Three-dimensional Poisson Solver Research Articles

A study of the avalanche-to-streamer transition in arbitrary gases by particle simulation

We systematically investigate the avalanche-to-streamer transition (AST) over a wide range of pressures and homogenous background electric fields and for a comprehensive list of gases, namely pure nitrogen, carbon dioxide, oxygen, argon, sulfur hexafluoride and synthetic air. The discharge starts from an initial seed electron and is temporally followed from the avalanche regime, through the first significant distortion of the background field and the subsequent increasing deviation from the Gaussian electron density profile, up to the occurrence of runaway electrons accompanied by the sudden and dramatic increase of electron energy and electron number multiplication. We detect weak influence of the background electric field value and the gas composition, but strong influence of the gas density on the electron number at which the transition occurs. The simulations are performed by means of a fully-interacting particle simulation program that combines a particle-in-cell/Monte Carlo collision model (PIC/MCC) with a three-dimensional Poisson solver in order to account for the space charge generated by the electrons and ions. The freely-available program is based on the METHES code and is universally applicable to arbitrary gas mixtures with complete cross section sets.

Efficient three-dimensional Poisson solvers in open rectangular conducting pipe

Three-dimensional (3D) Poisson solver plays an important role in the study of space-charge effects on charged particle beam dynamics in particle accelerators. In this paper, we propose three new 3D Poisson solvers for a charged particle beam in an open rectangular conducting pipe. These three solvers include a spectral integrated Green function (IGF) solver, a 3D spectral solver, and a 3D integrated Green function solver. These solvers effectively handle the longitudinal open boundary condition using a finite computational domain that contains the beam itself. This saves the computational cost of using an extra larger longitudinal domain in order to set up an appropriate finite boundary condition. Using an integrated Green function also avoids the need to resolve rapid variation of the Green function inside the beam. The numerical operational cost of the spectral IGF solver and the 3D IGF solver scales as O(Nlog(N)), where N is the number of grid points. The cost of the 3D spectral solver scales as O(NnN), where Nn is the maximum longitudinal mode number. We compare these three solvers using several numerical examples and discuss the advantageous regime of each solver in the physical application.

Nonequilibrium aspects of armchair graphene nanoribbon conduction

Electron quantum transport is theoretically studied for finite-size armchair graphene nanoribbons biased within source and drain metallic electrodes, using an extended-Hückel-based Green's function coupled to a three-dimensional Poisson solver. The analysis evidences dynamic nonequilibrium electron charging phenomena that can affect the conduction mechanism by provoking electronic structure alterations. The origin of such process can be traced in a tracking relationship between the device's local density of states and the electrochemical potentials of the contacts. Such effect has no equivalent in the semiclassical limit.

Contact Effects in Graphene Nanoribbon Transistors

The effects of the various contact types and shapes on the performance of Schottky barrier graphene nanoribbon field-effect-transistors (GNRFETs) have been investigated using a real-space quantum transport simulator based on the NEGF approach self-consistently coupled to a three-dimensional Poisson solver for treating the electrostatics. The device channel considered is a double gate semiconducting armchair nanoribbon. The types of contacts considered are (a) a semi-infinite normal metal, (b) a semi-infinite graphene sheet, (c) finite size rectangular shape armchair graphene contacts, (d) finite size wedge shape graphene contacts, and (e) zigzag graphene nanoribbon contacts. Among these different contact types, the semi-infinite graphene sheet contacts show the worst performance because of their very low density of states around the Dirac point resulting in low transmission possibility through the Schottky barrier, both at ON and OFF states. Although all other types of contacts can have significant enhancement in I ON to I OFF ratio, the zigzag GNR contacts show promising and size invariant performance due to the metallic properties.

Bias-driven local density of states alterations and transport in ballistic molecular devices

We study dynamic nonequilibrium electron charging phenomena in ballistic molecular devices at room temperature that compromise their response to bias and whose nature is evidently distinguishable from static Schottky-type potential barriers. Using various metallic/semiconducting carbon nanotubes and alkane dithiol molecules as active parts of a molecular bridge, we perform self-consistent quantum transport calculations under the nonequilibrium Green's function formalism coupled to a three-dimensional Poisson solver for a mutual description of chemistry and electrostatics. Our results sketch a particular tracking relationship between the device's local density of states and the contact electrochemical potentials that can effectively condition the conduction process by altering the electronic structure of the molecular system. Such change is unassociated to electronic/phononic scattering effects while its extent is highly correlated to the conducting character of the system, giving rise to an increase of the intrinsic resistance of molecules with a semiconducting character and a symmetric mass-center disposition.

Nonequilibrium electron charging in carbon-nanotube-based molecular bridges

We evidence the importance of electron charging under nonequilibrium conditions for carbon-nanotube-based molecular bridges, using a self-consistent Green’s function method with an extended Hückel Hamiltonian and a three-dimensional Poisson solver. Our analysis demonstrates that such feature is highly dependent on the chirality of the carbon nanotube as well as on the type of the contact metal, conditioning in a nongeneralized way the system’s conduction mechanism. Based on its impact on transport, we argue that self-consistency is essential for the current-voltage calculations of semiconducting nanotubes, whereas less significant in the case of metallic ones.

A parallel 3D Poisson solver for space charge simulation in cylindrical coordinates

This paper presents the development of a parallel three-dimensional Poisson solver in cylindrical coordinate system for the electrostatic potential of a charged particle beam in a circular tube. The Poisson solver uses Fourier expansions in the longitudinal and azimuthal directions, and Spectral Element discretization in the radial direction. A Dirichlet boundary condition is used on the cylinder wall, a natural boundary condition is used on the cylinder axis and a Dirichlet or periodic boundary condition is used in the longitudinal direction. A parallel 2D domain decomposition was implemented in the ( r , θ ) plane. This solver was incorporated into the parallel code PTRACK for beam dynamics simulations. Detailed benchmark results for the parallel solver and a beam dynamics simulation in a high-intensity proton LINAC are presented. When the transverse beam size is small relative to the aperture of the accelerator line, using the Poisson solver in a Cartesian coordinate system and a Cylindrical coordinate system produced similar results. When the transverse beam size is large or beam center located off-axis, the result from Poisson solver in Cartesian coordinate system is not accurate because different boundary condition used. While using the new solver, we can apply circular boundary condition easily and accurately for beam dynamic simulations in accelerator devices.

Efficient and accurate three-dimensional Poisson solver for surface problems

We present a method that gives highly accurate electrostatic potentials for systems where we have periodic boundary conditions in two spatial directions but free boundary conditions in the third direction. These boundary conditions are needed for all kinds of surface problems. Our method has an O(N log N) computational cost, where N is the number of grid points, with a very small prefactor. This Poisson solver is primarily intended for real space methods where the charge density and the potential are given on a uniform grid.

Three-dimensional Poisson solver for a charged beam with large aspect ratio in a conducting pipe

In this paper, we present a three-dimensional Poisson equation solver for the electrostatic potential of a charged beam with large longitudinal to transverse aspect ratio in a straight and a bent conducting pipe with open-end boundary conditions. In this solver, we have used a Hermite–Gaussian series to represent the longitudinal spatial dependence of the charge density and the electric potential. Using the Hermite–Gaussian approximation, the original three-dimensional Poisson equation has been reduced into a group of coupled two-dimensional partial differential equations with the coupling strength proportional to the inverse square of the longitudinal-to-transverse aspect ratio. For a large aspect ratio, the coupling is weak. These two-dimensional partial differential equations can be solved independently using an iterative approach. The iterations converge quickly due to the large aspect ratio of the beam. For a transverse round conducting pipe, the two-dimensional Poisson equation is solved using a Bessel function approximation and a Fourier function approximation. The three-dimensional Poisson solver can have important applications in the study of the space-charge effects in the high intensity proton storage ring accelerator or induction linear accelerator for heavy ion fusion where the ratio of bunch length to the transverse size is large.

Modeling of quantum effects in ultrasmall FD-SOI MOSFETs with effective potentials and three-dimensional Monte Carlo

In this work, the effective potential is employed to account for the quantum mechanical effects of charge setback and elevated ground-state energy in the inversion layer of fully depleted (FD) SOI MOSFETs. We use the effective potential along with a three-dimensional Poisson solver and a Monte Carlo transport kernel to illustrate these quantum mechanical effects on the output characteristics of the transistor. It is demonstrated that the inclusion of such effects has a significant influence on the threshold voltage, carrier energy, and drive current of the device.

Parallel 3D Poisson solver for a charged beam in a conducting pipe

In this paper, we present a parallel three-dimensional Poisson solver for the electrostatic potential of a charged beam in a round or rectangular conducting pipe with open-end boundary conditions. This solver uses an eigenfunction expansion in the transverse direction and a finite difference method in the longitudinal direction. The computational domain in the longitudinal direction contains only the beam since only the potential inside the beam will be calculated. The potential on both ends of the beam is matched into the source-free region for each eigenmode. This method avoids the use of a large computational domain outside the beam to implement the open boundary condition. This saves unnecessary computational time and memory storage that would be required if a large computational domain was used to simulate the open boundary. Parallel implementation using a two-dimensional domain decomposition approach and a message passing paradigm shows good scalability on both distributed memory machines and distributed shared-memory machines. This solver has important applications in accelerator physics studies that involve modeling high-intensity beam dynamics. As a specific example, we present results from large-scale simulations of beam halo formation in a linear accelerator.

Surface roughness of SiO2 from a remote microwave plasma enhanced chemical vapor deposition process

We have investigated the roughness of the top surface of silicon dioxide deposited via a remote plasma enhanced chemical vapor deposition (RPECVD) process in a microwave reactor. We find a roughening transition at a deposition temperature of approximately 250 °C. Above this temperature, the surface is fairly smooth (root mean square roughness ∼0.3 nm). Below this deposition temperature, the oxide surface becomes extremely rough. Rapid thermal annealing at 900 °C does not eliminate this roughness, which is very nonuniform at the nanometer scale. For very thin RPECVD oxide applications, oxide surface roughness could be a limitation. We have used our three-dimensional Poisson solver in order to investigate the effects of oxide surface roughness taken from actual atomic force microscopy measurements on the confining potential within the silicon inversion layer of a metal–oxide–semiconductor (MOS) field effect transistor. In order to assess the quality of our process and system, oxides are characterized electrically with MOS capacitors, and structurally with Fourier transform infrared spectroscopy, high-resolution cross-sectional transmission electron microscopy, and etch rates in HF containing solutions.