Analytic estimation and minimization of line edge roughness in electron-beam lithography

Abstract

Simulation of amine concentration dependence on line edge roughness after development in electron beam lithography J. Appl. Phys. Electron-beam patterning with sub-2 nm line edge roughnessAs the feature size is reduced well below 100 nm, the line edge roughness (LER) will eventually become a resolution-limiting factor in the electron-beam (e-beam) lithography since the LER does not scale with the feature size. Therefore, it is essential to minimize the LER in order to achieve the highest resolution possible by the e-beam lithographic process. A simulation or experiment based method for minimizing the LER can be very time-consuming and expensive since repetitive simulations or experiments may be required. In this study, a new analytic model and a method for estimating the LER are developed based on the model, and an analytic procedure for minimizing the LER is also derived based on the new analytic model. In this new approach, the LER is derived from the distribution of the stochastic developing rate in the resist, which is assumed to be known. The results obtained by the analytic estimation method and the minimization procedure are shown to be close to those by the simulation method. The current work includes generalization of the results of this study with more practical models.

Analytic estimation of line edge roughness for large-scale uniform patterns in electron-beam lithography

“…In this section, our previous work 15 on the analytic derivation of LER for a single line is briefly reviewed.…”

“…Since the developing process is isotropic, it is not easy to derive the development path analytically in one step, and therefore, an iterative method is used to derive the development path. 15 The fluctuation of developing time can be directly derived from the developing-rate distribution along the development path. The developing time T is expressed as the integral of 1=RðpÞ along the development path…”

“…In our previous study, 15 a new analytic method for estimating the LER at any layer of resist was developed for the case where a long single line is exposed with a uniform dose. Without having to obtain the remaining resist profile, the analytic (mathematical) expression of LER is derived explicitly from the stochastic fluctuation of the developing rate distribution on which the remaining resist profile mainly depends.…”