SBIR Phase I: Computational Tool for Plasma Equipment Design Using a Non-Statistical Boltzmann Solver

这个小企业创新研究第一阶段项目将开发一个CAD工具，用于等离子体设备/工艺，使用非统计玻尔兹曼求解器分析带电粒子动力学。目前使用的流体动力学模型缺乏必要的物理，而统计（蒙特卡罗）方法是太昂贵的实际应用。所提出的玻尔兹曼解算器将能够精确但负担得起的描述低压等离子体反应器的半导体制造。 该研究的创新方面包括：（i）开发适用于任意各向异性的速度分布函数（VDF）的椭圆表示，（ii）将最近发现的热等离子体效应纳入其中，以及（iii）将Boltzmann求解器与商业软件CFD-ACE+集成，以模拟工业等离子体系统。椭圆表示将玻尔兹曼方程简化为四维空间中的一组两个耦合方程，可以通过公认的技术求解。在第一阶段，该方法的可行性将被证明在选定的系统与小各向异性的VDF。第二阶段的工作将集中在扩展模型的任意VDF各向异性的问题和验证对实验数据和Monte Carlo模拟的工业等离子体reactor.The CFD-ACE+软件，加上玻尔兹曼求解器，将能够动力学建模的低压等离子体处理反应器。该软件的使用将大大减少开发IC制造新设备/工艺的设计周期时间/成本。此外，该工具将用于分析和优化深亚微米半导体器件中的电荷传输。

This Small Business Innovation Research Phase I project will develop a CAD tool for plasma equipment/ processes using a non-statistical Boltzmann solver for the analysis of charged particle kinetics. Currently used hydrodynamic models lack the necessary physics while the statistical (Monte Carlo) methods are too expensive for practical use. The proposed Boltzmann solver will enable precise yet affordable description of low-pressure plasma reactors for semiconductor manufacturing. The innovative aspects of the research include, (i) development of an elliptic representation of the velocity distribution function (VDF) valid for arbitrary anisotropy of the VDF, (ii) incorporation of the recently discovered hot plasma effects, and (iii) integration of the Boltzmann solver with a commercial software, CFD-ACE+, to enable simulations of industrial plasma systems. The elliptic representation reduces the Boltzmann equation to a set of two coupled equations in a four-dimensional space which can be solved by well-established techniques. In Phase I, the feasibility of the approach will be demonstrated on selected systems with small anisotropy of the VDF. The Phase II work will focus on extending the model to problems with arbitrary VDF anisotropy and on validation against experimental data and Monte Carlo simulations of industrial plasma reactors.The CFD-ACE+ software, with the addition of the Boltzmann solver, will be capable of kinetic modeling of low pressure plasma processing reactors. The use of this software will significantly reduce design cycle times/costs for developing new equipment/processes for IC fabrication. Additionally, this tool will be used to analyze and optimize charge transport in deep sub-micron semiconductor devices.