Modeling and Optimization of Electron-Beam Lithographic Process

Abstract

An important issue in electron-beam (e-beam) lithography is to minimize the critical dimension (CD) error and line edge roughness (LER). This dissertation presents a method to measure the CD and LER from scanning electron microscope (SEM) images, two methods to estimate the CD and LER, i.e., modeling the e-beam lithographic process and utilizing a neural network (NN), and the minimization results obtained based on the estimation. The 3-D modeling is also applied to SEM images from the massively-parallel e-beam system (MPES).

A common approach to the measurement of CD and LER from SEM images is to employ image processing techniques to detect feature boundaries from which the CD and LER are computed. SEM images usually contain a significant level of noise which affects the accuracy of measured CD and LER. This requires reducing the noise level by a certain type of low-pass filter before detecting feature boundaries. However, a low-pass filter also tends to destroy the boundary detail. Therefore, a careful selection of low-pass filter is necessary in order to achieve the high accuracy of CD and LER measurements. In this dissertation, a practical method to design a Gaussian filter for reducing the noise level in SEM images is developed. The method utilizes the information extracted from a given SEM image in adaptively determining the sharpness and size of a Gaussian filter.

Computational lithography is typically based on a model representing the lithographic process where a typical model consists of three components, i.e., line spread function (LSF), conversion formula (exposure-to-developing rate conversion), and noise process (exposure fluctuation). In a previous study, a practical approach to modeling the e-beam lithographic process by deriving the three components directly from SEM images was proposed. However, a 2-D model of a substrate system was employed, i.e., the exposure variation along the resist-depth dimension was not considered. In this dissertation, the possibility of improving the accuracy of modeling using a 3-D model is investigated. The 3-D model is iteratively determined by modeling the estimated CD based on the model to those measured in SEM images. This dissertation describes the 3-D modeling approach and new optimization procedures, and discusses in detail the results from an extensive simulation for an accuracy analysis of the 3-D modeling approach.

The 3-D modeling involves several parameters to be determined and tends to require a long computation time. The possibility of improving the accuracy and efficiency of the CD and LER estimation using a NN is investigated. In the NN-based estimation, the explicit modeling of the e-beam lithographic process can be avoided. This dissertation describes the method of estimating the CD and LER using a NN, including the issues of training, tuning, and sample reduction, and presents results obtained through an extensive simulation.

The accuracy of the 3-D modeling is further verified through the proximity effect correction. A dose modification with the reduction of the feature width is performed utilizing the modeled LSF and noise. The CD error and LER are considered for the performance analysis.

The 3-D modeling is extended and applied to SEM images from the MPES deriving the PSF and the noise. The accuracy is verified by estimating the CD and LER for different doses.