Analysis of pattern-dependent image placement of single-membrane stencil masks for electron-beam lithography

Large single-membrane stencil masks have been developed for electron-beam lithography. Since a large membrane induces large image placement (IP) error, which is pattern dependent, a method of correcting EB data has been studied to compensate the membrane distortion. In this study, firstly, the effect of crystal anisotropy of a Si membrane to the distortion is examined by making masks from blanks with different orientations. The influence of the anisotropy is found to be small and simulation based on isotropic modeling should be applicable. Secondly, a finite element method (FEM) called ANSYS and Pseudo-FEM are used to predict distortions for three masks with 8 mm-, 12 mm-, or 18 mm-square die of an opening ratio of 0.2 on a 24 mm-square membrane. The simulation results are compared with the results obtained in the experiment on anisotropy and a previous experiment. Qualitative agreement is observed between simulation and experiment but quantitative agreement is obtained only after introduction of adjustment factors. A suggestion is made to improve the IP correction scheme for EB data.