Signal Processing Using Karhunen–Loève Expansion for Wafer Focus Measurement in Lithography

Abstract

We propose a new signal processing method using Karhunen–Loève (KL) expansion for wafer focus measurement in lithography. With the improvement in the critical dimension (CD) accuracy, more high accuracy of wafer focus measurement becomes to be necessary. Recently, it is said that focus accuracy should be required within several ten nanometers. The accuracy of the focus measurement of the actual process wafer does not meet the requirement values due to the complexity of its structure. The objective of this study is the improvement of the focus accuracy for the actual process wafers. Our proposing focus signal processing has two steps. The first step is a supervised learning step in which main component signal waveforms (basis functions) are obtained by using KL expansion from many focus signals whose center positions are known in advance. The second step is a center position detecting step in which an input signal is approximated by using the basis functions obtained in the learning step and the center position of the signal is detected. From a comparison between the conventional signal processing and the proposing signal processing, we obtained the following result to simulated signal. Focus accuracy was rapidly improved (97%) when three basis functions were used for the approximation. By using this technology, the focus detection system can be achieved with a high accuracy and robust against various process wafers.