Derivation of line edge roughness based on analytic model of stochastic exposure distribution

Abstract

Simulation of amine concentration dependence on line edge roughness after development in electron beam lithography J. Appl. Phys.As the feature size is reduced well below 100 nm, the line edge roughness (LER) becomes a critical issue since it does not scale with feature size. For minimizing the LER, it is essential to be able to accurately estimate it. A possible method for LER estimation is to rely on simulation. However, it requires time-consuming procedures, i.e., the Monte Carlo simulation for computing the exposure distribution within resist, and a resist-development simulation. In this study, an analytic method for estimating the LER, defined as the standard deviation of edge location, is developed to overcome the drawback of simulation method. This new approach first relates the stochastic exposure to the statistics of point spread functions, i.e., mean and variance, and eventually derives the variation of edge location considering critical paths in the resist development process. The analytic method achieves good accuracy compared to a simulation method and has a good potential to be employed in practice.

Line-Edge Roughness from Extreme Ultraviolet Lithography to Fin-Field-Effect-Transistor: Computational Study

“…Through collisions between a photoelectron and an atom in resist materials, a photoelectron's direction is changed according to elastic scattering and inelastic scattering. Monte Carlo method can be used to compute a possible set of scattering events for a photoelectron as it travels inside a resist [27][28][29]. By repeating this process many times, a statistically valid and detailed picture of interaction processes can be constructed.…”

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

“…The interaction tends to decrease the variation (of path length) among the paths and reduces the LER. Therefore, an adjustment factor 16 is employed to compensate the interaction between paths, and the final expression of LER [from Eqs. (6) and (8)] is given as…”

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

“…CðxÞ ¼ x À x t þ 3 Á LERðsÞ: (15) Around the target edge location x t , the remaining resist profile is almost vertical and, therefore, hðsÞ % 0; cos hðsÞ % 1; q T ðsÞ % q T ðs t Þ; (16) rðTjsÞ changes very slowly around s t…”

“…An infinite contrast of development process was assumed to obtain the LER directly from the blocked polymer latent image without modeling the development process. In our previous analytic method of estimating the LER, 16 the final expression of the LER is not derived as a function of the e-beam lithographic parameters such as dose, etc. Therefore, it is not suitable for the analytic procedure of minimizing the LER with respect to those parameters.…”