Layer-by-layer design method for multilayers with barrier layers application to SiMo multilayers for extreme-ultraviolet lithography

Juan I. Larruquert

Abstract

A previous layer-by-layer multilayer design method [J. Opt. Soc. Am. A 19, 385 (2002)] is completed by adding the possibility of alternating layers with fixed thicknesses along with layers whose thicknesses are optimized for the largest possible reflectance at a desired wavelength. The previous algorithm did not allow for layers with fixed thicknesses. The current formalism is particularly suited for a multilayer design in which barrier layers of given thicknesses are used to prevent diffusion and/or reaction between the multilayer constituents. The design method is also useful both when intermixing zones develop at multilayer interfaces and when capping layers are used. The algorithm allows the design of multilayers with complex barrier layers with any number of layers of any optical constants. The optimization can be performed either for normal incidence or for nonnormal incidence with either s- or p-polarized radiation. The completed method provides a fast and accurate procedure for multilayer optimization regardless of the number of different materials used in the multilayer. The optimum layer thickness is determined by means of functions suitable for implementation in a computer code. The performance of the current algorithm is exemplified through the design of Si/Mo multilayers with intermixing layers or with barrier layers that are optimized for the largest reflectance at 13.4 nm. The use of specific barrier layers on each multilayer interface is also discussed.