Pixel-based finite-difference gradient probing for fast and high-fidelity curvilinear OPC with MBMW-compatible parametric curve output

Curvilinear masks are essential for advanced lithography. However, recent curvilinear OPC methods often lack a direct and efficient mechanism for the movement direction. Moreover, directly computing the gradient of the objective function with respect to the control points of curvilinear masks remains computationally challenging. To address these issues, this paper proposes a pixel-based finite-difference gradient probing method for fast and high-fidelity curvilinear OPC. This method calculates the influence of each control point movement on the objective function through finite-difference gradient probing along the normal direction of its corresponding parametric curve. It efficiently computes the derivative of the objective function with respect to the control points, and determines both the direction and magnitude of control point movement. These finite-difference gradient probing values are then used to directly update the control point vectors of the curvilinear mask. Simulation results across four representative patterns demonstrate that the proposed method converges within 8–21 iterations, achieving pattern error comparable to or lower than the level-set method while reducing total runtime by up to 50% and directly outputs the optimized curvilinear mask in a parametric format natively compatible with multi-beam mask writers (MBMW). It removes the requirement for post-processing conversion from pixelated results to curvilinear formats, offering a more efficient and practical solution for high-fidelity curvilinear OPC.