Development of virtual metrology in semiconductor manufacturing
Gill, Bhalinder Singh
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Virtual Metrology (VM) predicts end-of-batch properties (metrology data) from measurable input data composed of pre-process metrology and fault detection and classi cation (FDC) system outputs. This dissertation aims at moving a step closer to the realization of VM in semiconductor manufacturing by providing solutions to the challenges that present VM technology faces. First, various VM methods are introduced and compared in terms of prediction accuracy using four industrial datasets collected from a plasma etch system at Texas Instruments, Inc.. Kalman lter estimation is employed in a novel way to serve as a VM model for predicting outputs of a static process. Recursive PLS regression (R-PLSR) and Kalman filter show the best prediction results as they update the model whenever new measurements are available. Next, two PLS variants (PLS with EWMA mean update and recursive PLS) are proposed as robust VM algorithms that can predict process outputs fairly accurately in the presence of unexpected process drifts and noise. The obtained results reinforce VM technology by suggesting appropriate prediction methods when unexpected process changes occur. For a successful implementation of VM, the data entering the VM model needs to be free from faults. Fault-free (reconstructed) data are obtained by performing fault detection, fault identi cation, and fault reconstruction. A novel fault detection method based on statistics pattern analysis (SPA) is presented. The SPA method provides better fault detection performance for diff erent types of faults as compared to the MPCA-based methods. Next, three well-known fault identi cation methods present in literature are implemented. An equation that relates the RBC with the SVI is derived. The contribution plot method identi es a smaller number of faults correctly as compared to the RBC and the SVI methods. Fairly good estimates of the fault magnitude are obtained when the faults are identi ed correctly. An approach that combines physical measurements with the VM estimates to develop a more robust approach than using VM alone is presented. EWMA-R2R control is implemented using three well-known sampling methods in order to demonstrate the superior performance of two novel control schemes: B-EWMA R2R control and VM-assisted EWMA-R2R control. A new reliance index, which is attractive from a mathematical and practical point of view, is proposed. The VM-assisted EWMA-R2R control yields the best control results among the control schemes employed in this study. The simulation results demonstrate that VM has the potential to reduce measurement costs signi cantly while promising better process control.