diffusion control of the process on the flat part of the electrode surface occurs. 

In practice, deposits with high roughness factor and good mechanical resistance are of particular interest. Dendrites have low mechanical resistance and they are unsuitable as electrocatalysts, but the elucidation of the Ohmic-controlled electrodeposition of metals due to the dendritic growth is of a great theoretical importance. 

Fig. 1.8 Morphologies of Pb deposits electrodeposited from 0.30 M Pb(N03)2 in 2.0 M NaN03 (a) the ohmic control, rj = 30 mV, and the diffusion control, (b) ri = 55 mV, (c, d) rj= 120 mV (Reprinted from Ref. [12] with permission from Elsevier and Ref. [23] with kind permission from Springer)...

Dendritic Growth Inside Diffusion Layer of the Active Macroelectrode and Ohmic Diffusion and Activation-Diffusion-Controlled Deposition and Determination of tji and tjc... 

Fig. 3.19 (a) Simulation of a growth of the deposit from the model protrusion (h = 5 cm, / = 15 cm) calculated for a pure ohmic control employing Eqs. (3.57) and (3.58) and (b) schematic representation of microphotographs illustrating the comer weakness effect (Reprinted from Ref. [3] with permission from Springer and Ref. [7] with permission from the Serbian Chemical Society and adapted from [16])... 

Ohmic-Diffusion and Activation-Diffusion Controlled Deposition... 

The two major causes of uneven current distribution are diffusion and ohmic resistance. Nonuniformity due to diffusion originates from variations in the effective thickness of the diffusion layer 8 over the electrode surface as shown in Figure 10.13. It is seen that 8 is larger at recesses than at peaks. Thus, if the mass-transport process controls the rate of deposition, the current density at peaks ip is larger than that at recesses since the rate of mass transport by convective diffusion is given by... 

It should be understood that even for micro surface features the potential is uniform and the ohmic resistance through the bath to peaks and valleys is about the same. Also, electrode potential against SCE will be uniform. What is different is that over micro patterns the boundary of the diffusion layer does not quite follow the pattern contour (Fig. 12.3). Rather, it thus lies farther from depth or vias than from bump peaks. The effective thickness, 8N, of the diffusion layer shows greater variations. This variation of 8N over a micro profile therefore produces a variation in the amount of concentration polarization locally. Since the potential is virtually uniform, differences in the local rate of metal deposition result if it is controlled by the diffusion rate of either the depositing ions or the inhibiting addition (leveling) agents. 

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