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Scientists and engineers have been solving Poisson’s equation in PN junctions following two approaches: analytical solving or numerical methods. Although several efforts have been accomplished to offer accurate and fast analyses of the electric field distribution as a function of voltage bias and doping profiles, so far none achieved an analytic or semi-analytic solution to describe neither a double diffused PN junction nor a general case for any doping profile. The paper aims to discuss these issues.

In this work, a double Gaussian doping distribution is first considered. However, such a doping profile leads to an implicit problem where Poisson’s equation cannot be solved analytically. A method is introduced and successfully applied, and compared to a finite element analysis. The approach is then generalized, where any doping profile can be considered. 2D and 3D extensions are also presented, when symmetries occur for the doping profile.

These results and the approach here presented offer an efficient and accurate alternative to numerical methods for the modeling and simulation of mathematical equations arising in physics of semiconductor devices.

A general 3D extension in the case where no symmetry exists can be considered for further developments.

The paper strongly simplify and ease the optimization and design of any PN junction.

This paper provides a novel method for electric field distribution analysis.

Discusses the results of a study of the moduli of elasticity of concretes made with artificially manufactured lightweight aggregates subjected to uniaxial compression and uniaxial tension. Two artificially manufactured lightweight aggregates and one normal weight aggregate (for comparison) were used in the investigation. Concrete mixes designed to have compressive strengths varying from 20 MPa to 60 MPa were used in this study. Presents the results of static and dynamic moduli of elasticity, Poisson′s ratio, ultrasonic pulse velocity, compressive strength and tensile strength tests. Observes that the static modulus of elasticity in tension is nearly equal to the static modulus of elasticity in compression at a stress level of one‐third the ultimate stress. Compressive modulus values are shown to be dependent on the stress level and type of modulus, i.e. either secant or tangent. On the other hand, the tensile modulus is not affected by the stress level. The modulus of elasticity of lightweight aggregate concrete is about 60‐70 per cent of that of normal weight concrete. Compares the test results obtained in this study with research work carried out on other lightweight aggregate concretes by other investigators. Also presents the relationships between static modulus of elasticity, dynamic modulus of elasticity, compressive strength, and Poisson′s ratio, and equations for estimating elastic modulus and Poisson′s ratio.

The aim of the paper is to achieve textbook multigrid efficiency for some flow problems.

The steady incompressible Euler equations are decoupled into elliptic and hyperbolic subsystems. Numerous classical FAS‐MG algorithms are implemented and tested for convergence. A full multigrid algorithm that costs less than 10 work units (WUs) is sufficient to reduce the algebraic error below the discretization error. A new algorithm “NUVMGP” is introduced. A two‐step iterative procedure is adopted. First, given the pressure gradient, the convection equations are solved on the computational grid for the velocity components by performing one Gauss‐Seidel iteration ordered in the flow direction. second, a linear multigrid (MG) cycle for Poisson's equation is performed to update pressure values.

It is found that algorithm “NUVMGP‐FMG” requires less than 6 WU to attain the target solution. The convergence rates are independent on both the mesh size and the approximation order.

Lexicographic Gauss‐Seidel using downstream ordering is a good solver for the advection terms and provides excellent smoothing rates for relaxation. But it is complicated to maintain downstream ordering in case the flow directions change with location.

Although the scope of this work is limited to rectangular domains, finite difference schemes, and incompressible Euler equation, the same approaches can be extended for other flow problems. However, such relatively simple problems may provide deep understanding of the ideal convergence behavior of MG and accumulate experience to detect unacceptable performance and regain the optimal one.

Recent advances in the fabrication technology of heterojunction semiconductor nanostructures have made possible the realization of systems with extremely small sizes. In these devices, electrons are confined along some directions and are free to move in others. Semiconductor nanostructures have become so small that we have to take into account quantum effects. The two dimensional physical model consists of Poisson’s equation for the electrostatic potential φ, coupled with an eigenvalue problem for Schrödinger’s equation. Proposes

Solutions to the first three moments of the Boltzmann transport equation and Poisson's equation are obtained for a permeable base transistor (PBT) using linearized, block implicit (LBI) and ADI techniques. Two level electron transfer is considered. The results of the simulations are compared to results obtained from the drift and diffusion equations. The comparison indicates that nonequilibrium transport and velocity overshoot are important in the PBT. The predicted I‐V characteristics of the device show substantially higher current levels and a higher cutoff frequency are obtained with the moment equations.

Closed form solutions of the potential difference between the two depletion layer edges of a single‐diffused Gaussian p‐n junction are obtained by integrating Poisson's equation and equating the positive and negative charges in the depletion layer. Using the closed form solution of the Poisson's equation, the depletion layer width, junction capacitance and junction built‐in potential are calculated. The customary exponential factor m in the expression for the junction capacitance, i.e., Cj α(1 + Va/φ)−m is shown to vary with the applied reverse bias. The value of φ is found to be different from the conventional value of the junction built‐in potential especially at high voltages. A technique for modeling diffused p‐n junctions at various reverse biases is presented. These results will be useful in circuit simulation programs such as SPICE, particularly for applications involving digital integrated circuits.

In this paper, the 2‐D numerical analysis is used to investigate the electro‐thermal performance of a trench power VDMOS transistor having a much reduced quasi‐saturation effect over the conventional VDMOS structure. Taking into account all the appropriate physical mechanisms, the analysis self‐consistently solves Poisson's equation, the electron continuity equation and the heat flow equation. The results show that the trench structure introduced enables the device to operate at higher current levels due to a favorable change in current density distribution within the device. However, these two effects can increase the self‐heating of the device, decrease the forward current and degrade the thermal stability of the new structure. Nevertheless the new device is still found to provide a higher quasi‐saturation current than the conventional VDMOS device even when thermal effects are taken into account.

This paper is concerned with the application of radial basis function networks (RBFNs) as interpolation functions for all boundary values in the boundary element method (BEM) for the numerical solution of heat transfer problems. The quality of the estimate of boundary integrals is greatly affected by the type of functions used to interpolate the temperature, its normal derivative and the geometry along the boundary from the nodal values. In this paper, instead of conventional Lagrange polynomials, interpolation functions representing these variables are based on the “universal approximator” RBFNs, resulting in much better estimates. The proposed method is verified on problems with different variations of temperature on the boundary from linear level to higher orders. Numerical results obtained show that the BEM with indirect RBFN (IRBFN) interpolation performs much better than the one with linear or quadratic elements in terms of accuracy and convergence rate. For example, for the solution of Laplace's equation in 2D, the BEM can achieve the norm of error of the boundary solution of O(10⁻⁵) by using IRBFN interpolation while quadratic BEM can achieve a norm only of O(10⁻²) with the same boundary points employed. The IRBFN‐BEM also appears to have achieved a higher efficiency. Furthermore, the convergence rates are of O(h^1.38) and O(h^4.78) for the quadratic BEM and the IRBFN‐based BEM, respectively, where h is the nodal spacing.

The purpose of this study is to design numerical simulations of bubbly flow around a cylinder to better understand the characteristics of flow around a rigid obstacle.

The bubbly flow around a circular cylinder was numerically simulated using a semi-Lagrangian–Lagrangian method composed of a vortex-in-cell method for the liquid phase and a Lagrangian description of the gas phase. Additionally, a penalization method was applied to account for the cylinder inside the flow. The slip condition of the bubbles on the cylinder’s surface was enforced, and the outflow conditions were applied to the liquid flow at the far field.

The simulation clarified the characteristics of a bubbly flow around a circular cylinder. The bubbles were shown to move around and separate from both sides of the cylinder, because of entrainment by the liquid shear layers. Once the bubbly flow fully developed, the bubbles distributed into groups and were dispersed downstream of the cylinder. A three-dimensional vortex structure of various scales was also shown to form downstream, whereas a quasi-stable two-dimensional vortex structure was observed upstream. Overall, the proposed method captured the characteristics of a bubbly flow around a cylinder well.

A semi-Lagrangian–Lagrangian approach was applied to simulate a bubbly flow around a circular cylinder. The simulations provided the detail features of these flow phenomena.

Poisson’s equation and the electron continuity equation, together with heat flow equation are solved self‐consistently to obtain the lattice temperature profile under non‐isothermal conditions in a power VDMOS transistor. The effect of the variable lattice temperature on the forward characteristics of VDMOSTs is presented, and discussed. The results show that self‐heating in power VDMOSTs has a significant effect. The thermal coupling effects on the forward I—V characteristics are compared and discussed between the power VDMOST and the conventional MOSFET.