基于OpenFOAM的投影法磁流体求解器开发与验证

在开源计算流体力学C++工具包OpenFOAM环境下开发了低磁雷诺数条件下的磁流体求解器,并进行了验证。采用投影算法求解动量方程和压力泊松方程;采用非结构网格同位相容守恒算法求解电势泊松方程、感应电流和洛伦兹力;采用边界耦合方法求解流固耦合电势场。通过对均匀磁场下导电方管和导电圆管内的完全发展磁流体层流的数值模拟和解析解的对比,对求解器进行了验证。进一步对非均匀强磁场作用下导电方管和导电圆管内完全发展磁流体层流进行了数值模拟,并与ALEX实验结果进行了比较。数值解和实验结果吻合良好。所开发的求解器可用于复杂结构强磁场作用下磁流体的数值模拟研究。     

关于一道狄利克雷边界条件下电势计算题的思考

利用格林函数法计算了在狄利克雷边界(第一类边界)条件下,边界为无穷大平面、边界电势在由x=±1和y=±1的4个点形成的正方形区域内为1、其他地方为零的上半空间的电势精确解.利用函数图像辅助方法阐明如何得到狄利克雷边界条件下电势在z→0的近似解,分别用精确解和近似解讨论了在z→0时的边界电势,两者给出了相同的结果.求解过...     

基于OpenFOAM的投影法磁流体求解器开发与验证

在开源计算流体力学C++工具包OpenFOAM环境下开发了低磁雷诺数条件下的磁流体求解器,并进行了验证。采用投影算法求解动量方程和压力泊松方程;采用非结构网格同位相容守恒算法求解电势泊松方程、感应电流和洛伦兹力;采用边界耦合方法求解流固耦合电势场。通过对均匀磁场下导电方管和导电圆管内的完全发展磁流体层流的数值模拟和解析解的对比,对求解器进行了验证。进一步对非均匀强磁场作用下导电方管和导电圆管内完全发展磁流体层流进行了数值模拟,并与ALEX实验结果进行了比较。数值解和实验结果吻合良好。所开发的求解器可用于复杂结构强磁场作用下磁流体的数值模拟研究。     

堆叠栅介质对称双栅单Halo应变Si金属氧化物半导体场效应管二维模型

提出了一种堆叠栅介质对称双栅单Halo应变Si金属氧化物半导体场效应管(metal-oxide semiconductor field effect transistor,MOSFET)新器件结构.采用分区的抛物线电势近似法和通用边界条件求解二维泊松方程,建立了全耗尽条件下的表面势和阈值电压的解析模型.该结构的应变硅沟道有两个掺杂区域,和常规双栅器件(均匀掺杂沟道)比较,沟道表面势呈阶梯电势分布,能进一步提高载流子迁移率;探讨了漏源电压对短沟道效应的影响;分析得到阈值电压随缓冲层Ge组分的提高而降低,随堆叠栅介质高k层介电常数的增大而增大,随源端应变硅沟道掺杂浓度的升高而增大,并解释了其物理机理.分析结果表明:该新结构器件能够更好地减小阈值电压漂移,抑制短沟道效应,为纳米领域MOSFET器件设计提供了指导.     

孤立的带电导体的拉普拉斯方程解

一、前 言 解静电问题,常常是在一定的边界条件下,求解泊松方程或拉普拉斯方程.求孤立的带电导体的电场问题,就是求解满足已给定的边界条件的拉普拉斯方程.因为拉普拉斯方程是偏微分方程,所以求解边值问题往往是很困难的,在很多情况下甚至是解不出的. 本文提出一个解孤立带电导体的拉普拉斯方程的方法.这个方法是对导体外的电势的函数形式作一定的假设.从而把求解过程由解复杂的偏微分方程转变为解一般的积分,因此使求解过程变得简单得多了.如果这样求出的解满足一切给定的边值条件,那么从唯一性定理就可得知它代表真空的解. 二、方法的提出…     

混合电解质溶液中考虑介电饱和度的表面电位评估原理（英文）

基于非线性泊松-玻尔兹曼方程,推导了混合电解质溶液中考虑介电饱和度的表面电位的解析表达式.近似解析解和精确数值解计算出的表面电位在很大范围的电荷密度和离子强度条件下均具有很好的一致性.当表面电荷密度大于0.30 C/m~2时,介电饱和度对表面电位的影响变得尤为重要;当表面电荷密度小于0.30 C/m~2时,可忽略介电饱和度的影响,即基于经典泊松-玻尔兹曼方程可获得有效的表面电位解析模型.因此,0.3 C/m~2可作为是否考虑介电饱和度的颗粒临界表面电荷密度值.在低表面电荷密度时,考虑介质饱和度的表面电位解析模型可自然回归到经典泊松-玻尔兹曼理论的结果,得到的表面电位可以正确地预测一价和二价反离子之间的吸附选择性.     

应变绝缘层上硅锗p型金属氧化物场效应晶体管的阈值电压解析模型

分析研究了应变绝缘层上硅锗p型金属氧化物场效应晶体管(SGOI pMOSFET)的阈值电压模型,修正了应变作用下SGOI pMOSFET的能带模型,并提取了主要的物理参量.这些典型的参量包括禁带宽度、电子亲和能、内建势等.给出了应变硅SGOI pMOSFET内部电势分布的二维泊松方程,通过边界条件求解方程,得出了准确的阈值电压模型,并且验证了该模型的正确性.     

对称双弹簧振子横向振动的椭圆函数解

通过分析对称双弹簧振子横向振动的特点,在立方非线性振动精确解的基础上提出振动方程的椭圆函数型近似解析解,并与数值解结果进行了比较.     

向列相液晶中的(1+1)维呼吸子解

理论分析了(1+1)维呼吸子在向列相液晶中传输时的情况,通过对原始方程作归一化计算和相应的傅里叶变换,得到了特定情况下的强非局域非线性薛定谔方程,并且通过此方程最终求到了呼吸子解。在未作近似时可以计算出呼吸子的周期和最大(最小)束宽,在平衡点处将势函数近似展开到二阶,此时不仅得出了呼吸子解的周期和最大(最小)束宽,而且解出了波动振幅的解析解。通过数值模拟与解析解的比较,结果表明,解析结果成立于非局域程度较强的情况,并且未作近似的解析解始终比较接近模拟解。     

扩散p-n结内建电场的数值分析

对高斯分布的p-n结,通过建立相关的一维泊松分布方程,分析边界和初始条件,应用数值计算方法在耗尽层近似和考虑自由载流子两种情况下模拟电场、电势的分布。进一步讨论温度变化对电场、电势分布的影响。     

Hydrodynamical model for bulk and surface plasmons in cylindrical wires

In this paper, we study the electrostatic surface and volume modes of a cylindrical wire using the hydrodynamical model of plasmon excitation, which allows an analytical study of dispersion effects. We solve the hydrodynamical equations for a cylindrical wire geometry, obtaining new analytical expressions for the bulk and surface modes. New dispersion relations are obtained for each type of mode and numerical solutions are given. We analyze in detail the characteristics of the solutions and their differences with previous treatments based on non-dispersive models. These differences become important for wires of small radii, particularly in the range of few nanometers.     

Exact and approximate solutions for the electron nonsinglet structure function in QED

Two exact, valid up to infinite perturbative order, numerical solutions of the Lipatov equation for the nonsinglet electron structure function in the QED are presented. One of them is of the Monte Carlo type and another is based on the numerical inversion of the Mellin transform. They agree numerically to a very high precision (better than 0.05%). Within the leading logarithmic approximation, the exact solution is compared with the perturbative second and third order exponentiated solutions. It is shown that the perturbative second order solution inspired by the Yennie-Frautschi-Suura (exclusive) exponentiation is much closer to the exact solution than the other ones. New compact analytical formula for the third order exponentiated solution is given. It is shown to be in perfect numerical agreement with the infinite order solution of the Monte Carlo and Mellin type.     

γ射线作用下氧化铪基MOS结构总剂量效应研究

使用原子层淀积方法得到了7.8 nm厚度的HfO₂薄膜并通过直接溅射金属铝电极得到了Al/HfO₂/Si MOS电容结构,测量得到了HfO₂基MOS结构在60Co γ射线辐照前后的电容-电压特性,使用原子力显微镜得到了HfO₂薄膜在辐照前后的表面微观形貌,使用X射线光电子能谱方法测量得到了HfO₂薄膜在辐照前后的化学结构变化。研究发现,使用原子层淀积方法制备的HfO₂薄膜表面质量较高;γ射线辐照在HfO₂栅介质中产生了数量级为1012 cm-2的负的氧化层陷阱电荷;HfO₂薄膜符合化学计量比,介质内部主要的缺陷为氧空位且随着辐照剂量的增加而增加,说明辐照在介质中引入了陷阱从而导致MOS结构性能的退化。     

Analytical Solutions for the Two-Dimensional Gross-Pitaevskii Equation with a Harmonic Trap

Both the homotopy analysis method and Galerkin spectral method are applied to find the analytical solutions of the two-dimensional and time-independent Gross-Pitaevskii equation,a nonlinear Schrdinger equation used in describing the system of Bose-Einstein condensates trapped in a harmonic potential.The approximate analytical solutions are obtained successfully.Comparisons between the analytical solutions and the numerical solutions have been made.The results indicate that they are agreement very well with each other when the atomic interaction is not too strong.     

A unified charge-based model for SOI MOSFETs applicable from intrinsic to heavily doped channel

A unified charge-based model for fully depleted silicon-on-insulator (SOI) metal–oxide semiconductor field-effect transistors (MOSFETs) is presented. The proposed model is accurate and applicable from intrinsic to heavily doped channels with various structure parameters. The framework starts from the one-dimensional Poisson–Boltzmann equa- tion, and based on the full depletion approximation, an accurate inversion charge density equation is obtained. With the inversion charge density solution, the unified drain current expression is derived, and a unified terminal charge and intrinsic capacitance model is also derived in the quasi-static case. The validity and accuracy of the presented analytic model is proved by numerical simulations.     

Low-frequency variable charge solitary waves in a collisionless dusty plasma with a Cairns-Gurevich ion velocity distribution

In this paper, the problem of large amplitude dust acoustic (DA) solitons has been addressed in a charge varying dusty plasma with ions following a Cairns-Gurevich distribution. Based on the orbit motion limited approach, the correct Cairns-Gurevich ion charging current is presented for the first time. The expression relating the variable dust charge to the plasma potential is given in terms of the Lambert function and we take advantage of this transcendental function to, carefully, analyse DA solitons in a charge varying dusty plasma with trapped nonthermal ions. Our results show that the spatial patterns of the variable charge solitary wave are significantly changed due to the presence of ion population modelled by the Cairns-Gurevich distribution. An addition of a small concentration of trapped nonthermal ions makes the solitary structure less spiky, grows the net negative charge residing on the dust grain surface, and contributes to the electron depletion. Finally, our investigation is extended to highlight the effect of the grain dust charge variation. We have shown that under certain conditions, the impact of dust charge fluctuation may furnish an alternate physical mechanism rasing anomalous dissipation, which becomes more strong and may predominate over the dispersion as the nonthermal character of ions following the Cairns-Gurevich distribution increases.     

Dirac方程的数值解法及其在原子总能量计算中的应用

中心势近似下径向Dirac方程的求解是相对论性原子(离子)结构计算的基础.本文通过相对论性方程中径向波函数大分量与非相对论方程径向波函数的类比,提出了径向Dirac方程的一种数值解法.为了验证数值解法的精度和可靠性,首先将数值结果与类氢势作用下的解析解进行比较.然后,将这种算法扩展到基于解析势的相对论性原子结构计算中,并将计算出的总能量与实验结果和其他方法得到的结果进行对比.     

精确计算非旋波近似下二能级系统的能谱和动力学性质

利用相干态正交化展开法,精确求解了非旋波近似下Jaynes-Cummings模型的能谱和动力学性质.与近似下解析解比较发现,在弱耦合和强耦合区近似解析解与数值精确解符合很好,但在中间耦合区符合较差. 关键词： 相干态正交化展开 非旋波近似 Jaynes-Cummings模型     

Forming characteristics of recombination properties of InSb MOS structures

Build-up processes of small-signal photo-emf and space-charge layer capacitance following cooling of the structure are investigated as well as the effect on them of fixed charge in the oxide and length of exposure to a voltage applied to the structure. It is shown that there are two types of recombination centers in the semiconductor which differ in the dependences of the concentrations and build-up times on the applied voltage. The centers of the first type determine the carrier recombination velocity in the weak inversion region, while centers of the second type are deep acceptors operating in the region of strong surface inversion. The latter are produced in the structure in the presence of an electric field. It is assumed that the recombinations centers originate from structural defects in the semiconductor and at the interface, whereby centers of the second type include indium vacancy and hydrogen. A mechanism of their emergence is proposed.     

Silicon surface passivation by static charge

A properly passivated silicon surface is chemically stable, and all interface properties are constant. The silicon dioxide layers fulfil the chemical stability requirements; however, their surface and interface charges have effect on the silicon surface potential barrier. Positive charge is usually assumed at the oxide-silicon interface, thus depletion or inversion layer develops in the case of p and accumulation in the case of n-type silicon.The surface of silicon dioxide can be charged macroscopically by corona charger or by conductive rubber stamp, microscopically by a tip of some scanning probe microscope (STM or AFM). The oxide surface usually retains the charges for a long time, however in the case of ultra-thin or other leaky oxide continuous charging it is necessary to keep the constant surface potential.The main purpose of this work is to summarize the possibilities of charging up the surface, the effect of the surface and interface charge on the surface properties of the silicon. The rearrangement of the surface charges will also be discussed.