使用随机方法的微电子过程实验设计鲁棒优化

F. Pasqualini, E. Josse
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引用次数: 2

摘要

实验设计(DOE)是20多年来在微电子工业中广泛应用的一种结构化方法,用于研究具有同步因素和响应的物理现象。今天,这种方法被日常用于优化工艺和产品。考虑到这一点,市场上大约五年前推出的大多数DOE软件都包含了Derringer(1980)的Desirability函数。可取性函数允许在同一实验空间中同时优化若干特性。多响应优化的第一步对于DOE的工业应用是绝对必要的,但这种方法的缺点是它是基于确定性优化模型的。所提供的最优并不能保证解的鲁棒性,因为它没有考虑因素和响应模型系数的不确定性。为此,我们在意法半导体采用了一种基于随机优化研究方法的多响应优化方案。它考虑了所有响应模型的因子和系数的不确定性。得到的解为优化的准则提供了一个分布函数,这使我们能够欣赏统计确定的鲁棒性。将详细介绍优化的不同步骤。本文将给出一个应用实例,用于0.18 /spl mu/m技术的先进金属蚀刻工艺。这使我们能够指出随机解对过程鲁棒性的贡献,并将其与确定性解进行比较。在本例中,在实验空间中,最优之间的定位是不同的。对两种方案进行了物理实验,结果表明,随机最优方案的预测效果较好。工业化保留方案具有明显的随机最优性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Robust optimization of experimental designs in microelectronics processes using a stochastic approach
Design of Experiments (DOE) is a structured approach widely used in the Microelectronics industry for over 20 years to study physical phenomena with simultaneous factors and responses. Today this methodology is in daily use to optimize process and products. With this in mind most DOE software's available on the market introduced since around five years ago have included the Desirability functions of Derringer (1980). Desirability functions permit the optimization simultaneously of several characteristics in the same experimental space. This first step in multi-response optimization was absolutely essential for industrial use of DOE, but this approach's weakness is that it is based on a deterministic optimization model. The provided optimum does not guarantee the robustness of the solution because it does not take into account uncertainty on factors and Response model coefficients. For this reason we are deploying at STMicroelectronics a multi-response optimization solution based on a stochastic approach of optimum's research. It takes into account uncertainty on factors and on coefficients of all the response models. The obtained solution provides a distribution function for the optimized criteria, which permits us to appreciate the statistically determined robustness. The different steps of optimization will be detailed. An example of application, for an advanced metal etch process in 0.18 /spl mu/m technology, will be presented. This permits us to point out the contribution of the stochastic solution to the process robustness and to compare it to the deterministic solution. In this example, the localization between optimums was different in the experimental space. The two solutions were tested and the physical results concluded that the better prediction was obtained with the stochastic optimum. The retained solution for industrialization was obviously the stochastic optimum.
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