Solving Poisson Equation Research Articles

An Iterative Two-Fluid Pressure Solver Based on the Immersed Interface Method

AbstractAn iterative solver based on the immersed interface method is proposed to solve the pressure in a two-fluid flow on a Cartesian grid with second-order accuracy in the infinity norm. The iteration is constructed by introducing an unsteady term in the pressure Poisson equation. In each iteration step, a Helmholtz equation is solved on the Cartesian grid using FFT. The combination of the iteration and the immersed interface method enables the solver to handle various jump conditions across two-fluid interfaces. This solver can also be used to solve Poisson equations on irregular domains.

Image melding

Current methods for combining two different images produce visible artifacts when the sources have very different textures and structures. We present a new method for synthesizing a transition region between two source images, such that inconsistent color, texture, and structural properties all change gradually from one source to the other. We call this process image melding . Our method builds upon a patch-based optimization foundation with three key generalizations: First, we enrich the patch search space with additional geometric and photometric transformations. Second, we integrate image gradients into the patch representation and replace the usual color averaging with a screened Poisson equation solver. And third, we propose a new energy based on mixed L 2 /L 0 norms for colors and gradients that produces a gradual transition between sources without sacrificing texture sharpness. Together, all three generalizations enable patch-based solutions to a broad class of image melding problems involving inconsistent sources: object cloning, stitching challenging panoramas, hole filling from multiple photos, and image harmonization. In several cases, our unified method outperforms previous state-of-the-art methods specifically designed for those applications.

Image melding

Current methods for combining two different images produce visible artifacts when the sources have very different textures and structures. We present a new method for synthesizing a transition region between two source images, such that inconsistent color, texture, and structural properties all change gradually from one source to the other. We call this process image melding. Our method builds upon a patch-based optimization foundation with three key generalizations: First, we enrich the patch search space with additional geometric and photometric transformations. Second, we integrate image gradients into the patch representation and replace the usual color averaging with a screened Poisson equation solver. And third, we propose a new energy based on mixed L2/L0 norms for colors and gradients that produces a gradual transition between sources without sacrificing texture sharpness. Together, all three generalizations enable patch-based solutions to a broad class of image melding problems involving inconsistent sources: object cloning, stitching challenging panoramas, hole filling from multiple photos, and image harmonization. In several cases, our unified method outperforms previous state-of-the-art methods specifically designed for those applications.

DGMOSFET의 문턱전압과 스켈링 이론의 관계

This paper has presented the relation of scaling theory and threshold voltage of double gate(DG) MOSFET. In the case of conventional MOSFET, current and switching frequency have been analyzed based on scaling theory. To observe the possibility of application of scaling theory for threshold voltage of DGMOSFET, the change of threshold voltage has been observed and analyzed according to scaling theory. The analytical potential distribution of Poisson equation has been used, and this model has been already verified. To solve Poisson equation, charge distribution such as Gaussian function has been used. As a result, it has been observed that threshold voltage is grealty changed according to scaling factor and change rate of threshold voltages is traced for scaling of doping concentration in channel. This paper has explained for the best modified scaling theory reflected the influence of two gates as using weighting factor when scaling theory has been applied for channel length and channel thickness.

Surface-borehole electric potential survey in layered media and its applications

The method in which a source is set on the surface and electric potential is received in the borehole is called surface-borehole electric potential technique. Technique of surface-borehole electric potential was employed to study electric response of layered formation. The electric potential was obtained by solving Poisson equation with finite difference method. In the course of calculation, forward modeling with finite difference method was realized by adopting bandwidth non-zero storage technique and the incomplete Cholesky conjugate gradient method. The results show that method of surface-borehole can acquire anomalous electric potential corresponding to geo-electric layers. In addition, application of appropriate mathematical operator can improve the resolution. Moreover, overburden low resistivity layers have severe influence on measuring results of surface-borehole electric potential. However, bottom low resistivity layers play a positive role in the measurement.

InAs/InAsSb strain balanced superlattices for optical detectors: Material properties and energy band simulations

InAsSb/InAs type II strain balanced superlattices lattice matched to GaSb have recently been proposed as an alternative to InAs/(In)GaSb short period superlattices for mid- to long infrared photodetectors. Photoluminescence data at 4 K of OMVPE grown InAsSb (multi-) quantum wells in an InAs matrix on InAs and GaSb substrates is presented for Sb compositions between 4% and 27%. The measured transition energies are simulated with a self-consistent Poisson and Schroedinger equation solver that includes strain and band-offsets. The fitted parameters are then used to predict the type II transition energies of InAsSb/InAs strain balanced superlattice absorber stacks at 77 K for different compositions and periods. The optical matrix element was calculated and compared with InAs/(In)GaSb superlattices. The InAsSb/InAs structures can be designed with higher or equal matrix elements for longer periods. Finally, the initial optical response data of an unoptimized strain balanced InAs0.79Sb0.21/InAs detector with a 40 nm period are shown. Its cutoff wavelength is 0.15 eV (8.5 μm), in good agreement with the predicted type II transition energy of 0.17 eV.

Study of gate depletion effect in strained Si NMOSFET with polycrystalline silicon germanium gate

Based on the analysis of Poly-Si1-xGex gate work function and by solving Poisson equation, the models of vertical electric field and potential distribution in strained Si NMOSFET with Poly-Si1-xGex gate are obtained; threshold voltage model and the gate depletion thickness and it's normalization model are established in strained Si NMOSFET based on the above results, with the gate depletion effect of Poly-Si1-xGex taken into account. Then the influences of device geometrical and physical parameters of device especially the Ge fraction on Poly-Si1-xGex gate depletion thickness are investigated. Furthermore, the effect of gate depletion thickness on threshold voltage is analyzed. It shows that the poly depletion thickness decreases with the increases of Ge fraction and gate doping concentration, while it increases with the increase of substrate doping concentration. Furthermore, the threshold voltage increases with the increase of gate depletion thickness. The results can provide theoretical references to the design of strained Si devices.

Simulation of the Formation of an Ion Beam by Extraction From a Magnetically Confined Plasma

A computational simulation of the formation of an ion beam extracted from a magnetically confined ECR plasma is made. The first simulation stage consists of calculating of the electrostatic field produced by an extraction system. The extraction system is composed of three cylindrically hollow symmetrical electrodes and its respective shielding box. For the purpose of calculating the extraction and focalization electrostatic field, a finite-difference algorithm that solves Laplace equation within the ion propagation volume and allows studying the dependency of the electrostatic field on the geometrical configuration of the extraction system is developed. The second stage consists in calculating the electric and magnetic fields due to extracted ions themselves by solving Poisson equation using the fast Fourier transform technique based on a high-order difference approximation with identity expansion scheme. Finally, an algorithm based on Boris integration scheme to calculate ion trajectories with the objective of simulating the movement on an ion beam due to the field generated by electrodes and beam itself is developed. Based upon the results obtained, the search for an optimized ion extraction system from a 14-GHz ECR ion source is begun. Preliminary configurations are obtained and shown.

Gate Underlap Design for Short Channel Effects Control in Cylindrical Gate-all-around MOSFETs based on an Analytical Model

Gate underlap structure can be utilized to improve the immunity to short channel effects in MOSFET devices. In this work, gate underlap design scheme in cylindrical gate-all-around MOSFETs is explored based on an analytical model. This model takes into account the fringing field from gate electrode to underlap regions based on conformal mapping and a channel length transformation method. By solving Poisson equations in the underlap and channel regions and matching the boundary conditions, this model reproduces the channel potential profile in subthreshold operation region. Both symmetric and asymmetric underlap structures are covered. The developed model is verified extensively with TCAD simulations. A gate underlap design scheme is then provided based on this analytical model.

Evaluation of Two Acceleration Techniques in a Multithreaded 2D Poisson Equation Solver

Two acceleration techniques, based on additive corrections are evaluated with a multithreaded 2D Poisson equation solver. The popular multigrid algorithm with 2-level grid is compared with the traditional block-correction strategy. In both, single-processor and distributed architectures, block correction is faster than the multigrid due mainly to the smaller cost that the solution of a 1D linear system has over one 2D linear system. Results in both cluster tested show that block correction can reduce significantly the computing time in the solution of very large linear systems. These calculations confirm that the Red/Black ordering is effective only if data fit entirely in cache memory.

Determination of the electric field intensity and space charge density versus height prior to triggered lightning

[1] We infer the vertical profiles of space charge density and electric field intensity above ground by comparing modeling and measurements of the ground-level electric field changes caused by elevating grounded lightning-triggering wires. The ground-level electric fields at distances of 60 m and 350 m were measured during six wire launches that resulted in triggered lightning. The wires were launched when ground-level electric fields ranged from 3.2 to 7.6 kV m−1 and the triggering heights ranged from 123 to 304 m. From wire launch time to lightning initiation time, the ground-level electric field reduction at 60 m ranged from 2.2 to 3.4 kV m−1, with little ground-level electric field reduction being observed at 350 m. We observed that the triggering heights were inversely proportional to the ground-level electric field when the wires were launched. Our Poisson equation solver simulates the ground-level electric field changes as the grounded wires extend in assumed vertically varying profiles of space charge density and electric field intensity. Our model reproduces the measured ground-level electric field changes when the assumed space charge density decays exponentially with altitude, with ground-level charge densities between 1.5 and 7 nC m−3, space charge exponential decay height constants ranging from 67 to 200 m, and uniform electric field intensities far above the space charge layer ranging from 20 to 60 kV m−1. Our model predicts typical charge densities on the wires of some tens of μC m−1 with milliampere-range currents flowing into the wires from ground to supply the wire charge.

A spectral collocation method based on Haar wavelets for Poisson equations and biharmonic equations

In this work, we present a computational method for solving Poisson equations and biharmonic equations which are based on the use of Haar wavelets. The first transform the spectral coefficients into the nodal variable values. The second use Kronecker products to construct the approximations for derivatives over a tensor product grid of the horizontal and vertical blocks. Finally, solve the obtained system of algebraic equations. The efficiency of the method is demonstrated by four numerical examples.

A novel linearly-weighted gradient smoothing method (LWGSM) in the simulation of fluid dynamics problem

This paper describes a novel linearly-weighted gradient smoothing method (LWGSM). The proposed method is based on irregular cells and thus can be used for problems with arbitrarily complex geometrical boundaries. Based on the analysis about the compactness and the positivity of coefficients of influence of their stencils for approximating a derivative, one favorable scheme (VIII) is selected among total eight proposed discretization schemes. This scheme VIII is successively verified and carefully examined in solving Poisson equations, subjected to changes in the number of nodes, the shapes of cells and the irregularity of triangular cells, respectively. Strong form of incompressible Navier–Stokes equations enhanced with artificial compressibility terms are tackled, in which the spatial derivatives are approximated by consistent and successive use of gradient smoothing operation over smoothing domains at various locations. All the test cases using LWGSM solver exhibits its robust, stable and accurate behaviors. The attained incompressible LWGSM solutions show good agreements with experimental and literature data. Therefore, the proposed LWGSM can be reliably used for accurate solutions to versatile fluid flow problems.

2D analytical calculation of the electric field in lightly doped Schottky barrier double-gate MOSFETs and estimation of the tunneling/thermionic current

In this paper we present a new approach to calculate the channel electric field within a Schottky barrier Double-Gate MOSFET (SB-DG-MOSFET) in subthreshold region by solving Poissons equation. The Poisson equation is solved two dimensionally in an analytical closed-form with the conformal mapping technique. A comparison with data simulated by TCAD Sentaurus simulator for channel lengths down to 22 nm was made and shows an accurate agreement. Futhermore, a new way for the estimation of the tunneling current in SB-DG-MOSFET by applying the above 2D solution for the electric field and a 2D solution of the electrostatic potential is presented. Calculating the tunneling current, we use Wentzel–Kramers–Brillouin (WKB) approximation for the estimation of the tunneling probability. For the calculation of the tunneling and thermionic current a comparison with TCAD Sentaurus for channel lengths down to 65 nm was made.

P‐123: Basic Operation Mechanisms of Floating Metal Ball Actuator Mode as Novel Electronic‐Paper Displays

AbstractBasic operation mechanisms of newly proposed reflective display mode using metal coated ball were investigated for novel electronic‐paper displays, named as Floating Metal Ball Actuator (FMBA) mode. Most appropriate structures and driving conditions were simulated by Poisson's equation solver, and the optimized cell design and driving voltage can be determined. To confirm the conducting property of floating metal ball (FMB), electrical potential of FMB directly contacted on electrode was measured by non‐contact Kelvin probe microscopy and identical with that of the contact electrode. These are useful results to apply the FMBA mode to electrical‐paper displays.

Thermal lensing study based on the heat transfer of diode-pumped Yb3+:Y2SiO5lasers

Based on the features of diode-pumped Yb 3+ :Y 2 SiO 5 (Yb:YSO) lasers, a thermal model was established. According to the latest reports and measurements on thermal parameters, and further considering the heat transfer on side surface, thermal lensing effect of Yb:YSO was studied for the first time to our knowledge. Under the pump power of 17 W, the maximum temperature (488.4 °C) and the maximum distortion (1.24 μ m) were obtained by solving Poisson equation using finite difference method. Moreover, thermal lens focal length was measured through a plane-plane cavity. All the results demonstrate that the theoretical result will be closer to the reality if we take the heat transfer on side surfaces into account.

Theoretical investigation on thermal lensing effects of Yb:KY(WO 4) 2 in diode-pumped lasers

Based on the features of laser diode end-pumped lasers, a thermal model of Yb:KY(WO 4) 2(Yb:KYW) with square cross-section was established. Considering the heat transfer on side faces, the anisotropic of thermal conductivity and the latest reports about thermo-optic coefficient, thermal expansion coefficient and thermal conductivity, temperature distribution, end-pumped face distortion and thermal lens focal length of Yb:KYW were more precisely obtained using finite difference method to solve Poisson equation in a rectangular Cartesian coordinate for the first time. At the pump power of 14 W, the highest temperature located at the center of end-pumped face was 243.8 °C, the highest distortion was 0.28 μm, and the thermal lens focal length was 5.4 cm along z-axis and −4.9 cm along x-axis. The results show that thermal lensing effects in the b-cut Yb:KYW were mainly determined by the anisotropic thermal expansion of Yb:KYW, and further present thermal lensing effects become weaker after considering the heat transfer. This work is significant for compensating the thermal lensing effect and improving the resonator stability of diode-pumped anisotropy crystal lasers.

1706 Computations of Formation and Breakup of a Compound Liquid Jet in a Co-flowing Immiscible Fluid

In this paper, we numerically study the formation and breakup of an axisymmetric immiscible, viscous and laminar compound jet flowing in a coflowing immiscible outer fluid. We use a front-tracking/finite difference method to track the evolution and breakup of the compound jet, which is governed by the incompressible Navier-Stoke equations for Newtonian fluids. The method is modified to account for three-fluid flows. The density and viscosity jumps at interfaces are distributed to the nearby grid points by using area weighting and solving Poisson equations. Thereby, we investigate the effects of interfacial tensions, in terms of the Weber number We and interfacial tension ratio σ_<21>, on the various modes of the compound jet breakup: inner dripping - outer dripping, inner dripping - outer jetting, and inner jetting - outer jetting. Numerical results show that the transition from dripping to jetting is affected not only by the Weber number but also by interfacial tension ratio since the compound jet possesses two different interfaces, i.e., either decreasing We or increasing σ_<21> promotes the dripping regime. In addition, the orifice ratio also affects the transitional values of We and σ_<21>, i.e., as it increases the transition We decreases and the transition σ_<21> increases. The transition from dripping to jetting is mapped in the We - σ_<21> parameter space. However, the variations of We and σ_<21> do not affect the aspect ratio of the compound drops.

Threshold voltage model for quantum-well channelpMOSFET with poly SiGe gate

In this paper, threshold voltage model of quantum-well channel pMOSFET with p+polycrystalline SiGe gate and its cut-in voltage model were established based on solving Poisson equation while considering the impact of free carrier. The effects of relevant parameters (Ge concentration of poly SiGe gate, Ge concentration of quantum-well SiGe channel, thickness of oxide layer, thickness of Si cap layer, doping content of quantum-well SiGe channel, and doping content of substrate) on threshold voltage and cut-in voltage of the parasitic channel was analysed by numerical analysis, and obtained the methods to restrain the opening of parasitic channel. The results of the models are in good agreement wih that of experiment reported as well as of ISE simulation.

Collector junction depletion-layer width model of SiGeheterojunction bipolar transistor with intrinsic SiGe layer

By solving Poisson equation, models of voltage and electric field distribution are build respectively in collector junction depletion layer of SiGe HBT (heterojunction bipolar transistor) with intrinsic SiGe layer. On this basis, models of the collector junction depletion layer width and delay time are obtained. Applying MATLAB, the impact of physical and electrical parameters on SiGe HBT collector junction depletion layer width and depletion delay time are quantitatively analyzed. When base doping concentration and collector junction reverse bias are large, the depletion delay time is quite long. But, when base doping external diffusion depth and collector region doping are large, the depletion delay time is quite short.