Topology optimization of coupled heat problems

Abstract

In modern ASML machines optical components play an important role in the lithography process. EUV light is transported from the source to wafer by reflective optics. These mirrors are subjected to large thermal loading, as a large portion of the reflected light is absorbed in the mirror structure. The portion of the absorbed light is strongly dependent on the intensity and wavelength of the considered light, introducing varying amounts of thermally induced strains on the mirror structure and thereby limiting the optical performance. Current mirror designs typically use solid mirror structures for more predictable deformations. These structures are coupled to spiral cooling channels to extract the absorbed heat to achieve more uniform temperature distributions. However, as ASML strives towards ever smaller resolutions, advances have to be found on the mirror design methodology to further reduce the thermally induced strains.
In this research, topology optimization is used as a possible method of producing designs which can minimise the thermally induced surface deformations of a mirror typically encountered when exposed to thermal loading. Due to the "multi-physics" nature of this problem, the optimization problem has to encompass thermo-mechanics, thermo-fluidics and the conjugate heat transfer at the interface of these two domains. The topology optimization formulation presented in this research, minimises surface deformations by altering the topology of the mirror structure together with the cooling channel layout producing an integrated solution.