Computer simulation of diffraction focusing in proximity lithography

During a photoresist exposing through a photomask with actinic radiation via a micro gap, the resulting spatial intensity distribution is accompanied by diffraction. At the same time, there is a phenomenon of diffraction focusing, when the resulting image has the appearance of a sharp peak. This can facilitate the increase of the microlithography process resolution by the reducing the size of the image formed in the photoresist as compared to the window on the photomask. To increase the phenomenon efficiency, it is necessary to assess how acting factors influence the resulting profile of the intensity distribution and obtain quantitative estimation of such correlations. Based on the Kirchhoff-Fresnel diffraction scalar theory, we obtained estimated intensity distributions depending on key acting factors which are the photomask window width, gap-size and radiation wavelength. Analysis of the obtained dependences showed that they follow the law of similarity that connects these factors, which allowed to reduce considerably the calculation complexity. Introducing the dimensionless values of the coordinates and the window width, we obtained the intensity distributions of the same shape both for exposure to ultraviolet radiation as well as X-ray, whose wavelength is 1000 times shorter. As a quantitative parameter characterizing the interrelation of active factors, the Fresnel number was chosen. The combination of intensity distributions modeling and graphical results visualization, performed in Matlab, allowed to determine the intensity distributions most promising for the diffraction focusing realization. It is shown that such distributions are characterized by Fresnel numbers in the range of 0.5-0.6.