Current Distribution on Microprofiles - The 14th William Blum Lecture - Part 2
This article is the second of four parts of a re-publication of the 14th William Blum Lecture, presented at the 60th AES Annual Convention in Cleveland, on June 18, 1973. Dr. Otto Kardos gives a comprehensive discussion of how the deposit forms on surface textures, and how leveling and brightness are achieved.
Recipient of the 1972 William Blum
AES Scientific Achievement Award
Editor’s Note: Originally published as Plating, 61 (3), 229-237 (1974), this article is the second of four parts of a re-publication of the 14th William Blum Lecture, presented at the 60th AES Annual Convention in Cleveland, on June 18, 1973.
A printable PDF version of Part 2 is available by clicking HERE.
The printable PDF version of the complete 52-page paper is available HERE.
6. The definition of microprofiles and the meaning of mass transport control
A “typical” microprofile is sufficiently small-scale so that (1) the electrode potential E is practically uniform over the profile, and (2) the effective thickness of the diffusion layer δN varies over the profile.
The variation of δN leads to a variation of local current density if the metal deposition is, at least partly, controlled by the mass transport (mass transfer, or shorter and more familiar, diffusion) of the depositing metal ions or of an addition agent.
In absence of diffusion control, different orientation of crystal facets, or the presence of lattice dislocations, grain boundaries, impurities, etc., may cause a variation of the polarization parameter kc, and more particularly of i0 and perhaps αc, over the profile, but these influences will be rather random, not systematic, between micropeaks and microrecesses, except to some extent on microprofiles produced by electrodeposition. Wagner83 gave a basic analysis of the effects of a variation of the polarization parameter kc over an electrode.
If diffusion control is absent and if crystallographic differences can be neglected, the practical uniformity of the electrode potential over a microprofile leads from Equations (10) to (12) to practical uniformity of the current density.
If the metal deposition rate is controlled by the diffusion rate of an inhibitor, but not by the diffusion rate of the metal ions, one may still apply Equations (10) to (12) for activation overvoltage, if one replaces i by i/(1 - θ), where θ is the fractional surface coverage by the inhibitor. This modification of the equations is based on the simplifying assumption that the inhibiting action consists in a mere reduction of the surface area available for deposition and that the cathodic transfer coefficient αc is not affected by the inhibitor. Then the practical constancy of E, and consequently of ηact, over the microprofile leads to a practical constancy of i/(l - θ) and to ir/ip (l - θr)/(l - θp). Compare Ref. 78.
If, on the other hand, the metal deposition rate is controlled by the mass transfer rate of the depositing metal ions then the Nernst equation for concentration polarization applies:
where n is the valency of the depositing metal.
If one neglects a possible variation of the transport number tMe with current density, Eq. (19) may be transformed into:
If the overpotential can be expressed by this equation, practical constancy of E implies practical constancy of i/iL. Thus, the local current densities would be proportional to the local limiting current densities (which would vary approximately as the current densities in primary current distribution) or, from Eq. (16) inversely proportional to δN.
Although in cyanide baths Equations (19) and (20) would have a more complicated form (see, e.g., p. 174 of Ref. 7) we may use Eq. (20) to demonstrate why concentration polarization tends to throw a deposit into a macroprofile but out of a microprofile.2 Over a macroprofile iL and δN are practically constant. The higher i at a protruding point would thus produce a more negative ηconc, that is, a "greater" cathode polarization, which would oppose current flow to the peak points and tend to throw it into the recess. On micropeaks iL is much greater, or δN much smaller, than on the microrecess points and this would allow a proportional increase of the local current density without creating a local increase of overpotential.
At certain values of i/iL, which will be higher for metals with low exchange current density i0, such as nickel or iron, than for copper, zinc and especially silver (Ref. 35, pp. 17, 125), Eq. (10) has to be abandoned for Eq. (20). Good microthrow and "true" leveling will then be replaced by bad microthrow. If the formation of a diffusion layer of nonuniform thickness is suppressed by the use of interrupted current, good microthrow, but not true leveling, is restored (see Section 11).
Also, on descent into a microgroove, especially if the enclosed angle β is small and the current density medium to high, Eq. (20) may replace Eq. (10) or bad microthrow (hr/hp < 1) replace true leveling (hr/hp > 1) at some point. This may lead to an apparently leveled deposit which contains a void, as shown by Raub in Fig. 9.45 This figure shows also preferential etching in the peak areas due to greater codeposition rates, and an increase of lamination thickness on descent into the microgroove.