Weighted least squares regression for advanced overlay control

Controlling overlay performance has become one of the key lithographic challenges for advanced integrated circuit manufacturing. Overlay error budgets of 4 nm in the 2x node require careful consideration of all potential error sources. Overlay data modeling is a key component for reducing systematic wafer and field variation, and is typically based on ordinary least squares (OLS) regression. OLS assumes that each data point provides equally reliable information about the process variation. Weighted least squares (WLS) regression can be used to improve overlay modeling by giving each data point an amount of influence on the model which depends on its quality. Here we use target quality merit metrics from the overlay metrology tool to provide the regression weighting factors for improved overlay control in semiconductor manufacturing.