Modeling electrochemical deposition inside nanotubes to obtain metal-semiconductor multiscale nanocables or conical nanopores

Nanocables with a radial metal-semiconductor heterostructure have recently been prepared by electrochemical deposition inside metal nanotubes. First, a bare nanoporous polycarbonate track-etched membrane is coated uniformly with a metal film by electroless deposition. The film forms a working electrode for further deposition of a semiconductor layer that grows radially inside the nanopore when the deposition rate is slow. We propose a new physical model for the nanocable synthesis and study the effects of the deposited species concentration, potential-dependent reaction rate, and nanopore dimensions on the electrochemical deposition. The problem involves both axial diffusion through the nanopore and radial transport to the nanopore surface, with a surface reaction rate that depends on the axial position and the time. This is so because the radial potential drop across the deposited semiconductor layer changes with the layer thickness through the nanopore. Since axially uniform nanocables are needed for most applications, we consider the relative role of reaction and axial diffusion rates on the deposition process. However, in those cases where partial, empty-core deposition should be desirable (e.g., for producing conical nanopores to be used in single nanoparticle detection), we give conditions where asymmetric geometries can be experimentally realized.