A Novel Analytic Approach to Model Line Edge Roughness using Stochastic Exposure Distribution in Electron-beam Lithography

TL;DR

This paper introduces an analytical method to model line edge roughness in electron-beam lithography by analyzing stochastic exposure distributions, providing insights into the relationship between process parameters and LER.

Contribution

It presents a new analytical approach based on stochastic exposure distribution to understand and predict LER, complementing existing simulation-based methods.

Findings

Derives standard deviation of exposure analytically

Analyzes variance of edge location after development

Shows strong relationship between LER and process parameters

Abstract

The line edge roughness (LER) becomes a issue of e-beam lithography when feature size is reduced into nanometers. Therefore, minimizing the LER is a important method to increase the density of circuit patterns. One of the possible ways is through simulation. The stochastic exposure distributions in the resist is generated by the Monte Carlo simulation. In addition a resist development simulation needs to be carried out. Although there are several ways to simulate or estimate LER but none of them can reveal as much the inner relationship between LER and different parameters as theocratical analysing methods can do. In this paper, a new approach to analytically derive the LER based on the statistical exposure, is described. Our approach is based on analytic model of stochastic exposure distribution, deriving standard deviation of exposure and analyzing the variance of edge location after development. Even though it may not be a complete modeling of LER, it can still show some strong relationship between LER and some inner parameters.