2003/06/24 by Andreas Weichselbaum, A. Weichselbaum, S. E. Ulloa +1
Engineering · Mathematics · Physics and Astronomy · #Advancements in Semiconductor Devices and Circuit Design #Boundary (topology) #Boundary value problem #Capacitance #Charge (physics) #Classical mechanics #Computer science #Electrode #Electrostatics #Function (biology) #Geometry #Grid #Materials science #Mathematical analysis #Mathematics #Matrix (chemical analysis) #Physics #Poisson's equation #Quantum mechanics #Relaxation (psychology) #Semiconductor materials and devices #Space (punctuation) #Statistical physics #Surface and Thin Film Phenomena #cond-mat.mes-hall
paper · pdf · doi:10.1103/physreve.68.056707
6 pages, 6 figures, submitted to PRE
arxiv created 2003/06/24 · openalex publication_date 2003/11/25 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.