Block-based mask optimization for optical lithography

Abstract

Pixel-based optical proximity correction (PBOPC) methods have been developed as a leading-edge resolution enhancement technique (RET) for integrated circuit fabrication. PBOPC independently modulates each pixel on the reticle, which tremendously increases the mask's complexity and, at the same time, deteriorates its manufacturability. Most current PBOPC algorithms recur to regularization methods or a mask manufacturing rule check (MRC) to improve the mask manufacturability. Typically, these approaches either fail to satisfy manufacturing constraints on the practical product line, or lead to suboptimal mask patterns that may degrade the lithographic performance. This paper develops a block-based optical proximity correction (BBOPC) algorithm to pursue the optimal masks with manufacturability compliance, where the mask is shaped by a set of overlapped basis blocks rather than pixels. BBOPC optimization is formulated based on a vector imaging model, which is adequate for both dry lithography with lower numerical aperture (NA), and immersion lithography with hyper-NA. The BBOPC algorithm successively optimizes the main features (MF) and subresolution assist features (SRAF) based on a modified conjugate gradient method. It is effective at smoothing any unmanufacturable jogs along edges. A weight matrix is introduced in the cost function to preserve the edge fidelity of the printed images. Simulations show that the BBOPC algorithm can improve lithographic imaging performance while maintaining mask manufacturing constraints.

Gradient-based inverse extreme ultraviolet lithography

“…Hence, we adopt the block-based mask configuration proposed in Ref. [36] and extend it for an EUV mask. This paper only considers the EUV binary mask, and the proposed algorithm can also be applied to EUV phase-shifting masks.…”

“…In our prior work, we have proposed a BBOPC method for DUV lithography [36]. In that work, we first optimized the MFs without inserting the SRAFs, then inserted and optimized the SRAFs by fixing the MFs.…”

“…To preserve the mask manufacturability, this paper adopts three major manufacturing constraints described in Ref. [36]: Constraint I:…”

“…By treating the mask as a set of overlapped basis blocks, BBOPC is capable of enforcing the mask manufacturing constraints during the optimization process. In prior work, we had proposed a BBOPC approach for DUV lithography systems that successively optimized the main features (MFs) and SRAFs on the mask pattern [36]. However, that method was not able to achieve the global optimal solution, since the subsequent SRAF optimization invariably changed the optimum MFs.…”

Parametric source-mask-numerical aperture co-optimization for immersion lithography

“…In addition, current pixelated SMO methods dramatically increase the complexity and fabrication cost of the optimized source and mask patterns; thus, they suffer from an inherent disadvantage in manufacturing. 14,15 To overcome these limitations, this paper proposes a parametric source-mask-NA co-optimization (SMNO) method to improve the pattern fidelity within a large DOF and the complexity of the source and mask patterns. To our knowledge, this paper is the first to solve for the parametric SMNO problem based on a vector imaging model.…”