Evaluation of permissible pixel positioning errors for displaying computer-generated holograms in projection photolithography

The authors carried out the estimation of the permissible positioning errors when displaying reflective phase holograms intended for application in holographic photolithography on solid media using electron-beam lithography devices. The work deals with the projection of holographic photolithography based on computer generated Fresnel holograms. The synthesis of holograms involved mathematical modeling of the physical processes of hologram recording and reconstruction using the following parameters: the characteristic size of the binary object is 20 × 20 nm or 80 × 80 nm, the wavelength of the radiation is 13.5 nm, the pixel size of the hologram is 20 × 20 nm, the distance between the planes of the object and the hologram is from 20.4 to 31.6 microns, the angle of incidence of the reference wave is 14º42′. For each of the three objects used in the modeling (namely, “Angles”, “Line grid target” and “Enlarged angles”), four computer-generated holograms were synthesized with different values for standard deviation of the pixel positioning error. The simulation of these errors was carried out by violating the equidistance of the points (pixels) on the hologram aperture. The holograms distorted in this way were subjected to the standard procedure of numerical reconstruction in virtual space. Comparison of the quality of the images obtained at different values of the positioning errors of the hologram pixels made it possible to evaluate their influence on the quality of the reconstructed image. It has been shown that the criterion used for estimating the permissible value of the positioning error in analog holography cannot be applied to synthesized holograms, because of the peculiar properties of interference fringes in discrete holograms. The results demonstrated a significant dependence of the permissible (in terms of image quality) pixel positioning errors on the object presentation method. The analysis revealed the impossibility of applying a single tolerance for pixel positioning errors to all possible synthesis conditions of computer-generated holograms and hence indicates the necessity of including a feature for estimating permissible hologram positioning errors into the software package for the synthesis and reconstruction of holograms. Based on the analysis of the technological parameters of modern electron-beam lithography devices, the authors confirmed the possibility of their use for manufacturing computer-generated holograms in modern high-resolution photolithography. Modeling the permissible positioning errors of computer-generated holograms by the proposed method allows evaluating the practical possibility of producing holograms with the required structure and high quality of the reconstructed image with a specific electron beam lithography device.