By Xu Ma
A Unified precis of the types and Optimization equipment utilized in Computational Lithography
Optical lithography is likely one of the so much difficult components of present built-in circuit production know-how. The semiconductor is depending extra on solution enhancement thoughts (RETs), on the grounds that their implementation doesn't require major adjustments in fabrication infrastructure. Computational Lithography is the 1st ebook to deal with the computational optimization of RETs in optical lithography, delivering an in-depth dialogue of optimum optical proximity correction (OPC), part transferring masks (PSM), and off-axis illumination (OAI) RET instruments that use model-based mathematical optimization approaches.
The ebook begins with an creation to optical lithography structures, electrical magnetic box ideas, and the basics of optimization from a mathematical perspective. It is going directly to describe intimately sorts of optimization algorithms to enforce RETs. many of the algorithms constructed are in accordance with the applying of the OPC, PSM, and OAI techniques and their combos. Algorithms for coherent illumination in addition to partly coherent illumination structures are defined, and diverse simulations are provided to demonstrate the effectiveness of the algorithms. moreover, mathematical derivations of all optimization frameworks are presented.
The accompanying MATLAB® software program records for all of the RET equipment defined within the booklet make it effortless for readers to run and examine the codes for you to comprehend and follow 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 study and improvement actions of their educational or commercial companies. An accompanying MATLAB® software program consultant is additionally incorporated. An accompanying MATLAB® software program advisor is incorporated, and readers can obtain the software program to exploit with the consultant 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 firms whose study or profession box is semiconductor IC fabrication, optical lithography, and RETs. Computational lithography attracts from the wealthy idea of inverse difficulties, optics, optimization, and computational imaging; as such, the ebook is usually directed to researchers and practitioners in those fields.
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In general, N is very large, and the SVD is resource consuming. Although accurate, the above SOCS models are computationally expensive. Different from the SOCS models, the average coherent approximation model decomposes the partially coherent imaging system into the superposition of a coherent and an incoherent illumination component. This model avoids the SVD and uses only two terms to represent the partially coherent imaging system, thus more computationally efficient than the SOCS models. However, the accuracy of the average coherence approximation model depends on the spatial coordinates, mask pattern, optical system kernel, and the complex degree of coherence.
In Fig. 7, while in Fig. 2. It can be observed from Eq. 22) that larger NA corresponds to a sharper amplitude impulse response. The simulations show that the average coherent approximation model gives more accurate aerial imaging for sharper amplitude impulse response. 4 Discussion and Comparison In this section, three kinds of approximation models of the partially coherent imaging system are discussed. Both the Fourier series expansion model and the SVD model belong to the SOCS models, which approximate the partially coherent system as a sum of coherent systems.
8 illustrates a mask of dimensions 1035 nm × 1035 nm and the corresponding aerial images formed by the annular illuminations having large, medium, and small partial coherence factors. The mask consists of 45 nm features. The pitch p = 90 nm is indicated by dashed lines. The aerial images are synthesized by the Fourier series expansion model. 25 nm]. 63 nm. Note that the aerial images increasingly become more blurred, as the partial coherence factor is decreased. 8 (Top left) Target mask pattern containing 45 nm features with pitch p = 90 nm is indicated by dashed lines.