title: A generalized Poisson solver for first-principles device simulations.
abstract: 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.
authors.affiliation: Nanoscale Simulations, ETH Zürich, 8093 Zürich, Switzerland.
authors.forename: Mohammad Hossein
authors.initials: MH
authors.lastname: Bani-Hashemian
authors.affiliation: Integrated Systems Laboratory, ETH Zürich, 8092 Zürich, Switzerland.
authors.forename: Sascha
authors.initials: S
authors.lastname: Brück
authors.affiliation: Integrated Systems Laboratory, ETH Zürich, 8092 Zürich, Switzerland.
authors.forename: Mathieu
authors.initials: M
authors.lastname: Luisier
authors.affiliation: Nanoscale Simulations, ETH Zürich, 8093 Zürich, Switzerland.
authors.forename: Joost
authors.initials: J
authors.lastname: VandeVondele