Regularization of inverse photomask synthesis to enhance manufacturability

Abstract

Mask manufacturability has been considered as a major issue in the adoption of inverse lithography (IL) in practice. With smaller technology nodes, IL distorts the mask pattern more aggressively. The distorted mask often contains curvilinear contour and irregular shapes, which cast a heavy computation burden on segmentation and data preparation. Total variation (TV) has been used for regularization in previous work, but it is not very effective in regulating the mask shape to be rectangular. In this paper, we apply TV regularization not only on the mask image but also on the mask edges, which forces the curves of edges to be more vertical or horizontal, because they give smaller TV values. Except for rectilinearity, a group of geometrical specifications of the mask pattern set by mask manufacture rule control (MRC) is also important for mask manufacturability. To prevent these characteristics from appearing, we also propose an intervention scheme into the optimization framework.

Regularization in Inverse Lithography: Enhancing Manufacturability and Robustness to Process Variations

“…Two masks are designed with ILT, one aiming at the nominal focus point only using the algorithm in [22] and one using the robust design in [16]. We can (d) Output of (a) (e) Output of (b) (f) Output of (c) Figure 2: Experimental results of another two-rectangle pattern [17].…”

“…The form of ℛ{⋅} is under much study; possibilities include using a total variation (TV) norm, and a regularization on the image edges [17]. Figure 2 shows a representative result on another two-rectangle pattern.…”

Block-based mask optimization for optical lithography

“…In the past, a set of methods have been proposed to preserve the geometrical regularity or to improve the manufacturability of PBOPC masks. Some of these methods use regularization terms in the optimization cost function to bias the solution space to solutions with lower complexity [9,11,17,19,20]. However, these approaches can only marginally improve the resultant mask patterns since they cannot strictly guarantee the manufacturing constraints.…”

“…Other methods invoke mask manufacturing rule checks (MRCs) to verify the mask features, clean any MRC violation regions, and enforce the manufacturing constraints [17,[21][22][23][24]. MRCs in these approaches are used as intervention schemes during the mask optimization loop, or as a postprocessing step after the optimization.…”

“…However, the aggressive use of PBOPC poses new challenges to mask manufacturability, which has become a challenging problem for current mask fabrication [17,18]. As shown in Fig.…”