Potential landscapes and induced charges near metallic islands in three dimensions.
We calculate electrostatic potential landscapes for an external probe charge in the presence of a set of metallic islands. Our numerical calculation in three dimensions (3D) uses an efficient grid relaxation technique. The well-known relaxation algorithm for solving the Poisson equation in two dimensions is generalized to 3D. In addition, all charges on the system, free as well as induced charges, are determined accurately and self-consistently to satisfy the desired boundary conditions. This allows the straightforward calculation of the potential on the outer boundary using the free space electrostatic Green's function, as well as the calculation of the entire capacitance matrix of the system. Physically interesting examples of nanoscale systems are presented and analyzed.
Weichselbaum
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Department of Physics and Astronomy, and Nanoscale and Quantum Phenomena Institute, Ohio University, Athens, OH 45701, USA.
Ulloa
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