Optical proximity correction (OPC) methods are resolution enhancement techniques (RET) used extensively in the semiconductor industry to improve the resolution and pattern fidelity of optical lithography. In pixel-based OPC (PBOPC), the mask is divided into small pixels, each of which is modified during the optimization process. Two critical issues in PBOPC are the required computational complexity of the optimization process, and the manufacturability of the optimized mask. Most current OPC optimization methods apply the steepest descent (SD) algorithm to improve image fidelity augmented by regularization penalties to reduce the complexity of the mask. Although simple to implement, the SD algorithm converges slowly. The existing regularization penalties, however, fall short in meeting the mask rule check (MRC) requirements often used in semiconductor manufacturing. This paper focuses on developing OPC optimization algorithms based on the conjugate gradient (CG) method which exhibits much faster convergence than the SD algorithm. The imaging formation process is represented by the Fourier series expansion model which approximates the partially coherent system as a sum of coherent systems. In order to obtain more desirable manufacturability properties of the mask pattern, a MRC penalty is proposed to enlarge the linear size of the sub-resolution assistant features (SRAFs), as well as the distances between the SRAFs and the main body of the mask. Finally, a projection method is developed to further reduce the complexity of the optimized mask pattern.
Optical proximity correction (OPC) and phase shifting masks (PSM) are resolution enhancement techniques (RET) used extensively in the semiconductor industry to improve the resolution and pattern fidelity of optical lithography. In this paper, we develop generalized gradient-based RET optimization methods to solve for the inverse lithography problem, where the search space is not constrained to a finite phase tessellation but where arbitrary search trajectories in the complex space are allowed. Subsequent mask quantization leads to efficient design of PSMs having an arbitrary number of discrete phases. In order to influence the solution patterns to have more desirable manufacturability properties, a wavelet regularization framework is introduced offering more localized flexibility than total-variation regularization methods traditionally employed in inverse problems. The proposed algorithms provide highly effective four-phase PSMs capable of generating mask patterns with arbitrary Manhattan geometries. Furthermore, a double-exposure optimization method for general inverse lithography is developed where each exposure uses an optimized two-phase mask.
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