Electrochemical self-organization of ordered nanoscale structures: Experiment, model, and theoretical analysis

Fabricated nanostructured materials often demand highly regimented periodic nanoscale patterns and morphologies. Frequently, these patterns act as a template and/or substrate for the preparation of electronic devices. The periodicity and regimentation of the surface patterns hence define the quality of the final electronic function. The control of the uniformity of the template pattern and the geometry at such a small scale is, however, extremely difficult.; Using atomic force microscopy, we find that the surface morphology of a dissolving aluminum anode in a variety of electropolishing electrolytes under a constant applied voltage can exhibit both highly regular and randomly packed patterns of stripes and hexagonal hills. These patterns have amplitudes of 2--5 nm and wavelengths in the 80--150 nm range. The dependence of the pattern type and the wavelength on electrolyte composition was studied for perchloric, phosphoric, and sulfuric acid-based solutions containing a variety of organic additions such as ethanol, methanol, and diethyl ether. The patterns were found to establish in electrolytes that contain organic molecules with permanent dipole moments similar to water molecules and with a viscosity close to that of ethanol.; The driving instability of this pattern formation phenomenon is proposed to be the preferential adsorption of polar or polarizable organic molecules on surface ridges, where the contorted double layer produces a higher electric potential gradient. The enhanced relative coverage shields the anode and induces a smaller dissolution rate at the ridges. The instability is balanced by surface diffusion of the adsorbate to yield a length scale of 4pDs/kd 1/2, where Ds is the surface diffusivity and kd is the desorption coefficient of the adsorbate. This correlates well with the measured wavelength. Nonlinear effects also select the pattern (stripes or hexagons) that give rise to the same overall diffusion-controlled constant flux despite the lower rates at the relatively uncovered valleys as the voltage is increased. The hexagon pattern is preferred at high voltage due to its larger valley area. A mathematical model for pattern formation is developed to successfully correlate the experimental data. The model includes a long-wavelength expansion of the double-layer field yielding an interface evolution equation that reproduces all of the observed patterns. In particular, bifurcation analysis and numerical simulation yield a single voltage-dependent dimensionless parameter xi that measures a balance between smoothing of adsorbate concentration by electric-field-dependent surface diffusion and fluctuation due to interfacial curvature and stretching. Randomly oriented stripes are favored at large xi (low voltage), while random hills dominate at small xi (high voltage) with perfectly periodic stripes and hexagonal hill patterns occurring within a small window near xi = 1. These predictions are in qualitative and quantitative agreement with our measurements. The model hence demonstrates that electropolishing-pattern formation is a very common phenomenon provided the right organic additive is placed in the electrolyte.; The patterned surface of the metal was used as the template for anodization in order to fabricate regular and very anisotropic porous alumina films. The obtained self-assembled nanostructured materials demonstrate a high potential for electronic applications.