(92g) Variance Component Analysis Based Fault Diagnosis of Multi-Layer Overlay Lithography Processes

As is well known, the lithography process is one of the most critical steps in semiconductor manufacturing and largely responsible for driving improvement in the design of device circuits. During the fabrication, the lithography process is utilized repeatedly to make each layer properly sized and aligned with its adjoining layers to create a functional device. Therefore, overlay serves as one of the key metrics in the lithography processes and the accuracy of multi-stepper overlay in metrology determines the quality and performance of semiconductor products.

There are a number of root causes leading to overlay misalignment errors, including reticle distortion errors, exposure tool image field distortion, alignment error, tracking error, wafer distortion error and so on. Traditional effort in manufacturing industries is focused in product-inspection-oriented measurement approaches. The final and all the intermediate products are measured and compared with the design specification. Once the specification limits are violated, an exhaustive search is conducted to find out the root causes primarily based on the experience of the operation personnel with tools like Statistical Process Control (SPC). However, SPC largely depends on historical data to generate references or benchmarks for effective monitoring and it cannot determine the root causes of faults. The major difficulty for the root-cause identification of the overlay process is due to the large amount of required measurements and complicated variation propagation through the multi-layer steps.

Our work attempts to address the challenging issue by utilizing the statistical technique of variance component analysis (VCA) for error source identification and diagnosis in multi-stage overlay process. In this presentation, a state space realization is first given from the fundamental models on the misalignment errors of lithography process. The general mixed linear input-output model is then formulated to include both fixed and random effects and describe the stochastic fault-quality relationship. Further, the minimum norm quadric unbiased estimation (MINQUE) strategy is employed to estimate the mean and variance components of various fault sources, and their asymptotic distributions are used to test the hypothesis concerning the statistical significance of each potential fault. With the derived confidence limits, the testing results can be applied to statistically determine the active faults in different layers of the lithography process.

A number of simulation examples are designed and implemented to verify the validity and effectiveness of the proposed approach in multi-step overlay process monitoring. The computational results indicate that different types of misalignment error sources can be isolated and diagnosed effectively without any misdiagnosis of faults. In addition, the orientation of the misalignment errors can be identified by the sign of the estimated components. The proposed method can save most of the measurement data in the intermediate stages and improve the accuracy of error source identification in the overlay lithography process.