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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

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.

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.

Prior to carrying out the proximity effect correction by optimizing the spatial distribution of dose in electron beam lithography, one first needs to determine the minimum total dose required. A conventional method typically used to determine the minimum total dose is the trial-and-error approach, which can be unnecessarily costly and wasteful. In this paper, two new dose determination methods are described, which utilize the concept of a "critical path" without any proximity effect correction effort. Also, the dependency of the minimum total dose and dose distribution on the feature and lithographic parameters is investigated. The simulation results show that the proposed dose-determination methods can adaptively and efficiently determine the minimum total dose. Thus, they have the potential to provide a practical and effective alternative to the conventional trial-and-error approach. V