Modélisation des procédés pour la correction des effets de proximity en lithographie électronique

摘要

Since the development of the first integrated circuit, the number of components fabricated in a chip continued to grow while the dimensions of each component continued to be reduced. For each new technology node proposed, the fabrication process had to cope with the increasing complexity of its scaling down. The lithography step is one of the most critical for miniaturization due to the tightened requirements in both precision and accuracy of the pattern dimension printed into the wafer. Current mass production lithography technique is optical lithography. This technology is facing its resolution limits and the industry is looking for new approaches, such as Multi-patterning (MP), EUV lithography, Direct Write (DW), Nano-imprint or Direct Self-Assembly (DSA). Although these alternatives present significant differences among each other, they all present something in common: they rely on e-beam writers at some point of their flow. E-beam based lithography is subject to phenomena that impact resolution such as are electron scattering, fogging, acid diffusion, CMP loading, etc. The solution the industry adopted to address these effects is to predict and compensate for them. This correction requires predicting the effects, which is achieved through modeling. Hence the importance of developing accurate models for e-beam process. In this thesis, the basic concepts involving modeling are presented. Topics such as data quality, model selection and model validation are introduced as tools for modeling of e-beam lithography. Moreover, the concepts of local and global sensitivity analysis were also presented. Different strategies of global sensitivity analysis were presented and discussed as well as one of the main aspects in its evaluation, which is the space sampling approach. State-of-the-art strategies for todays and future lithography processes were presented and each of their main steps were described. First Principle models that explain the physics and chemistry of the most influential steps in the process resolution were also discussed. Moreover, general Compact models for predicting the results from e-beam lithography were also presented. Finally, some of the limitations of the current approach were described. New compact models described as Point-Spread-Function (PSF) are proposed based on new distributions, such as Gamma and Voigt. Besides, a technique using Splines for describing a PSF is also proposed. Moreover, a flexible resist model able to integrate most of the observed behavior was also proposed, based on evaluating any pattern on the layout using metrics. Results using such method further improved the any of the PSF distribution approach on the critical features that were limiting the future technology nodes. Other specific models and strategies for describing and compensating for extreme-long-range effects and for matching two different fabrication processes are also proposed and described in this work. The calibration layout is a key factor for providing the calibration algorithm with the experimental data necessary to determine the values of each of the parameters of the model. Several strategies from the literature were briefly described before introducing one of the main propositions of this thesis, which is employing variance-based global sensitivity analysis to determine which patterns are more suitable to be used for calibration. A complete flow for selecting patterns for a calibration layout was presented. A study regarding the impact of process and metrology variability over the calibration result was presented, indicating the limits one may expect from the generated model according to the quality of the data used. Finally, techniques for assuring the quality of a model such as cross-validation were also presented and demonstrated in some real-life situations.