Calculation method of intra-field CDU and inter-field CDU revisited for advanced immersion lithography

Wafer critical dimension uniformity (CDU) is a key parameter to characterize the performance of lithography process control. Although there have been many past studies on this topic, the difference between different calculation methods becomes increasingly significant with the continued shrink of semiconductor fabrication design rules. We present a simple study from the statistical point of view on the difference between two representative methods for the calculation of wafer CDU. The overall wafer CDU can usually break down into two parts, within-shot uniformity, or intra-field uniformity, and among-shot uniformity, or inter-field uniformity. The way to calculate intra-field uniformity is to calculate linewidth variation across the shot with each data point being averaged over difference shots. The way to calculate inter-field uniformity, however, can be different. One method is to calculate the linewidth variation across a wafer with each data point being deducted the intra-field component. The other method is to calculate the linewidth variation among different shots for each location in the shot and then average the results over all locations. We compared the CDU results calculated by the two statistical methods. And it is found that the differences are more significant when the sample is small. Also, data measured on wafers is used to well illustrate the differences.