Diffusion controlled-electrodeposition

Johans et al. derived a model for diffusion-controlled electrodeposition at liquid-liquid interface taking into account the development of diffusion fields in both phases [91]. The current transients exhibited rising portions followed by planar diffusion-controlled decay. These features are very similar to those commonly observed in three-dimensional nucleation of metals onto solid electrodes [173-175]. The authors reduced aqueous ammonium tetrachloropalladate by butylferrocene in DCE. The experimental transients were in good agreement with the theoretical ones. The nucleation rate was considered to depend exponentially on the applied potential and a one-electron step was found to be rate determining. The results were taken to confirm the absence of preferential nucleation sites at the liquid-liquid interface. Other nucleation work at the liquid-liquid interface has described the formation of two-dimensional metallic films with rather interesting fractal shapes [176]. 

Mechanisms describing the formation of holes of this type are based on the amplification of electrode surface coarseness52,53 in diffusion-controlled electrodeposition and to the tip54 and edge55 effects of current density distribution at electrode surface. More about these mechanisms can be found in Ref.13... 

The polarization curves consist of two parts in the mixed ohmic-diffusion-controlled electrodeposition [12]. The first part corresponds to the ohmic control... 

Fig. 2.4 Copper deposits obtained from 0.10 M CUSO4 in 0.50 M H2SO4. Quantity of electricity, Q 20 mA h cm (a) activation-controlled electrodeposition rj = 90 mV, initial current density 3.3 mA cm, (b) mixed activation-diffusion-controlled electrodeposition rj= 140 mV, initial current density 4.2 mA cm, and (c) dominant diffusion-controlled electrodeposition ri = 210 mV, initial current density 6.5 mA cm (Reprinted from Refs. [7, 8, 13] with kind permission from Springer and Ref [16] with permission from Elsevier)...

The current density under a mixed activation-diffusion-controlled electrodeposition is given by Eq. (1.13), and substitution of the corresponding limiting diffusion current density from Eqs. (2.62) and (2.63) into the Eq. (1.13) produces after rearrangement ... 

The initiation of dendritic growth in the case of very fast electrodeposition processes also will be 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 mixed ohmic diffusion-controlled electrodeposition of metals can be determined as [108] ... 

PritzkerMD (1988) Voltammetric response for the diffusion-controlled electrodeposition onto growing hemispherical nuclei. J Electroanal Chem 243 57-80... 

Hills, G.J., D.J. Schiffrin, and J. Thompson, Electrochemical nucleation fixim molten salts. I. Diffusion controlled electrodeposition of silver fixim alkali molten nitrates. Electrochim. Acta, 1974. 19 p. 657-70. 

By electrodeposition of CuInSe2 thin films on glassy carbon disk substrates in acidic (pH 2) baths of cupric ions and sodium citrate, under potentiostatic conditions [176], it was established that the formation of tetragonal chalcopyrite CIS is entirely prevalent in the deposition potential interval -0.7 to -0.9 V vs. SCE. Through analysis of potentiostatic current transients, it was concluded that electrocrystallization of the compound proceeds according to a 3D progressive nucleation-growth model with diffusion control. 

Although electroless deposition seems to offer greater prospects for deposit thickness and composition uniformity than electrodeposition, the achievement of such uniformity is a challenge. An understanding of catalysis and deposition mechanisms, as in Section 3, is inadequate to describe the operation of a practical electroless solution. Solution factors, such as the presence of stabilizers, dissolved O2 gas, and partially-diffusion-controlled, metal ion reduction reactions, often can strongly influence deposit uniformity. In the field of microelectronics, backend-of-line (BEOL) linewidths are approaching 0.1 pm, which is much less than the diffusion layer thickness for a... 

Properties of thin layers of lead electrodeposited on vitreous carbon have been found identical with that of metallic lead [304]. Therefore Pb and Pb02 coated reticulated vitreous carbon (RVC) electrodes [185] can be applied as electrodes in lead-acid batteries, as reviewed in [305]. The deposition of lead on carbon is through the diffusion-controlled process with instantaneous or progressive nucleation, for high and low Pb + concentration, respectively, and three-dimensional growth mechanism. The number of nucleation sites increases with deposition overpotential, as shown for vitreous [306] and glassy carbon [307] electrodes. The concentration dependence of the nucleation... 

Electrodeposition on transparent material such as indium tin oxide (ITO) can be used for electrochromic applications [328]. Pb deposition on indium-tin oxide electrode occurs by three-dimensional nucle-ation with a diffusion-controlled growth step for instantaneous nucleation [329], and the electrode process has also been studied using electrochemical impedance spectroscopy [328]. 

Figure 6.2-12 Cyclic voltammogram of 0.1 - 1 mmol dm Geb on gold in dry [BMIMj PFg , starting at-500 mV towards cathodic (a) and anodic (b) regime. Two quasireversible (E, and E2) and two apparently irreversible (E4 and E5) diffusion-controlled processes are observed. E3 is correlated with the growth of two-dimensional islands on the surface, E4 and E5 with the electrodeposition of germanium, Ej with gold step oxidation, and E, probably with the iodine/iodide couple. Surface area 0.5 cm (picture from [59] - with permission of the Peep owner societes).

Laplace transformation, 1215 Nemst s equation and. 1217 non-steady, 1254 as rate determining step, 1261 Schlieren method, 1235 semi-infinite linear, 1216, 1234, 1255 in solution and electrodeposition, 1335 spherical. 1216. 1239 time dependence of current under, 1224 Diffusion control, 1248... 

Vii ial equation of state in two dimensions, 931 Virial isotherm, 936 Visible radiation, 797 Volcanoes, in electrocatalysis, 1284 Volmcr, Max, 1048,1474 Volmer. Weber, electrodeposition. 1303. 1306 Volta, 1423, 1455 Volta potential difference, 822 Voltammetry. 1432 1434 cyclic, 1422 1423 diffusion control reactions, 1426 electron transfer reaction, 1424... 

Anyway, the structure of copper deposits obtained at overpotentials of 800 and 1,000 mV with a quantity of the electricity of 20 mA h cm-2 was similar to those obtained at lower overpotentials before the beginning of dendritic growth. The absence of copper dendrites at overpotentials of 800 and 1,000 mV after the electrodeposition with 20 mAh cm-2, as well as the similarity of the obtained morphologies of copper deposits with those obtained at lower overpotentials before dendritic growth initiation clearly indicates that there is really lower degree of diffusion control at these overpotentials than at overpotentials of 550 and 700 mV respectively. 

This concept can be also applied for the case of the electrodeposition of copper. As mentioned earlier, the morphology of the copper deposit obtained at cathodic potential of -500 mV/SCE under the parallel field was of cauliflower-like structure (Fig. 12b), while the morphology of the copper deposit obtained without the applied magnetic field had very dendritic structure (Fig. 12a). It is known that dendritic structures are main characteristic of electrodeposition in conditions of full diffusion control, while cauliflower-like structures are a characteristic of a dominant diffusion in mixed control of electrodeposition process.13... 

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. 

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. 

From these three contributions, the progressive nucleation and two-dimensional growth corresponded to the charge of a monolayer, and were attributed to two-dimensional nuclei of Re produced by the reduction of adsorbed perrhenate. The three-dimensional growth under diffusion control was the most important contribution, and represented 70-80% of the mass increase. The FE for the electrodeposition process was in the range of 12-18%. The nature of the adsorbed layer, however, was not identified in this study. 

It was proposed by Andricacos et al This mechanism considers one-additive system. It is noted in Ref. 47 (Ch. 10, Sections 10.4 and 10.5) that in general, adsorption of additives (inhibitor) at the cathode affects the kinetics and growth mechanism of electrodeposition. The surface coverage of the additive (inhibitor), 0, is a function of the diffusion controlled rates of the adsorption-desorption processes. In the differential-inhibition mechanism it is assumed that a very wide range of additive fluxes over the micro-profile (vias and trenches) exists, that is, extremely low flux in deep interior comers, low flux at the bottom center, moderate flux at the sidewalls, and high flux at shoulders. 

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