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.