Expedited Award for Novel Research: Analytical Methods for VLSI Semiconductor Device Design

首席研究员建议对基本的非线性偏微分方程组和边界条件进行新的数学分析，这些方程和边界条件定义了一大类VLSI半导体器件的操作。首席研究员建议利用非线性偏微分方程组理论的最新进展来创建和分析新的程序，以处理设备设计中的二维和(短通道)三维空间问题，而不会导致传统算法的常见数值分歧。此外，首席研究员建议分析研究在芯片小型化过程中出现的几个新的重要效应(例如电子不稳定性和参数依赖性)，这些效应似乎会导致分叉现象。

The Principal Investigator proposes to carry out new mathematical analyses of the basic nonlinear partial differential equations and boundary conditions, that define the operation of a large class of VLSI semiconductor devices. The Principal Investigator proposes to utilize state of the art advances in the theory of nonlinear partial differential equations to create and analyze new procedures to handle problems in both two and (short channel) three spatial dimensions in device design without leading to the usual numerical divergences of conventional algorithms. Moreover, the Principal Investigator proposes to investigate analytically several new important effects that appear as the miniaturization process proceeds to chips at the submicron level (e.g. electronic instabilities, and parameter dependence), which seems to lead to bifurcation phenomena.