Direction-oriented partition of unity finite element method for lithography simulation of the image formation problem in photoresist

Abstract

The direction-oriented partition of unity finite element method (PUFEM) for simulating the image in a photoresist illuminated by partially coherent light is described. The exposure process of DUV lithography is modeled as Helmholtz equations solved by direction-oriented PUFEM. In the present work, a particular emphasis is placed on the application of PUFEM to the scattering problem for periodic structures and the embedding of the direction-oriented angle into the finite element space in order to utilize the nature of the scattering problem. In this article, two excimer laser wave lengths have been used in this investigation. Several numerical experiments illustrate the methodology. These include detailed convergence studies for the problem of scattering of a TE polarized plane wave on the top surface of a resist-coated wafer and the comparison of the results of non-direction-oriented PUFEM and direction-oriented PUFEM. The numerical experiments conclude that the method converges for the scattering problem of the periodic structures.