A generalized Poisson solver for first-principles device simulations

• Published in: The Journal of chemical physics Vol. 144; no. 4; p. 044113
• Main Authors: Bani-Hashemian, Mohammad Hossein, Brück, Sascha, Luisier, Mathieu, VandeVondele, Joost
• Format: Journal Article
• Language: English
• Published: United States American Institute of Physics 28.01.2016
• Subjects: ALGORITHMS; BOUNDARY CONDITIONS; Computer simulation; Continuum modeling; CONVERGENCE; DENSITY; DENSITY FUNCTIONAL METHOD; Density functional theory; DIELECTRIC MATERIALS; DIRICHLET PROBLEM; ELECTRIC POTENTIAL; Electronic devices; ELECTRONIC STRUCTURE; First principles; INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; ITERATIVE METHODS; LAPLACIAN; Mathematical analysis; Molecular dynamics; MOLECULAR DYNAMICS METHOD; PERMITTIVITY; Physics; POISSON EQUATION; Saddle points; WAVE PROPAGATION
• ISSN: 0021-9606; 1089-7690
• DOI: 10.1063/1.4940796

Electronic structure calculations of atomistic systems based on density functional theory involve solving the Poisson equation. In this paper, we present a plane-wave based algorithm for solving the generalized Poisson equation subject to periodic or homogeneous Neumann conditions on the boundaries of the simulation cell and Dirichlet type conditions imposed at arbitrary subdomains. In this way, source, drain, and gate voltages can be imposed across atomistic models of electronic devices. Dirichlet conditions are enforced as constraints in a variational framework giving rise to a saddle point problem. The resulting system of equations is then solved using a stationary iterative method in which the generalized Poisson operator is preconditioned with the standard Laplace operator. The solver can make use of any sufficiently smooth function modelling the dielectric constant, including density dependent dielectric continuum models. For all the boundary conditions, consistent derivatives are available and molecular dynamics simulations can be performed. The convergence behaviour of the scheme is investigated and its capabilities are demonstrated.