Imaging Systems Laboratory: Research on Computation Lithography

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Objective

We develop computational algorithms  —  mostly inverse imaging  —  for optical lithography in IC manufacturing.

The current landscape

Computation lithography has its root in lithography simulation, but has since grown to encompass many technologies that are indispensable for IC development. These include, among many others, the computation of partially coherent imaging and resist development modeling. This “virtual world,” however, can be divided into two categories: tools with sensible specifications and performance meeting the targets (the “virtual reality”), and those that fall short of one or both criteria (the “virtual virtuality”). Many technologies today still live in the second realm; our view of the boundary today is shown in Figure 1 below [1].

Reality Virtuality space

Fig 1: The reality-virtuality space of computation lithography (not to scale) [1].

This boundary, of course, is not static, and our aim is to enlarge the virtual reality region through better imaging algorithms. Below are some of our work in this area.

Inverse lithography

(1) Phase-shifting masks

Inverse lithography is a powerful technique for model-based optical proximity correction (OPC). We tackle the challenging scenario of designing an alternating phase-shifting mask using inverse lithography. In particular, we show that a simple initialization scheme can enhance the image robustness at a very moderate cost. An example is given in Figure 2 below [2].

Reality Virtuality space
       
Reality Virtuality space

Fig 2: [left] Aerial image without phase initialization; [right] Aerial image with phase initialization using our scheme [2].

(2) Manufacturing variability

Many OPC designs assume a particular set of nominal conditions, but in reality, the manufacturing contains variabilities, such as focus and dose variations. We have devised several schemes to incorporate focus variation expicitly, and show that they generally outperform other methods over a range of focus errors. An example is given in Figure 3. Techniques we have developed include:

  • machine learning algorithms [3];

  • level set methods [4] [5].

Reality Virtuality space
       
Reality Virtuality space

Fig 3: [left] Aerial image with defocus; [right] Aerial image with defocus, designed with our scheme [3].

Algorithm variability

Computation lithography relies on algorithms. These algorithms exhibit variability that can be as much as 5% of the critical dimension for the 65-nm technology. Using hotspot analysis and fixing as an example, such variability can be addressed on the algorithm level via controlling and eliminating its root causes, and on the application level by setting specifications that are commensurate with both the limitations of the algorithms and the goals of the application [6].

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Selected references

  1. Edmund Y. Lam and Alfred K.K. Wong, “Computation lithography: virtual reality and virtual virtuality,” Optics Express, vol. 17, no. 15, pp. 12259–12268, July 2009.
    (pdf copy)  (bibtex entry)  (Keynote address at ISTC/CSTIC)
    This paper pioneers the demarcation of “virtual reality” and “virtual virtuality” in the space of computation lithography, and argues that engineering sensible-ness and technical feasibility are the two main metrics in evaluating various technologies.

  1. Stanley H. Chan, Alfred K. Wong, and Edmund Y. Lam, “Initialization for robust inverse synthesis of phase-shifting masks in optical projection lithography,” Optics Express, vol. 16, no. 19, pp. 14746–14760, September 2008.
    (pdf copy)  (bibtex entry)
    This paper gives a phase-shifting mask design using inverse lithography, and provides a simple initialization scheme that enhances the image robustness at a very moderate cost.

  1. Ningning Jia and Edmund Y. Lam, “Machine learning for inverse lithography: Using stochastic gradient descent for robust photomask synthesis,” Journal of Optics, vol. 12, no. 4, pp. 045601, April 2010.
    (pdf copy)  (bibtex entry)  (ASML/Cymer best student paper award)
    We show in this paper that we can specifically take the defocus variation into account in the inverse lithography formulation to synthesis a robust mask.

  1. Yijiang Shen, Ngai Wong, and Edmund Y. Lam, “Level-set-based inverse lithography for photomask synthesis,” Optics Express, vol. 17, no. 26, pp. 23690–23701, December 2009.
    (pdf copy)  (bibtex entry)
    This paper gives a complete derivation and investigation in the level set approach for inverse lithography.

  1. Yijiang Shen, Ningning Jia, Ngai Wong, and Edmund Y. Lam, “Robust level-set-based inverse lithography,” Optics Express, vol. 19, no. 6, pp. 5511–5521, March 2011.
    (pdf copy)  (bibtex entry)
    This paper shows how level set algorithms can lead to robust mask design. Our technique is picked up by the industry magazine Laser Focus World.

  1. Edmund Y. Lam and Alfred K. Wong, “Nebulous hotspot and algorithm variability in computation lithography,” Journal of Micro/Nanolithography, MEMS, and MOEMS, vol. 9, no. 3, pp. 033002, July 2010.
    (pdf copy)  (bibtex entry)
    We show for the first time that algorithm variability is a significant issue in computation lithography, as a moderate variability in critical dimension can lead to significant discrepancy in hotspot detection results with different algorithms.

News

  • (2009/09/25) Feature article in SPIE newsroom regarding our pioneering work on algorithm variability.

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Current members

External collaborators and former members

Funding

The work is supported in part by grants from the Research Grants Council of the Hong Kong Special Administrative Region, and by the Areas of Excellence project Theory, Modeling, and Simulation of Emerging Electronics.