A WENO-solver for the transients of Boltzmann-Poisson system for semiconductor devices: performance and comparisons with Monte Carlo methods
A WENO-solver for the transients of Boltzmann-Poisson system for semiconductor devices: performance and comparisons with Monte Carlo methods
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DOI：
10.1016/s0021-9991(02)00032-3
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发表时间：
2003-01
影响因子：
4.1
通讯作者：
J. Carrillo;I. Gamba;A. Majorana;Chi-Wang Shu
中科院分区：
文献类型：
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作者：
J. Carrillo;I. Gamba;A. Majorana;Chi-Wang Shu
本文开发了半导体器件一维玻尔兹曼-泊松系统的确定性高阶精确有限差分WENO求解器。我们遵循Fatemi和Odeh以及Majorana和Pidatella的工作，将能量作为坐标变量之一，在球坐标系中制定Boltzmann-Poisson系统，从而将计算复杂度降低到相空间的二维，并大大简化了碰撞项的评估。求解器在时间上是准确的，因此对时间相关的模拟可能有用，尽管在本文中我们只对稳态设备进行了测试。求解器的高阶精度和非振荡特性使我们能够使用非常粗糙的网格来获得满意的分辨率，从而使在今天的计算机上开发二维求解器（当相空间离散时将是五维加时间）成为可能。将计算结果与蒙特卡罗模拟结果进行了比较，发现两者非常吻合。与蒙特卡罗求解器相比，当前求解器的优点包括速度更快、无噪声分辨率和易于进行任意矩评估。因此，该求解器是检验各种水动力和能量输运模型的物理有效性的有用基准。本文还进行了一些比较。
In this paper we develop a deterministic high order accurate finite-difference WENO solver to the solution of the 1-D Boltzmann–Poisson system for semiconductor devices. We follow the work in Fatemi and Odeh and in Majorana and Pidatella to formulate the Boltzmann–Poisson system in a spherical coordinate system using the energy as one of the coordinate variables, thus reducing the computational complexity to two dimensions in phase space and dramatically simplifying the evaluations of the collision terms. The solver is accurate in time hence potentially useful for time-dependent simulations, although in this paper we only test it for steady-state devices. The high order accuracy and nonoscillatory properties of the solver allow us to use very coarse meshes to get a satisfactory resolution, thus making it feasible to develop a 2-D solver (which will be five dimensional plus time when the phase space is discretized) on today’s computers. The computational results have been compared with those by a Monte Carlo simulation and excellent agreements have been found. The advantage of the current solver over a Monte Carlo solver includes its faster speed, noise-free resolution, and easiness for arbitrary moment evaluations. This solver is thus a useful benchmark to check on the physical validity of various hydrodynamic and energy transport models. Some comparisons have been included in this paper.