Machine learning for inverse lithography: using stochastic gradient descent for robust photomask synthesis

Abstract

Inverse lithography technology (ILT) synthesizes photomasks by solving an inverse imaging problem through optimization of an appropriate functional. Much effort on ILT is dedicated to deriving superior masks at a nominal process condition. However, the lower k1 factor causes the mask to be more sensitive to process variations. Robustness to major process variations, such as focus and dose variations, is desired. In this paper, we consider the focus variation as a stochastic variable, and treat the mask design as a machine learning problem. The stochastic gradient descent approach, which is a useful tool in machine learning, is adopted to train the mask design. Compared with previous work, simulation shows that the proposed algorithm is effective in producing robust masks.

Improving the Quality of Delay-Based PUFs via Optical Proximity Correction

“…Let M y x ∈ {0, 1} denote the pixels at the location x, y for the mask M where zero (one) refers to opaque (transparent) pixels. For a coherent imaging system, the aerial image is given by [19] and [22] I a = |M * h| 2 (3)…”

“…Thus, there has been a great deal of work devoted toward developing techniques that make the fabrication process more robust. For example, OPC [18], [19] is a widely used technique that modifies the lithography mask in order to improve the chance of obtaining desired patterns on the wafer. There have been two types of OPC algorithms discussed in the literature.…”

“…Optical proximity correction (OPC) is one such technique that is applied to the patterning step. OPC provides better manufacturability, better resolution, and less fabrication variation in ICs by modifying the lithography mask [16]- [19]. OPC has been critical to manufacturing because without it ICs would cease to scale.…”

Cascadic multigrid algorithm for robust inverse mask synthesis in optical lithography

“…In order to synthesize masks that are robust to process variations, the average wafer performance is optimized via minimizing the expectation of the difference between the desired pattern and the output pattern with respect to process fluctuations. [31][32][33][34][35][36] This approach takes into account process variations explicitly, and is well understood and easily accomplished. However, it further increases the computational complexity.…”

Mask-filtering-based inverse lithography

“…Instead of using process penalty terms, such as the image slope term and the MEEF, a statistical strategy is applied to minimize a cost function under different process variations weighted by their statistical probability to enhance the robustness of layout patterns. 7,[22][23][24][25][26][27] This method is directly related to the fabrication process and is well understood and easily accomplished, while using the process penalty terms can be considered as a roundabout regularization approach and requires deeper understanding of mask topology and the imaging system. The remainder of this paper is organized as follows.…”