A.M. Lerer, G.P. Sinyavsky, E.S. Tolstolutskaya, S.I. Tolstolutsky

The progress in the solving of a problem of reduction of the minimal characteristic size of elements of the integral circuits in microelectronics is provided with some improvements of photolithography using a visible part, ultraviolet and near extra ultraviolet ranges of electromagnetic emission [1]. To increase the permission it is possible also by improvement of a photomask, in particular: by introduction of transparent dielectric between a mask and wafer with photoresist; by application of phase-shifting photomask allowing to change a emission phase so that to improve permission on a photoresist [2]. The purpose of the present work is development of mathematical model of the method of increase of the permission indicated above and research of a possibility of application of a Kirhhoff method for the calculating of a near field. The main stages of the solution: 1. The solving of a boundary - value problem are reduced to the solution of the paired integral equations (PIE) relatively of the Fourier transform of tangential components of electric field intensity on the slots. 2. To obtained formulas for the calculating electric field intensity in the any point researching structure. 3. PIE is solved by two methods. The first it is Galerkin´s method. The second is Kirchhoff method. 4. At the solving was used regularization PIE, based on allocation and analytical transformation of a static part of cores PIE. The conclusion. The mathematical model of phase-shifting masks is developed. The application of a Kirchhoff method for account of a near electromagnetic field is proved. The ways of increase of the permission of photolithography is introduction transparent dielectric between a mask both wafer with photoresist, and application of phase-shifting photo masks are theoretically investigated.