2D Poisson Equation Research Articles

Analytical Modeling of Silicon Nanowire Dielectric Modulated Reconfigurable FET Biosensor

Abstract In this paper, we present an analytical modeling of a Silicon Nanowire Dielectric Modulated Reconfigurable FET (SiNW-DMRFET) biosensor having a cavity under the control gate. By employing the 2D Poisson equation, we accurately model the electrostatic characteristics of the proposed biosensor such as surface potential, threshold voltage, electric field, and drain current. The main parameters used to identify biomolecules present in the cavity are the variations detected in the threshold voltage (VTH ) and ON-current. The simulated and analytical results are compared with the performance of the published literature. We validate the reliability of our analytical approach by conducting simulations of the proposed device on Silvaco TCAD tool. The research conducted through both theoretical and experimental studies indicated that the proposed biosensor exhibited significant improvements in its sensitivity to ION and VTH . Specifically, there was a rise of 54.65% in ION sensitivity and 85.71% in VTH sensitivity. Furthermore, we show that our model is accurate and reliable by carefully comparing the results of our analysis with the results of the simulation.

Mesh-Free Solution of 2D Poisson Equation with High Frequency Charge Patterns Using Data-Free Physics Informed Neural Network

Abstract In this paper, we present a data-free physics-informed neural networks (PINNs) approach for solving two-dimensional (2D) Poisson equation, which is pivotal in fields such as electromagnetics, mechanical engginering, and thermodynamics. Traditional numerical method for solving this equation often require structured mesh generation such as Finite Element Method (FEM), which can be computationally expensive when dealing with high resolution Poisson Equation Solution. To address this challenge, we leverage the capabilities of PINNs capturing pattern of complex system by incorporating physical law and boundary condition as part of loss function on training model. While PINNs provide a robust framework for solving differential equations within boundary condition, they have struggle with capturing high-frequency pattern due to smooth nature of typical activation function used in neural networks. To evercome this issue, we enhance our model by incorporating Fourier Features Networks, which map inputs through a series of sinusoidal functions before feeding the input into the neural network. The result show that Fourier feature network can enhance convergence of training of PINNs model faster and obtained better result than PINNs without Fourier feature networks.

Revealing two-dimensional electric field crowding effect in breakdown performance of DPPT-TT polymer-based OFETs

The diketopyrrolopyrrole-based polymer (DPPT-TT) has been employed in organic power field effect transistors due to its exceptional off-state breakdown performance. The impact of organic semiconductor layer thickness on the breakdown performance has not been explored. In this study, we investigate the impact of DPPT-TT layer thickness on the breakdown voltage (BV) by fabricating organic field effect transistors (OFETs) with various DPPT-TT layer thicknesses. Our findings reveal that the devices' BV is a strong function of DPPT-TT layer thickness, and reducing the DPPT-TT layer thickness from 68 to 15 nm results in a decrease in BV from 291 to 86 V, attributed to the two-dimensional (2D) electric field crowding effect. An analytical model utilizing the 2D Poisson equation reveals an electric field at the DPPT-TT layer's surface. Thinner DPPT-TT layer exhibits larger electric field peak, leading to premature breakdown near the drain electrode. The relationship between breakdown electric field and DPPT-TT layer thickness was established by fitting the experimental data to the model, revealing an average BV error of only 8.8%. This phenomenon is validated to be ubiquitous in polymer based OFETs via DPPT-TT-based and P3HT-based devices. According to the proposed model, this 2D electric field crowding effect can be mitigated by adjusting the dielectric layer thickness (tD) and/or the dielectric material.

Accurate Description of Coulombic Interactions in Organic Field‐Effect Transistors Enabled by Efficient 3D Poisson's Equation Solver with Mixed Boundary Conditions

AbstractThe rational development of organic electronic devices can greatly benefit from a molecular‐level description, where an accurate description of the Coulombic interactions among charge carriers holds paramount importance. However, the molecular‐level organic field‐effect transistor (OFET) simulations do not fully include the short‐range charge‐carrier Coulombic interactions, thus limiting their accuracy. Here, an efficient solution is demonstrated to the 3D Poisson's equation with mixed boundary conditions, optimized for integration into the simulations of organic electronic devices. It leverages the finite difference method for discretization, the Krylov subspace iterative methods for solving the linear system, the algebraic multigrid algorithm for preconditioning, and OpenMP and CUDA parallelization for acceleration. For the organic field‐effect transistors of micrometer sizes or smaller dimensions, obtaining the electric potential within the device takes less than 0.1 s, which is sufficiently efficient for molecular‐level modeling. As a result, both short‐ and long‐range electrostatic interactions are successfully incorporated in the molecular‐level modeling of OFET devices. This integration significantly enhances the robustness of OFET modeling for future applications.

Computational modelling of cylindrical-ferroelectric-dual metal-nanowire field effect transistor (C-FE-DM-NW FET) using landau equation for gate leakage minimization

In order to address and resolve the significant problem of gate-induced drain leakage (GIDL) current and enhance device reliability, band-to-band tunnelling (BTBT), and OFF-state leakages, a computational model of a cylindrical-ferroelectric-dual-metal-nanowire-field effect transistor (C-FE-DM-NW-FET) has been proposed in this manuscript. The proffered structure is a symmetric gate structure with ferroelectric layer sandwiched between the gate terminal and oxide layer which reduces the BTBT which in term reduces the OFF-state leakage hence making the device definitive for low power applications. In this manuscript, there has been a reduction in the leakage current by a magnitude of 104 times in 50 nm and 107 times in 60 nm channel length which translates to a reduction in gate leakage (IGIDL) of more than 100 % in C-FE-NW-FET over C-NW FET. To analyze the Electric Field, Surface Potential, and IGIDL with the proper boundary conditions, the 2D Poisson's equation is solved analytically with Landau-Khalatnikov (LK) equation. The analytical findings are quite similar to the simulated outcomes.

Efficient truncated randomized SVD for mesh-free kernel methods

This paper explores the utilization of randomized SVD (rSVD) in the context of kernel matrices arising from radial basis functions (RBFs) for the purpose of solving interpolation and Poisson problems. We propose a truncated version of rSVD, called trSVD, which yields a stable solution with a reduced condition number in comparison to the non-truncated variant, particularly when manipulating the scale or shape parameter of RBFs. Notably, trSVD exhibits exceptional proficiency in capturing the most significant singular values, enabling the extraction of critical information from the data. When compared to the conventional truncated SVD (tSVD), trSVD achieves comparable accuracy while demonstrating improved efficiency. Furthermore, we explore the potential of trSVD by employing scale parameter strategies, such as leave-one-out cross-validation and effective condition number. Then, we apply trSVD to solve a 2D Poisson equation, thereby showcasing its efficacy in handling partial differential equations. In summary, this study offers an efficient and accurate solver for RBF problems, demonstrating its practical applicability. The code implementation is provided to the scientific community for their access and reference.

Enhanced Seamless Video Fusion: A Convolutional Pyramid-Based 3D Integration Algorithm.

Video fusion aims to synthesize video footage from different sources into a unified, coherent output. It plays a key role in areas such as video editing and special effects production. The challenge is to ensure the quality and naturalness of synthetic video, especially when dealing with footage of different sources and qualities. Researchers continue to strive to optimize algorithms to adapt to a variety of complex application scenarios and improve the effectiveness and applicability of video fusion. We introduce an algorithm based on a convolution pyramid and propose a 3D video fusion algorithm that looks for the potential function closest to the gradient field in the least square sense. The 3D Poisson equation is solved to realize seamless video editing. This algorithm uses a multi-scale method and wavelet transform to approximate linear time. Through numerical optimization, a small core is designed to deal with large target filters, and multi-scale transformation analysis and synthesis are realized. In terms of seamless video fusion, it shows better performance than existing algorithms. Compared with editing multiple 2D images into video after Poisson fusion, the video quality produced by this method is very close, and the computing speed of the video fusion is improved to a certain extent.

Modeling of inner-outer gates and temperature dependent gate-induced drain leakage current of junctionless double-gate-all-around FET

In this paper, the temperature-dependent gate-induced drain leakage (GIDL) current model is proposed with the help of a lateral electric field (EL) across the inner and outer gate interfaces of the junctionless double-gate-all-around (JL-DGAA) field-effect transistor (FET). The EL at the interface is obtained from the surface potential equation after solving the 3D Poisson equation with appropriate boundary conditions. The derived model is validated using the well-calibrated TCAD simulator platform with experimental data. A higher GIDL current at the outer gate-channel interface is observed compared to the inner gate-channel interface in the OFF-state conditions due to the high EL between the channel and drain, which is reported for the first time here. The effect of temperature (from 200 K to 500 K) on the GIDL current is also observed, which increases linearly with increasing temperature. Further, the impact of induced mechanical stress (MS) is investigated on the GIDL current, where the GIDL current increases exponentially with increasing induced MS due to effective mass and band gap reduction. Finally, the dynamic performance is investigated in terms of the gate delay time as a function of channel length and temperature. The gate delay diminishes with decreasing channel length and increasing temperature, which shows the switching speed and ability of the device.

Reconstructing the baryonic acoustic oscillations in the presence of photo-z uncertainties

ABSTRACT The reconstruction method has been widely employed to improve the baryon acoustic oscillations (BAO) measurement in spectroscopic survey data analysis. In this study, we explore the reconstruction of the BAO signals in the realm of photometric data. By adapting the Zel’dovich reconstruction technique, we develop a formalism to reconstruct the transverse BAO in the presence of photo-z uncertainties under the plane-parallel approximation. We access the performance of the BAO reconstruction through comoving N-body simulations. The transverse reconstruction potential can be derived by solving a 2D potential equation, with the surface density and the radial potential contribution acting as the source terms. The solution is predominantly determined by the surface density. As is evident in dense samples, such as the matter field, the transverse BAO reconstruction can enhance both the strength of the BAO signals and their cross correlation with the initial conditions. At z = 0, the cross-correlation is increased by a factor of 1.2 at $k_\perp = 0.2 \, \mathrm{Mpc}^{-1}h$ and 1.4 at $k_\perp = 0.3 \, \mathrm{Mpc}^{-1}h$, respectively. We contrast the 2D potential results with the 3D Poisson equation solution, wherein we directly solve the potential equation using the position in photo-z space, and find good agreement. Additionally, we examine the impact of various conditions, such as the smoothing scales and the level of photo-z uncertainties, on the reconstruction results. We envision the straightforward application of this method to survey data.

Modeling of negative capacitance underlap graded-channel junction accumulation mode junctionless FET in nano-scale regime

Analytical modeling of negative capacitance (NC) graded-channel (GC) underlap junction accumulation mode (JAM) JL-FET is presented in this literature. Here, the surface potential, threshold voltage, sub-threshold drain current, sub-threshold swing (SS) and DIBL are obtained by solving the 2D Poisson's equation and Landau-Khalatnikov (LK) equation simultaneously. Performances of the proposed NC-GC-JAM-JL-FET is analyzed in detail for the variations in FE-layer thickness, gate-length, underlap length, graded channel ratio and Si-film thickness. The proposed model is calibrated with the experimental data to establish its acceptability. The proposed device is also simulated in the Silvaco ATLAS device simulator, which shows very good agreement with the analytical model. The present paper establishes the remarkable prospect of the proposed architecture to be operated for low-power application in nano-scale regime.

A new analytical method for modeling a 2D electrostatic potential in MOS devices, applicable to compact modeling

This paper presents a new conformal mapping method to solve 2D Laplace and Poisson equations in MOS devices. More specifically, it consists of an analytical solution of the 2D Laplace equation in a rectangular domain with Dirichlet boundary conditions, with arbitrary values on the boundaries. The advantages of the new method are that all four edges of the rectangle are taken into account and the solution consists of closed-form analytical expressions, which make it fast and suitable for compact modeling. The new model was validated against other similar methods. It was found that the new model is much faster, easier to implement, and avoids many numerical issues, especially near the boundaries, at the cost of a very small loss in accuracy.

Physics-based modeling of surface potential and leakage current for vertical Ga2O3 FinFET

Gallium oxide (Ga2O3) is a promising ultra-wide bandgap material offering a large bandgap (>4.7 eV) and high critical electric fields. The increasing demand for electronic devices for high-power applications in electric automobiles, high-performance computing, green energy technologies, etc., requires higher voltages and currents with enhanced efficiency. Vertical transistors, such as fin-shaped field-effect transistors (FinFETs) have emerged to meet the growing need with improved current handling capabilities, reduced resistance, and enhanced thermal performance. However, to fully exploit the Ga2O3 power transistors, precise and reliable physics-driven models are crucial. Therefore, a comprehensive surface potential model has been developed in this work for a vertical Ga2O3 FinFET. The electric potential across the channel is explained by analyzing the two-dimensional (2D) Poisson equation employing parabolic approximation. Such a surface potential model is instrumental in determining the performance of the Ga2O3 FinFET as it affects the threshold voltage, the drain current, and fringing capacitance. Exploiting the surface potentials, a fringing capacitance model is derived which is crucial in analyzing the speed of the device in compact integrated circuits. In addition, statistical analysis of the Ga2O3 FinFET using the Monte Carlo simulation technique is performed to determine the leakage current fluctuation due to doping variations. The validation of the analytical model with experimental results confirms the effectiveness and prospects of the developed models in the rapid development and characterization of next-generation high-performance vertical Ga2O3 power transistors.

Improved MPS models for simulating free surface flows

Two improved Laplacian models are introduced in this study for more accurate simulation of free surface flows in the context of the moving particle semi-implicit (MPS) method, a well-known mesh-less approach. The Euler equations are the governing equations of these flows without considering viscous forces which are solved in the Lagrangian frame by the MPS and two-step projection methods for spatial and temporal discretization, respectively. Considering the similarity between the MPS and SPH (smoothed particle hydrodynamics) methods, one of the introduced Laplacian models is formulated by a corrective matrix firstly proposed in an improved SPH method [28]. The other modified Laplacian model is also derived from the divergence of a newly developed MPS gradient model proposed for solving elasticity problems [33]. The higher accuracy of these methods compared to the classic SPH, MPS and even three modified SPH and MPS Laplacian models [7, 34, 44] is verified by solving 2D Poisson equations. Moreover, the excellent performance of the Laplacian models and the improved gradient model in obtaining smooth pressure field is validated by solving three benchmark free surface flows. Furthermore, the problem of wave damping in the original MPS computations can be resolved by using the applied models.

Implementation of the HHL Algorithm for Solving the Poisson Equation on Quantum Simulators

The Poisson equation is a fundamental equation of mathematical physics that describes the potential distribution in static fields. Solving the Poisson equation on a grid is computationally intensive and can be challenging for large grids. In recent years, quantum computing has emerged as a potential approach to solving the Poisson equation more efficiently. This article uses quantum algorithms, particularly the Harrow–Hassidim–Lloyd (HHL) algorithm, to solve the 2D Poisson equation. This algorithm can solve systems of equations faster than classical algorithms when the matrix A is sparse. The main idea is to use a quantum algorithm to transform the state vector encoding the solution of a system of equations into a superposition of states corresponding to the significant components of this solution. This superposition is measured to obtain the solution of the system of equations. The article also presents the materials and methods used to solve the Poisson equation using the HHL algorithm and provides a quantum circuit diagram. The results demonstrate the low error rate of the quantum algorithm when solving the Poisson equation.

Layer engineering piezotronic effect in two-dimensional homojunction transistors

The semiconductor junctions based on piezoelectric materials are of great importance for the realization of functionality and versatility in sensing devices. Two-dimensional (2D) stacked materials provide a promising route to design novel semiconductor junctions due to their layer-dependent electronic and optical properties. However, the combination of layer-dependent band structure and piezoelectricity in device designs is rarely explored to date. In this work, we propose piezotronic transistors designed by layer engineering 2D homojunction. A 2D Poisson equation including the piezoelectric polarization is derived and then combined self-consistently with the non-equilibrium Green function to explore the carrier transport. We find a peculiar symmetrical modulation mechanism of piezotronic effect on carrier transport, i.e., flipping the sign of externally applied strain can drive symmetrical transport process regarding bias polarity. Additionally, the results show that the transport is a mixing of thermionic and tunneling current, which are comparable at low bias but predominated by the quantum tunneling effect at high bias. Although our 2D homojunction transistor is similar to Schottky diodes, the on/off ratio and gauge factors are higher than most of metal-semiconductor contact piezotronic devices. Moreover, for the device with symmetrical stacking configurations, increasing layer number in 2D homojunction can decrease the output current but enhance the gauge factors. By contrast, the device performance in asymmetrical stacking systems is insensitive to the variation of layer number. Our demonstration of layer engineering 2D homojunction transistor not only enriches the fundamental physics of piezotronics, but also open an avenue for designing highly sensitive strain sensors based on diverse 2D layered junctions.

Testing of the accelerated two-dimensional model of surface potential waves

The paper focuses on the validation of the accelerated method for simulation of 2D-surface waves with a use of 2D-model derived by simplifications of 3D-equations for potential periodic waves at infinite depth. The separation of the velocity potential into nonlinear and linear components is used. A derivation of the equation for the total kinetic energy calculation in the surface-following coordinate system is given for the first time. The spectral characteristics of the wave field calculated with the accelerated model are compared with the results from the equivalent full 3D-model. The 3D-model is based on the numerical solution of the 3D-Poisson equation written in surface coordinates for the nonlinear component of the velocity potential. The similarity of the results obtained from the two versions of the model confirms that the new accelerated model can be used to quickly reproduce the wave field dynamics and thereby increase a speed of calculations by about two orders.

Analytical analysis and linearity performance of dual metalhigh‐KSchottky nanowireFET(DM‐HK‐SNWFET)

AbstractThis study's objectives are to deliver a relative analysis of non‐uniformly doped (NUD) and uniformly doped Dual Metal High‐K Schottky nanowire FET (DM‐HK‐SNWFET). Surface potential, subthreshold current, subthreshold swing, and drain current have been expressed and analyzed by resolving 2D Poisson's equation with suitable boundary conditions. The analog performance of the device is verified by examining cut‐off frequency (fT), trans‐conductance frequency product (TFP), gain frequency product (GFP), and gain trans‐conductance frequency product (GTFP). The results show suitable RF circuit parameters with a high switching ratio (≈3 × 109) and low subthreshold swing (61 mV/decade) for NUD‐DM‐HK‐SNWFET. Additionally, linearity frequency of merits (FOMs) and distortion performance are also studied by numerically calculating higher order voltage and current intercept point (VIP2,VIP3, IIP3, IMD3); 1‐dB compression point and Harmonics distortions (HD2 and HD3) using transconductance (gm1) along with its higher derivativesgm2andgm3. These parameters exhibit high‐level linearity and low‐level distortion at zero crossover points in NUD‐DM‐HK‐SNWFET, making it a better contender for low‐power and high‐performance applications.

The simplest node-based equilibrium finite element for 2D Poisson equation with exploration of the equivalence among hybrid, flux-based and stress-function-based equilibrium elements

The simplest node-based equilibrium finite element for 2D Poisson equation with exploration of the equivalence among hybrid, flux-based and stress-function-based equilibrium elements

Efficient GPU implementation of a Boltzmann-Schrödinger-Poisson solver for the simulation of nanoscale DG MOSFETs

A previous study by Mantas and Vecil (Int J High Perform Comput Appl 34(1): 81–102, 2019) describes an efficient and accurate solver for nanoscale DG MOSFETs through a deterministic Boltzmann-Schrödinger-Poisson model with seven electron–phonon scattering mechanisms on a hybrid parallel CPU/GPU platform. The transport computational phase, i.e. the time integration of the Boltzmann equations, was ported to the GPU using CUDA extensions, but the computation of the system’s eigenstates, i.e. the solution of the Schrödinger-Poisson block, was parallelized only using OpenMP due to its complexity. This work fills the gap by describing a port to GPU for the solver of the Schrödinger-Poisson block. This new proposal implements on GPU a Scheduled Relaxation Jacobi method to solve the sparse linear systems which arise in the 2D Poisson equation. The 1D Schrödinger equation is solved on GPU by adapting a multi-section iteration and the Newton-Raphson algorithm to approximate the energy levels, and the Inverse Power Iterative Method is used to approximate the wave vectors. We want to stress that this solver for the Schrödinger-Poisson block can be thought as a module independent of the transport phase (Boltzmann) and can be used for solvers using different levels of description for the electrons; therefore, it is of particular interest because it can be adapted to other macroscopic, hence faster, solvers for confined devices exploited at industrial level.

A compact sixth-order implicit immersed interface method to solve 2D Poisson equations with discontinuities

This paper proposes a compact sixth-order accurate numerical method to solve Poisson equations with discontinuities across an interface. This scheme is based on two techniques for the second-order derivative approximation: a high-order implicit finite difference (HIFD) formula to increase the precision and an immersed interface method (IIM) to deal with the discontinuities. The HIFD formulation arises from Taylor series expansion, and the new formulas are simple modifications to the standard finite difference schemes. On the other hand, the IIM allows one to solve the differential equation using a fixed Cartesian grid by adding some correction terms only at grid points near the immersed interface. The two-dimensional equation is then solved by a nine-point compact sixth-order scheme named HIFD-IIM. Fourth- and second-order methods result in particular cases of the proposed method. Furthermore, the sixth-order method requires similar computational resources to a fourth-order formulation because the resulting matrices in both discretizations are the same. However, higher-order methods require the knowledge of more jump conditions at the interface. From the theoretical derivation of the proposed method, we expect fully six-order accuracy in the maximum norm. This order has been confirmed from our numerical experiments using nontrivial analytical solutions.