Modeling and Simulation of Deterministic and Stochastic Nano systems

集成超大规模集成电路(VLSI)电路技术(从深亚微米到纳米级)的不断缩小增加了预测系统性能或估计其基本优值的挑战水平。造成这一困难的主要原因是围绕设计参数的实际(即，硅布局后)值的不确定性增加。在本文中，设计参数指的是广泛的电路设计参数，包括几何和结构参数、工艺参数或电气参数。传统的建模和仿真方法将这些参数视为具有明确数值的确定性变量。然而，由于上述参数制造后或实际值的不确定性，这些参数必须被视为具有一定概率密度函数(PDF)特征的随机变量，如高斯或均匀概率密度函数。随着这一新的发展，系统性能指标在其设计参数中不再是确定性函数，而需要被视为随机过程，其完全特征可以通过计算其PDF来最好地逼近。这个计算系统PDF的目标在数学文献中通常被称为不确定性量化(UQ)。

The relentless downscaling drive in the integrated Very Large Scale Integration (VLSI) circuit technology (from the deep submicron and down to the nano-scale level) has increased the level of challenges in predicting the system performance or estimating its basic figures-of-merit. The main reason for that difficulty stems from the increasing uncertainty that surrounds the actual (i.e., post Silicon-layout) values of the design parameters. Design parameters, in this context, refer to a wide range of circuit design parameters including geometrical and structural parameters, process parameters or electrical parameters. Traditional modeling and simulation approaches have treated those parameters as deterministic variables with well-specified numerical values. However, with the above-mentioned uncertainty surrounding their post-fabrication or actual values, those parameters must be regarded as random variables that are characterized with certain probability density functions (PDF), such as Gaussian or Uniform PDF. With this new development, system performance metrics are no longer deterministic functions in its design parameters, but need to be treated as stochastic processes whose full characterization can be best approached through calculating their PDFs. This goal of computing the PDF of a system is generally known in the mathematical literature as Uncertainty Quantification (UQ).