By Xu Ma
A Unified precis of the versions and Optimization equipment utilized in Computational LithographyOptical lithography is among the such a lot hard components of present built-in circuit production know-how. The semiconductor is depending extra on answer enhancement ideas (RETs), considering the fact that their implementation doesn't require major alterations in fabrication infrastructure. Computational Lithography is the 1st booklet to handle the computational optimization of RETs in optical lithography, offering an in-depth dialogue of optimum optical proximity correction (OPC), section moving masks (PSM), and off-axis illumination (OAI) RET instruments that use model-based mathematical optimization approaches.The publication begins with an advent to optical lithography platforms, electrical magnetic box rules, and the basics of optimization from a mathematical standpoint. It is going directly to describe intimately types of optimization algorithms to enforce RETs. lots of the algorithms built are in accordance with the applying of the OPC, PSM, and OAI methods and their mixtures. Algorithms for coherent illumination in addition to in part coherent illumination platforms are defined, and various simulations are provided to demonstrate the effectiveness of the algorithms. additionally, mathematical derivations of all optimization frameworks are presented.The accompanying MATLAB® software program records for all of the RET equipment defined within the e-book make it effortless for readers to run and examine the codes on the way to comprehend and observe the optimization algorithms, in addition to to layout a collection of optimum lithography mask. The codes can also be utilized by readers for his or her learn and improvement actions of their educational or business organisations. An accompanying MATLAB® software program advisor is usually incorporated. An accompanying MATLAB® software program consultant is integrated, and readers can obtain the software program to exploit with the advisor at ftp://ftp.wiley.com/public/sci_tech_med/computational_lithography.Tailored for either entry-level and skilled readers, Computational Lithography is intended for school, graduate scholars, and researchers, in addition to scientists and engineers in commercial companies whose study or occupation box is semiconductor IC fabrication, optical lithography, and RETs. Computational lithography attracts from the wealthy conception of inverse difficulties, optics, optimization, and computational imaging; as such, the publication is additionally directed to researchers and practitioners in those fields.
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Extra info for Computational Lithography (Wiley Series in Pure and Applied Optics)
M denotes the demagnification of the lens, satisfying sin(θ) = M sin(θ ). 2 An optical projection system. 1 PARTIALLY COHERENT IMAGING SYSTEMS 21 is located in the image plane. The location of (x, y) on the image plane corresponds to the vector r, and rˆ = r/|r| = (rx , ry , rz )T . Eimage (x, y; px , py ) denotes the electric field at the location of (x, y) on the wafer, contributed by the effective point source of (px , py ). xˆ , yˆ , and zˆ represent the unit vectors along the x, y, and z axes, respectively.
Hybrid RETs To overcome the limits of both rule-based and model-based RETs, hybrid RETs have been considered. Hybrid RET methods combine rule-based and model-based RETs, where their synergy is exploited to adjust the mask pattern. In most of current hybrid RETs, the image distortion is mainly compensated by model-based RETs. The residual error is subsequently reduced using the rule-based RETs . The main challenges of hybrid RETs include decomposition of the design process into the rule-based and model-based realms and consistency between these two methods .
5) Based on Abbe’s method, the intensity on the wafer is the superposition of all components contributed by every effective source point (px , py ). Let the effective source point of (px , py ) generate a time-average intensity of Isource (px , py ). Then, the aerial image at the location of (x, y) on the wafer is I(x, y) = p2x +p2y ≤NA2c Isource (px , py )Eimage (x, y; px , py ) ∗ (x, y; px , py )dpx dpy . 6) Hopkins Diffraction Model Hopkins diffraction model is a simplified and approximate version of the Abbe’s model, where the integration over the source is carried out before summing up the diffraction angles accepted by the lens [7, 28, 29].