Multi-step virtual metrology for semiconductor manufacturing: A multilevel and regularization methods-based approach

In semiconductor manufacturing, wafer quality control strongly relies on product monitoring and physical metrology. However, the involved metrology operations, generally performed by means of scanning electron microscopes, are particularly cost-intensive and time-consuming. For this reason, in common practice a small subset only of a productive lot is measured at the metrology stations and it is devoted to represent the entire lot. Virtual Metrology (VM) methodologies are used to obtain reliable predictions of metrology results at process time, without actually performing physical measurements. This goal is usually achieved by means of statistical models and by linking process data and context information to target measurements. Since semiconductor manufacturing processes involve a high number of sequential operations, it is reasonable to assume that the quality features of a given wafer (such as layer thickness and critical dimensions) depend on the whole processing and not on the last step before measurement only. In this paper, we investigate the possibilities to enhance VM prediction accuracy by exploiting the knowledge collected in the previous process steps. We present two different schemes of multi-step VM, along with dataset preparation indications. Special emphasis is placed on regression techniques capable of handling high-dimensional input spaces. The proposed multi-step approaches are tested on industrial production data.