A generalized Poisson solver for first-principles device simulations

Journal Article · Thu Jan 28 04:00:00 EST 2016 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.4940796· OSTI ID:22493686

Bani-Hashemian, Mohammad Hossein; VandeVondele, Joost ^[1]; Brück, Sascha; Luisier, Mathieu ^[2]

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1. Nanoscale Simulations, ETH Zürich, 8093 Zürich (Switzerland)
2. Integrated Systems Laboratory, ETH Zürich, 8092 Zürich (Switzerland)

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.

• OSTI ID: 22493686
• Journal Information: Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 4 Vol. 144; ISSN JCPSA6; ISSN 0021-9606
• Country of Publication: United States
• Language: English

Related Subjects

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
ALGORITHMS
BOUNDARY CONDITIONS
CONVERGENCE
DENSITY
DENSITY FUNCTIONAL METHOD
DIELECTRIC MATERIALS
DIRICHLET PROBLEM
ELECTRIC POTENTIAL
ELECTRONIC STRUCTURE
ITERATIVE METHODS
LAPLACIAN
MOLECULAR DYNAMICS METHOD
PERMITTIVITY
POISSON EQUATION
WAVE PROPAGATION