Exact stability conditions in upwinding‐scheme FDTD for the Boltzman transport equation

An in‐depth stability analysis of the FDTD method under the upwinding scheme for the Boltzmann transport equation (BTE) under the relaxation time approximation is provided. Both time forward and time backward difference equations are considered. In the time forward differencing case, a sufficient stability condition is derived for the BTE with variable coefficients, and a necessary and sufficient condition is derived for the BTE with constant coefficients. In the time backward differencing case, it is shown that the differencing equations are unconditionally stable. It is shown numerically that the previously reported stability conditions in the literature are not accurate. Copyright © 2013 John Wiley & Sons, Ltd.     

Kinetic-energy transport equation for the modeling of ballistic MOSFETs

Using the first two moment equations of the Vlasov equation, we have developed a transport model based on the convective kinetic energy. This K.E. transport model is applied to the simulation of a ballistic gate-all-around MOSFET. The simulation results show that the current increases substantially under ballistic transport compared to the drift-diffusion model. Limitation and errors of this transport model are associated with the one parameter modeling of the stress tensor for the closure of the moment equation hierarchy.     

Inclusion of the Pauli principle in a deterministic Boltzmann equation solver based on a spherical harmonics expansion

The Pauli principle is included in a deterministic Boltzmann solver based on a spherical harmonics expansion of the distribution function. The Newton-Raphson scheme is applied to solve the nonlinear Boltzmann equation, and it is found that the inclusion of the Pauli principle introduces no numerical problems, even for multi-dimensional semiconductor devices. As a numerical example, the impact of the Pauli principle is numerically investigated for a double-gate MOSFET.     

Some practical aspects of a nonrecursive solution to the discrete Riccati equation

The design of computer-based optimal controllers for synchronous machines has been the subject of a number of recent research papers. The design of such controllers generally involves the solution of the steady-state discrete Riccati equation. A method of checking the solution accuracy of a nonrecursive technique based on the eigen-value properties of the canonical state equation, and an example to illustrate the technique, are presented.     

An iterative matrix solution of the Boltzmann equation for the calculation of diffusion and noise in semiconductors

We extend the iterative matrix method for the solution of the Boltzmann transport equation in multi-band semiconductors to the calculation of second order parameters such as correlation functions and the noise temperature. The method allows also the extraction of the diffusion coefficient in each valley. The results for the case of GaAs with two valleys show that the diffusion in this material is dominated mainly by interactions in the Γ valley. The calculated noise temperature is in good agreement with Monte Carlo results.     

A fully coupled scheme for a Boltzmann-Poisson equation solver based on a spherical harmonics expansion

The numerical properties of a deterministic Boltzmann equation solver based on a spherical harmonics expansion of the distribution function are analyzed and improved. A fully coupled discretization scheme of the Boltzmann and Poisson equations is proposed, where stable equations are obtained based on the H-transformation. It is explicitly shown that the resultant Jacobian matrix for the zeroth order component has property M for a first order expansion, which improves the stability even of higher order expansions. The detailed dependence of the free-streaming operator and the scattering operator on the electrostatic potential is exactly considered in the Newton-Raphson scheme. Therefore, convergence enhancement is achieved compared with previous Gummel-type approaches. This scheme is readily applicable to small-signal and noise analysis. As numerical examples, simulation results are shown for a silicon n ⁺ nn ⁺ structure including a magnetic field, an SOI NMOSFET and a SiGe HBT.     

Electro-thermal simulation based on coupled Boltzmann transport equations for electrons and phonons

To study the thermal effect in nano-transistors, a simulator solving self-consistently the Boltzmann transport equations for both electrons and phonons has been developed. It has been used to investigate the self-heating effects in a 20 nm-long double-gate MOSFET (Fig. 1). A Monte Carlo solver for electrons is coupled with a direct solver for the steady-state phonon transport. The latter is based on the relaxation time approximation. This method is particularly efficient to provide a deep insight of the out-of-equilibrium thermal dissipation occurring at the nanometer scale when the device length is smaller than the mean free path of both charge and thermal carriers. It allows us to evaluate accurately the phonon emission and absorption spectra in both real and energy spaces.     

Accuracy balancing for the finite-difference-based solution of the discrete Wigner transport equation

The Wigner transport equation based on the Wigner function which is defined on the phase space describes two actions in orthogonal directions of the phase space: movement (diffusion) in position space and transition in momentum space. Here, we show that for the proper analysis of a resonant tunneling diode using the finite-difference-based solution of the Wigner transport equation, the degree of numerical accuracy in the calculation of the movement in position space should be balanced with that in the evaluation of the transition in momentum space.     

水舌运动界面的格子Boltzmann仿真研究

应用格子Boltzmann两相流模型,采用Young的界面重构技术,对水舌在空气中的运动进行了数值模拟,得到水舌在空气中的运动界面和流速矢量,数值模拟结果与实际问题的物理规律一致,验证了模型的有效性与可靠性.     

Numerical constraints and non-spatial open boundary conditions for the Wigner equation

Journal of Computational Electronics - We discuss boundary value problems for the characteristic stationary von Neumann equation (stationary sigma equation) and the stationary Wigner equation in a...     

锅炉燃烧状态的数值模拟和改造方案

以1台50 MW燃煤发电机组为研究对象,对炉内燃烧状态进行了数值模拟,结果表明锅炉费斯顿管上部的温度比下部的温度约低100 ℃,中间位置处的温度比两边位置处的要高,这样将造成费斯顿管下部以及位于中间处的费斯顿管易结焦.分析原因主要是燃烧器布置不太合理,针对其存在的问题,提出了2种改造方案,并对这2种方案进行了比较.     

Dynamics of an HVDC system in the presence of unbalanced AC transmission line faults and a stabilization scheme

The introduction of an HVDC system into the trunk power supply system requires transmitting as much dc power as possible for improving the whole ac/dc system stability. The continued operation scheme of an HVDC system which makes it possible to operate even under very low commutation bus voltage is adopted to cope with such system requirement. Further stability improvement can be achieved by adding damping control which modulates converter active and/or reactive power. To take full advantage of these control effects, it is essential that the HVDC system can maintain stable operation during the ac system faults and reclosing. Particular attention should be given to a repetitive commutation failure following the unbalanced ac transmission line faults. This paper discusses first the cause of the repetitive commutation failure when supplied with unbalanced ac system voltage based on an experiment using the CRIEPI AC-DC Power System Simulator. Then a stabilization control scheme with an on-line extinction angle estimation is proposed and the effect is verified by digital simulation.     

Voltage stabilization system in traction substation of urban electric transport

The direct current-voltage stabilization system using a high-frequency link in traction substations of urban electric transport based on applying modern semiconductor, the operating principle of these stabilizers, and the results of modeling the power part in OrCAD 9.2 are described.     

TVD格式在水击数值模拟中的应用

本文将TVD格式运用于水击方程,模拟水击压力变化,并同双曲型方程的经典求解格式MacCormark格式和Lax-Ffiedrichs格式的计算结果相对比,结果表明:TVD格式具有耗散性低,不产生虚假数值振荡.计算精度高等优点,能有效模拟水击现象.之后本文将TVD格式应用于阿拉山水电站水击问题的计算中,效果较好.     

Implementation of the Wigner-Boltzmann transport equation within particle Monte Carlo simulation

In this paper, we detail the main numerical issues of the Monte Carlo method developed to solve the Wigner-Boltzmann transport equation and simulate the quantum transport in semiconductor nanodevices. In particular, we focus on the boundary conditions regarding the injection of particles and the limits of integration for the calculation of the Wigner potential which are of crucial importance for the physical correctness of simulation results. Through typical examples we show that this model is able to treat correctly purely quantum coherent and semi-classical transport situations as well. It is finally shown that to investigate devices operating in mixed quantum/semi-classical regimes and to analyze the transition between both regimes, this approach takes advantage of its full compatibility with Boltzmann algorithm.     

Partially coherent electron transport in terahertz quantum cascade lasers based on a Markovian master equation for the density matrix

We derive a Markovian master equation for the single-electron density matrix, applicable to quantum cascade lasers (QCLs). The equation conserves the positivity of the density matrix, includes off-diagonal elements (coherences) as well as in-plane dynamics, and accounts for electron scattering with phonons and impurities. We use the model to simulate a terahertz-frequency QCL, and compare the results with both experiment and simulation via nonequilibrium Green’s functions (NEGF). We obtain very good agreement with both experiment and NEGF when the QCL is biased for optimal lasing. For the considered device, we show that the magnitude of coherences can be a significant fraction of the diagonal matrix elements, which demonstrates their importance when describing THz QCLs. We show that the in-plane energy distribution can deviate far from a heated Maxwellian distribution, which suggests that the assumption of thermalized subbands in simplified density-matrix models is inadequate. We also show that the current density and subband occupations relax toward their steady-state values on very different time scales.     

二维有限元超声波动方程的研究

现在超声检测主要发展方向之一是能监控生产过程中构件的损伤速率和材料的完整性及质量的级别判断。检测设备和方法在分析检测过程是一个相当复杂的,其中包括分析超声波在构件中的传播规律和一系列的电信号转换为机械信号和相反过程的信号转换。超声波在构件中传播的规律可以由材料的属性和各向同性预先确定。本文重点阐述了机械振动产生超声波,并利用有限元(FEM)和有限差分(FED)方法模拟在无损检测过程中的波动传播过程。并且通过计算机程序模拟二维超声波的传播,散射的数值模拟与几何理论结果是相符合的。