Mathematical Sciences: Analytical and Numerical Studies of Partial Differential Equations of Semiconductor Devices

数学科学：半导体器件偏微分方程的分析和数值研究

• 批准号: 9015878
• 负责人: Julian Cole
• 金额: $ 15万
• 依托单位: Rensselaer Polytechnic Institute
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-03-15 至 1993-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9015878&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Analytical; Numerical; Studies

The principal investigators will study the partial differential equations and integro-differential equations that model semiconductor devices by using analytical and numerical methods. Their work will span the entire range from the actual derivation of the basic equations to the solution of concrete boundary value problems. In particular, the investigators will study the Boltzmann equation and systems derived from it such as the hydrodynamic model and the drift-diffusion model using asymptotic methods. The systems of differential equations that describe the behavior of semiconductor devices are difficult to solve analytically. Even large computers are unable to resolve aspects of the solutions accurately. Thus there is a great need for approximate theories that contain enough of the physics of the devices to be realistic and yet are tractable mathematically. The principal investigators will derive approximate models of semiconductors and study them with asymptotic and numerical methods, in order to understand the workings of actual devices.

主要研究人员将使用解析和数值方法研究半导体器件模型的偏微分方程组和积分-微分方程组。他们的工作将跨越从基本方程的实际推导到具体边值问题的解决的整个范围。特别是，研究人员将使用渐近方法研究玻尔兹曼方程及其衍生的系统，如流体动力学模型和漂移-扩散模型。描述半导体器件行为的微分方程组很难解析求解。即使是大型计算机也无法准确地解析解决方案的各个方面。因此，非常需要包含足够多的器件物理知识的近似理论，使之符合实际，并且在数学上是容易处理的。主要研究人员将推导出半导体的近似模型，并用渐近和数值方法研究它们，以了解实际器件的工作原理。