Application of linear iterative methods for the proximity effect correction in electron beam lithography

The Jacobi linear iterative method and weight Jacobi method (WJM) are introduced for solving the large-scale linear problem in the proximity effect correction (PEC) of electron beam lithography. Based on the discussion of PEC physics, a symmetrical and positive defined proximity interaction matrix is constructed to ensure the convergence of the methods. It shows that zeroing the center exposure fraction in the point spread function matrix is equal to the operation of splitting the proximity interaction matrix. Then, the Jacobi method is ready for the PEC calculation. The iterative can be performed in the Fourier domain due to the inherent parallelization of the Jacobi method. The convergent property of the Jacobi method is discussed and then testified by the PEC simulation. Compared with the classical Jacobi method, an improvement of 100% in convergence efficiency can be achieved by introducing the optimized relaxation parameter quasi-ωopt in the WJM. By combining the WJM and Gold nonlinear iteration method, a new method that shows an order of magnitude superior in accuracy to the WJM is proposed. Results indicate the methods introduced here could be used to calculate the PEC problem efficiently.