Electrodeposition current distribution

One of these is the "shape change" phenomenon, in which the location of the electrodeposit is not the same as that of the discharge (deplating) process. Thus, upon cycling, the electrode metal is preferentially transferred to new locations. For the most part, this is a problem of current distribution and hydrodynamics rather than being a materials issue, therefore it will not be discussed further here. 

The morphological stability of initially smooth electrodeposits has been analyzed by several authors [48-56]. In a linear stability analysis, the current distribution on a low-amplitude sinusoidal surface is found as an expansion around the distribution on the flat surface. The first order current distribution is used to calculate the rate of amplification of the surface corrugation. A plot of amplification rate versus mode number or wavelength separates the regimes of stable and unstable fluctuation and... 

A second application of current interest in which widely separated length scales come into play is fabrication of modulated foils or wires with layer thickness of a few nanometers or less [156]. In this application, the aspect ratio of layer thickness, which may be of nearly atomic dimensions, to workpiece size, is enormous, and the current distribution must be uniform on the entire range of scales between the two. Optimal conditions for these structures require control by local mechanisms to suppress instability and produce layer by layer growth. Epitaxially deposited single crystals with modulated composition on these scales can be described as superlattices. Moffat, in a report on Cu-Ni superlattices, briefly reviews the constraints operating on their fabrication by electrodeposition [157]. 

There are other cases in practical electrochemical devices in which current distribution is important. Because of the interplay of interfacial and electrolyte resistance effects (primary and secondary current distribution, respectively , the detailed calculation involve much mathematics. Electroplating deep into crevices of the object to be plated is an example of where current distribution considerations often dominate behavior. Throwing power is a term that describes the degree of penetration of the current— hence the plating—into fissures and irregularities in electrodeposition. 

Current Distribution and Shape Change in Electrodeposition of Thin Films for Microelectronic Fabrication... 

In order for the deposition rate to be uniform, the local current density at all electroactive surfaces must be identical. If there are two adjacent zones of equal size on the cathode surface, the zone with the higher resist coverage will receive less Current. We can say that the superficial current density at zone (1) is lower than at zone (2). If this is the case, there will be a lower ohmic potential drop associated with zone (1). Consequently, there will be a tendency for zone (1) to attract more current than zone (2). This would upset the uniformity in the electrodeposition rate distribution. 

Perhaps the first numerical investigation of lithographically patterned electrodeposition was published by Alkire et al. [46]. In this work, the finite-element method was used to calculate the secondary current distribution at an electrode patterned with negligibly thin insulating stripes. (This is classified as a secondary current distribution problem because surface overpotential effects are included but concentration effects are not.) Growth of the electrodeposit was simulated in a series of pseudosteady time steps, where each node on the electrode boundary was moved at each... 

Peskin [49] used the Galerkin finite-element method to compute current distribution and shape change for electrodeposition into rectangular cavities. A concentration-dependent overpotential expression including both forward and reserve rate terms was used, and a stagnant diffusion layer was assumed. An adaptive finite-element meshing scheme was used to redefine the problem geometry after each time step. 

Enough is known about the fundamental forces that determine the current distribution to carry out fairly accurate simulations of simple systems. Although in the electronics industry predictions are currently quite useful for guiding the design and production of components made by patterned electrodeposition, there is ample opportunity for improvement, especially in the following areas. 

S. Mehdizadeh, The Influence of Auxiliary Electrodes and Lithographic Patterning on Current Distribution in Electrodeposition, PhD thesis, Columbia University (1991), Chap. 4, pp. 112-159. 

The thickness distribution of electrodeposits depends on the current distribution over the cathode, which determines the local current density on the surface. The current distribution is determined by the geometrical characteristics of the electrodes and the cell, the polarization at the electrode surface, and the mass transfer in the electrolyte. The primary current distribution depends only on the current and resistance of the electrolyte on the path from anode to cathode. The reaction overpotential (activation overpotential) and the concentration overpotential (diffusion overpotential) are neglected. The secondary... 

Simultaneously, holes of irregular shapes (Fig. 29f) were formed from nuclei of copper formed in the initial stage of the electrodeposition between the hydrogen bubbles.18 The current distribution at the growing copper surface was responsible for the formation of this type of hole. 

In the majority of the Laplace equation solutions, the electrical potential, subject to appropriate boundary conditions, is determined. These primary or secondary current-distribution problems may appear to be particularly relevant for electrodeposition, where useful deposit properties are obtained at small fractions of the limiting current. However, the fact that industry has paid considerable attention to fluid flow in reactor design suggests that flow effects can be important, even at a relatively small fraction of the limiting current density. ... 

For example, practical electrodeposition processes use additives that are present in very small concentrations to control deposit microstracture. Consumption of the additives at an electrode surface is likely to lead to concentration variations that may affect current distribution. Even in an... 

The effect of current density on the structure of electrodeposits has been investigated in a special trapezoidal cell with a purposely nonuniform current distribution known as the Hull cell... 

The first treatment of the current distribution was applied for the case of a metal deposition [8,9] for the purpose of preparing a homogeneous metal layer on the substrate. It was observed that the thickness was completely heterogeneous as the rate of the electrodeposition was much higher on the edges of the electrode surface. The result was unsatisfactory and required an analysis of the current distribution to be performed. 

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