Porous anodic alumina (PAA) films are widely used as templates for functional nanostructures, because of the high regularity and controllability of the pore morphology. However, growth mechanisms have not yet been developed that can explain quantitative relationships between processing conditions and oxide layer geometry. Here, we present a model for steady-state growth of these amorphous films, incorporating the novel feature that metal and oxygen ions are transported by coupled electrical migration and viscous flow. The oxide flow in the model arises near the film-solution interface at the pore bottoms, in response to the constraint of volume conservation. The hypothesis of viscous flow was successfully validated through detailed comparisons to observations of the motion of tungsten tracers in the film. Predictions of localized tensile stress near nanoscale ridges at the metal-film interface were supported by observations of voids at these sites. We suggest that the ordering of PAA may be explained by a mechanism in which metal-film interface motion is regulated by the combination of ionic migration in the oxide and stress-driven interface diffusion of metal atoms.

Porous anodic alumina ͑PAA͒ films, formed by anodic oxidation in acidic solutions, contain hexagonal arrays of parallel cylindrical pores, with pore diameter and spacing between ten and several hundred nanometers. Simulations were developed for the electrical potential distribution in the film during steady-state PAA growth, and used to calculate the rates of metal-film and film-solution interface motion. In particular, a model using the assumption of no space charge ͑Laplace's equation͒ and one based on the current continuity equation, in each case coupled with high-field ionic conduction, were evaluated with respect to the requirement that the interface profiles are time invariant. Laplace's equation, on which prior simulations of PAA growth were based, yielded unrealistic behavior with highly nonuniform interface motion, suggesting the presence of significant space charge. In contrast, interface motion predicted by the current continuity equation was uniform, except near convex ridges on the metal-film interface between pores. To fully rationalize the steady-state PAA geometry, phenomena other than conduction should be considered, which are able to provide inhibition of the oxidation rate on these ridges.

A model for transport in amorphous anodic oxide films was developed in which ion migration was driven by gradients of mechanical stress as well as electric potential and which included viscoelastic creep of the oxide. Simulations were presented for the galvanostatic growth of planar barrier-type anodic aluminum oxide films. It is assumed that stress originates at the metal-film interface due to the volume change upon oxidation. The average stress in the film decayed during growth and evolved from compressive to tensile with increasing applied current density. The model was fit to stress-thickness measurements using a viscosity of 1×1012Pas on the same order of magnitude as that of many other amorphous materials displaying viscous creep. The current density increased exponentially with electric field, in agreement with an empirical high field conduction behavior. The metal ion transport number was predicted based on the motion of markers in the film and increased with current density in quantitative agreement with experimental measurements. The model represents a unified quantitative interpretation of ionic conduction, transport numbers, and mechanical stress measurements in anodic films.

Poly͑ethylene glycol͒ ͑PEG͒ is an important additive to electroplating baths used for the deposition of copper interconnects on semiconductor wafers. In an earlier paper, Yokoi et al., Denki Kagaku oyobi Kogyo Butsuri Kagaku, 52, 218 ͑1984͒ found a direct relationship between the deposition rate in the presence of PEG and chloride ions with the open-circuit potential measured after plating, suggesting that the rest potential reflects the chemical state of reactive copper ions within a surface polymer film. Here, these measurements were corroborated and then interpreted in terms of a proposed mechanism of copper deposition in the presence of PEG. In this mechanism, aqueous Cu 2+ ions are reduced to an intermediate complex at the PEG-Cu interface detected earlier by Raman spectroscopy ͓Z. V. Feng et al., J. Phys. Chem. B, 107, 9415 ͑2003͔͒, in which Cu + ions associate with adsorbed Cl − ions and ether oxygen ligands of PEG. The rest potential measurements are quantitatively explained on the basis of competition for these ligands at open circuit with Cu 2+ ions absorbing from solution. The results indicate that deposition is mediated though ions partially solvated with the polymer, the concentration of which is controlled by the PEG concentration and molecular weight. PEG then behaves as a polymer electrolyte film as opposed to a passive barrier.

Ionic transport in porous anodic alumina (PAA) films during steady‐state growth was simulated, including effects of ionic migration in the electric potential and stress gradients, as well as material flow. The calculated flow patterns display similar characteristics to those revealed by experimental studies. The results indicate that the stress field driving the flow originates from three sources: volume change at the metal–film interface during oxidation, the nonlinear current–electric field relationship governing ionic conduction, and insertion of species at the film–solution interface. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)