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The computational lithography is a common approach to various optimizations of the electron-beam lithographic process. An essential step in most of the optimization problems is to estimate the exposure distribution in the resist, which is typically done through the convolution of the dose distribution of a circuit pattern with a point spread function (PSF). Although most of the computational lithographic methods employ a deterministic PSF, a PSF is stochastic in reality due to the shot noise and electron scattering. The feature size estimated from the stochastic exposure can be substantially different from that of the corresponding deterministic exposure. This difference stems from the fact that the rough development-front caused by the stochastic exposure makes the developing rate effectively larger. In this study, the effects of stochastic exposure on the critical dimension (linewidth) and their dependency on the lithographic parameters are analyzed in detail. Results obtained through an extensive simulation are presented and thoroughly discussed in this paper. [ABSTRACT FROM AUTHOR]

As the feature size continues to be reduced well below nanoscale, 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, to achieve the highest resolution possible by the e-beam lithography, the LER needs to be minimized. A simulation-based or experimental approach for estimating and minimizing the LER normally requires a great deal of effort to analyze the relationship between the LER and e-beam parameters and thus is time-consuming. Previously, an analytic method for estimating and minimizing the LER was developed for the case of a single line. In this paper, an extension of the estimation method for large-scale uniform patterns is described. In a large pattern, the exposure distribution over a feature varies with the location within the pattern, and the location dependency is due to the global exposure. The analytic expression of LER derived for a single line is adjusted depending on the location. The amount of adjustment for each of the critical locations is determined by the stochastic information on the global exposure at that location. The LER at a location is obtained through an interpolation using the LERs at the critical locations. The LER evaluated by the analytic expression of LER has been compared with that obtained through simulation. [ABSTRACT FROM AUTHOR]

Measurements of the line edge roughness (LER) and critical dimension (CD) from scanning electron microscope (SEM) images are often required for analyzing circuit patterns transferred onto substrate systems. A common approach is to employ image processing techniques to detect feature boundaries from which the LER and CD are computed. SEM images usually contain a significant level of noise which affects the accuracy of measured LER and CD. This requires reducing the noise level by a certain type of low-pass filter before detecting feature boundaries. However, a low-pass filter also tends to destroy the boundary detail. Therefore, a careful selection of low-pass filter is necessary in order to achieve the high accuracy of LER and CD measurements. In this paper, a practical method to design a Gaussian filter for reducing the noise level in SEM images is proposed. The method utilizes the information extracted from a given SEM image in adaptively determining the sharpness and size of a Gaussian filter. The results from analyzing the effectiveness of the Gaussian filter designed by the proposed method are provided. [ABSTRACT FROM AUTHOR]

Two main factors which limit the minimum feature size and the maximum circuit density achievable by electron-beam (e-beam) lithography are the line edge roughness (LER) and the proximity effect. Since the LER is caused by the stochastic nature of the exposing and development processes, it does not scale with the feature size. Therefore, reducing the LER is essential as the feature size continues to decrease. Accurate modeling of the LER and the proximity effect analytically or via simulation for their minimization is either difficult or costly in many cases. In this study, a practical method for extracting the essential information from SEM images, needed to characterize the e-beam lithographic process, and an effective method for minimizing the LER and critical dimension error based on the extracted information have been developed. The main objective is that the methods utilize only the information extracted from SEM images without having to know the complete setup of e-beam lithographic process. It has been shown that they have a good potential to be further developed into practical and useful tools. [ABSTRACT FROM AUTHOR]

As 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. [ABSTRACT FROM AUTHOR]

It is often necessary to achieve a vertical sidewall in the remaining resist profile obtained through electron-beam lithographic process. For nanoscale features, the spatial dose distribution of V-shape typically used in a conventional two-dimensional proximity effect correction scheme cannot easily achieve a vertical sidewall while also minimizing the critical dimension (CD) error. In an earlier study, it was shown through simulation based on a three-dimensional model that new types of spatial dose distributions, i.e., M- and A-shapes, are effective in achieving vertical sidewalls and minimizing the CD error and total dose. These two dose distributions exploit the fact that the exposure varies along the depth dimension with high and low contrasts at the top and bottom layers of resist, respectively. In this study, a number of experiments have been carried out in order to verify the simulation results reported earlier. This paper includes a review of the new dose distribution types and experimental results with a detailed discussion. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The relative critical dimension variation of nanoscale features has become large enough to significantly affect the minimum feature size and maximum circuit density realizable in most lithographic processes. One source of such variation is the line edge roughness (LER). In the electron-beam lithographic process, the fluctuation of exposure (energy deposited) in the resist is one of the main factors contributing to the LER. It is essential to accurately estimate the exposure fluctuation for developing an effective method to reduce the LER. A possible method is to rely on the Monte Carlo simulation in computing the exposure distribution in a circuit pattern, i.e., generating a point spread function (PSF) for each point to be exposed, where the PSF is stochastic. While this approach can lead to a more realistic estimation, it is not practical due to its tremendous amount of computation required. In this paper, a new method to greatly reduce the number of PSF's to be generated without sacrificing the accuracy of estimating the exposure fluctuation is described. It generates only a small number of stochastic PSF's and uses them randomly in the exposure calculation for a circuit pattern. Through an extensive simulation, it is shown that the new method is statistically equivalent to generating a PSF for each point with an acceptable error. Since it is not necessary to know the exact spatial distribution of exposure for estimation of the LER, the new method has a good potential to be employed in practice to reduce the computation time by orders of magnitude. [ABSTRACT FROM AUTHOR]

The spatial dose distribution across a feature, derived by a conventional 2-D proximity effect correction scheme, is a "V-shape," i.e., higher dose closer to edges. With such a dose distribution, it is extremely difficult to realize a vertical sidewall in the resist profile for nanoscale features while reducing the critical dimension (CD) error. In this paper, it is shown that, in order to achieve a vertical sidewall of nanoscale feature with the minimum total dose, a dose distribution of a shape other than the V-shape must be used. This is due to the fact that the lateral development of resist becomes comparable to the vertical development for nanoscale features and the exposure varies along the depth dimension with high and low contrasts at the top and bottom layers of resist, respectively. Based on these characteristics, new types of dose distributions, i.e., "M-shape" and "A-shape," have been derived to achieve a target resist profile of a vertical sidewall while minimizing the total dose. The simulation results show that the new dose distribution types lead to a more vertical sidewall, a smaller CD error, and a lower total dose. [ABSTRACT FROM AUTHOR]