Two-dimensional Poisson Solver Research Articles

Fast simulations of extragalactic microlensing

We present a new and very fast method for producing microlensing magnification maps at high optical depths. It is based on the combination of two approaches: (a) the two-dimensional Poisson solver for a deflection potential and (b) inverse polygon mapping. With our method we extremely reduce the computing time for the generation of magnification patterns and avoid the use of highly demanding computer resources. For example, the generation of a magnification map of size 2000 × 2000 pixels, covering a region of 20 Einstein radii, takes a few seconds on a state-of-the-art laptop. The method presented here will facilitate the massive production of magnification maps for extragalactic microlensing studies within the forthcoming surveys without the need for large computer clusters. The modest demand of computer power and a fast execution time allow the code developed here to be placed on a standard server and thus provide the public online access through a web-based interface.

Tip geometry effects in dopant profiling by scanning microwave microscopy

In this paper, the impact of the tip radius on dopant profiling by scanning microwave microscopy is investigated. The cantilevers are very likely to erode in such measurements, and thus, a two-dimensional Poisson solver was used to calculate the lateral spatial resolution as a function of tip radius and doping. Moreover, a strong correlation between the slope of the calibration curves and the tip diameter was found. The slope of the calibration curves increases toward −0.5 and saturates as the radius approaches values of 150 nm, which is in agreement with experimental data obtained from scanning microwave microscopy.

Plasmonic noise in silicon nanolayers

We report a microscopic investigation of the spectrum of voltage fluctuations in nanometric n-Si layers. Theory makes use of a Monte Carlo simulator self-consistently coupled with a two-dimensional Poisson solver. We consider layers of variable thickness W in the range of 2–100 nm and variable length L in the range of 10–1000 nm embedded in an external dielectric medium. Calculations are performed at T=300 K for different doping levels and in the presence of an applied voltage of increasing strength. The spectra are found to exhibit peaks centered on the terahertz region. For W≥100 nm and carrier densities of 5×1017 and 5×1018 cm−3, the frequency peaks agree with the value of the three dimensional plasma frequency. For W≤100 nm, the results exhibit a plasma frequency that depends on L, thus implying that the oscillation mode is dispersive. The corresponding frequency covers a wide range of values of 0.2–10 THz and is in agreement with the values of the two-dimensional plasma frequency predicted by existing analytical models. At sufficiently high voltages, the two-dimensional plasma peak is washed out and we observe the onset of a peak in the subterahertz region which is associated with transit time instabilities induced by current saturation conditions.

Scalable Direct Vlasov Solver with Discontinuous Galerkin Method on Unstructured Mesh

This paper presents the development of parallel direct Vlasov solvers with discontinuous Galerkin (DG) method for beam and plasma simulations in four dimensions. Both physical and velocity spaces are in two dimesions (2P2V) with unstructured mesh. Contrary to the standard particle-in-cell (PIC) approach for kinetic space plasma simulations, i.e., solving Vlasov-Maxwell equations, direct method has been used in this paper. There are several benefits to solving a Vlasov equation directly, such as avoiding noise associated with a finite number of particles and the capability to capture fine structure in the plasma. The most challanging part of a direct Vlasov solver comes from higher dimensions, as the computational cost increases as $N^{2d}$, where d is the dimension of the physical space. Recently, due to the fast development of supercomputers, the possibility has become more realistic. Many efforts have been made to solve Vlasov equations in low dimensions before; now more interest has focused on higher dimensions. Different numerical methods have been tried so far, such as the finite difference method, Fourier Spectral method, finite volume method, and spectral element method. This paper is based on our previous efforts to use the DG method. The DG method has been proven to be very successful in solving Maxwell equations, and this paper is our first effort in applying the DG method to Vlasov equations. DG has shown several advantages, such as local mass matrix, strong stability, and easy parallelization. These are particularly suitable for Vlasov equations. Domain decomposition in high dimensions has been used for parallelization; these include a highly scalable parallel two-dimensional Poisson solver. Benchmark results have been shown and simulation results will be reported.

Monte Carlo simulation of ballistic transport in high-mobility channels

By means of Monte Carlo simulations coupled with a two-dimensional Poisson solver, we evaluate directly the possibility to use high mobility materials in ultra fast devices exploiting ballistic transport. To this purpose, we have calculated specific physical quantities such as the transit time, the transit velocity, the free flight time and the mean free path as functions of applied voltage in InAs channels with different lengths, from 2000 nm down to 50 nm. In this way the transition from diffusive to ballistic transport is carefully described. We remark a high value of the mean transit velocity with a maximum of 14×105 m/s for a 50 nm-long channel and a transit time shorter than 0.1 ps, corresponding to a cutoff frequency in the terahertz domain. The percentage of ballistic electrons and the number of scatterings as functions of distance are also reported, showing the strong influence of quasi-ballistic transport in the shorter channels.

Orientation Effects in Ballistic High-Strained P-type Si Nanowire FETs

In order to design and optimize high-sensitivity silicon nanowire-field-effect transistor (SiNW FET) pressure sensors, this paper investigates the effects of channel orientations and the uniaxial stress on the ballistic hole transport properties of a strongly quantized SiNW FET placed near the high stress regions of the pressure sensors. A discrete stress-dependent six-band k.p method is used for subband structure calculation, coupled to a two-dimensional Poisson solver for electrostatics. A semi-classical ballistic FET model is then used to evaluate the ballistic current-voltage characteristics of SiNW FETs with and without strain. Our results presented here indicate that [110] is the optimum orientation for the p-type SiNW FETs and sensors. For the ultra-scaled 2.2 nm square SiNW, due to the limit of strong quantum confinement, the effect of the uniaxial stress on the magnitude of ballistic drive current is too small to be considered, except for the [100] orientation. However, for larger 5 nm square SiNW transistors with various transport orientations, the uniaxial tensile stress obviously alters the ballistic performance, while the uniaxial compressive stress slightly changes the ballistic hole current. Furthermore, the competition of injection velocity and carrier density related to the effective hole masses is found to play a critical role in determining the performance of the nanotransistors.

Monte Carlo analysis of the noise behavior in Si bipolar junction transistors and SiGe heterojunction bipolar transistors at radio frequencies

We present a comparative analysis of the current spectral densities in a Si bipolar junction transistor (BJT) and a SiGe heterojunction bipolar transistor (HBT) of identical geometry performed by means of an ensemble Monte Carlo simulator self consistently coupled with a two-dimensional Poisson solver. We focus on the physical origin of the different noise sources in the transistors at rf when varying the injection level conditions. At low injection the spectral density of base current fluctuations, SJB(0), is governed by thermal noise related to the base resistance, while the collector spectral density, SJC(0), reaches a typical shot noise response. At high current density the onset of high injection in the base and the base push-out play an important role in the noise behavior of both transistors. Thus, SJC(0) deviates from the typical shot noise response. Hot carrier effects are also present. In the HBT, these effects are less important than in the BJT due to the SiGe/Si heterointerface, and SJB(0) can be neglected in the overall noise analysis because of the Ge content benefits when the structure enters the high-injection regime.

An efficient multigrid Poisson solver for device simulations

The aim of this paper is to show that the multigrid approach can provide an efficient two-dimensional Poisson solver used in the analysis of realistic semiconductor devices based on particle simulators. Our robust implementation of the multigrid method is faster by one or two orders of magnitude than standard successive over-relaxation solvers and is capable, at the same time, of efficiently handling highly inhomogeneous grids and irregular boundary conditions relevant for realistic devices. All essential parts of the algorithm, such as coarsening, prolongation, restriction, and relaxation, have been adapted and optimized to deal with these complex geometries and large variations in the charge density. In particular, a new variant of the Gauss-Seidel-type relaxation scheme is introduced that is particularly suited for grids that lack globally dominant directions. As an example, the multigrid Poisson solver has been applied to two different electronic devices, a GaAs High Electron Mobility Transistor and a Si Metal Oxide Semiconductor Field Effect Transistor.

Monte Carlo simulation of 0.35- mu m gate-length GaAs and InGaAs HEMTs

A first-principles theoretical comparison of the performances of identical Al/sub 0.32/Ga/sub 0.68/As/GaAs and Al/sub 0.15/Ga/sub 0.15/As/In/sub 0.15/Ga/sub 0.85/As/GaAs pseudomorphic HEMTs based on an ensemble Monte Carlo simulation coupled with a two-dimensional Poisson solver is presented. The Monte Carlo calculations incorporate the full physics of the device operation. As a test of the accuracy with which the calculations successfully model a real device, the calculated current-voltage characteristic of the pseudomorphic device is first compared to recent experimental measurements made on a comparable structure, showing excellent agreement over a full range of gate and drain biases. The device performance as measured in terms of the transconductance, cutoff frequency, and current-voltage characteristics of both devices can then be compared as a function of gate and drain bias. It is found that the pseudomorphic HEMT outperforms the conventional GaAs/AlGaAs device by approximately a factor of two in the above-mentioned criteria. The greatly improved performance of the pseudomorphic HEMT over the GaAs device stems predominantly from greater confinement of the electrons within the high-mobility two-dimensional system, higher electron drift velocity, and greater gamma valley confinement. >

Calculation of the breakdown voltage of a vertical MOSFET using a modified finite-difference model

A two-dimensional Poisson solver is introduced which employs a modified finite-difference model with build-in depletion-layer logic, making it unnecessary to include the semiconductor equations. The results obtained are restricted to reverse-breakdown calculations for voltages exceeding the internal potentials. Any number of dielectrics, contacts or semiconductor regions may be included. The avalanche multiplication calculations are based on the coefficients of Van Over-straeten and DeMan (1970).

Calculation of the electron velocity distribution in high electron mobility transistors using an ensemble Monte Carlo method

The electron velocity distribution is calculated for an idealized model of the high electron mobility transistor using a many-particle Monte Carlo model and a self-consistent two-dimensional Poisson solver. Hot electron effects, nonstationary effects, and real space transfer are analyzed. The results show that significant velocity overshoot, 2.8×107 cm/s at 300 K and 3.7×107 cm/s at 77 K exists under the gate and that the velocity overshoot is limited by both k-space transfer and real-space transfer. The values of the overshoot velocities are much smaller than those obtained from the more conventional drift-diffusion model.