Minimization of line edge roughness and critical dimension error in electron-beam lithography

Abstract

As the minimum feature size continues to decrease, the line edge roughness (LER) has become a critical issue to be addressed. The LER is caused by a number of stochastically fluctuating effects involved in the fabrication process using electron-beam lithography. Since the LER does not scale with the feature size, it can significantly limit the minimum feature size and the maximum circuit density that can be achieved in a pattern of nanoscale features. Many of the efforts to decrease the LER in the past took an empirical or trial-and-error approach. In this study, a computational approach is taken in developing effective methods to minimize the LER, taking the critical dimension (CD) error due to the proximity effect also into account. Since the LER and the CD error vary with the resist-depth dimension, a 3D model is employed instead of a 2D model used in most of the previous work. The simulation results show that the proposed methods have potential to provide a practical and effective way to minimize the LER. V

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

“…Inside an exposed area of a feature, the LER decreases rapidly toward the boundary of the exposed area. 12 It continues to decrease over the boundary and right outside the exposed area, and then almost levels off or slightly increases in some cases. Therefore, the LER is not minimal at the feature boundary (where the critical dimension (CD) error is minimal, i.e., zero) in general.…”

“…Many of the previous efforts made to reduce the LER are based on an empirical or trial-and-error approach via experiment or simulation. [10][11][12] However, such a method can be very time-consuming and expensive since repetitive simulations or experiments may be required. In order to avoid the simulation and experiment, one may take an analytic approach for estimating and minimizing the LER.…”

Practical approach to modeling e-beam lithographic process from SEM images for minimization of line edge roughness and critical dimension error

“…The LER is caused by a number of stochastically fluctuating effects such as shot noise, distributions of chemical species in the resist such as photoacid generator (PAG), resist development process, etc. 11,13 Such fluctuations can be reflected in the developing rate. Through the conversion formula, the fluctuation of developing rate can be converted into the fluctuation of exposure.…”

“…These behaviors indicate that it might be possible to reduce the LER by shrinking the area of a feature to be exposed, from the feature boundary inward. Based on this observation, the shape control method was developed earlier, 11 which reduces the area to be exposed by DW on each side of the feature, instead of exposing the whole feature, as illustrated in Fig. 9.…”

“…This difference may be due to the particular model employed, the assumptions made, and the phenomena ignored. For example, in our previous study, 11 a computational approach to minimizing the LER was taken. Two methods developed for the LER minimization are based on the results obtained through the Monte Carlo (MC) and development simulations.…”