Photonic crystals (PhC) are structures with a spatially periodic variation of the refractive index resulting in special optical properties [1]. They can be designed in a very broad range of frequencies from microwaves (e.g. [2-4]) to the visible light [5] and the extreme ultraviolet (EUV) [6]. PhCs can be also found in nature [7]. The numerical methods used for the design are based on Maxwell’s equations taking into account the spatial index variation. They are applicable to ideal structures (one- and three-dimensional photonic crystals in this talk) as well as disordered systems (multi-component rocks in the talk by T. Antretter et al.).
Since more than 50 years the down-scaling of microelectronic components follows Moore’s law [8]. Near-UV lithography (193 nm wavelength) is approaching its limits at structural dimensions of 7 - 10 nm, e.g. for the transistor gate length. For next-generation lithography (≤7 nm [6]) the EUV (13.5 nm wavelength) is considered as the most promising alternative. There, the refractive index n is close to unity and no refractive elements like lenses are feasible in EUV optical systems. Mirrors, however, can be made employing the constructive interference of multi-layers with “large” index contrast of two consecutive layers. These Bragg reflectors are one-dimensional (1D) PhCs. The best Bragg reflector with reflectivity R= 0.73 for normal incidence uses 40 layers of Mo and Si.
In this talk results of numerical investigations are presented regarding: a) a modulation of the 1D PhC, i.e. a superposition of a superstructure on the basic 1D periodic structure and b) 3D PhC structures. The intention is to design EUV mirrors with improved reflection properties. This is very advantageous for EUV lithography systems where several mirrors are used in the illumination and projection optics [6].

[1] E. Yablonovitch, Phys. Rev. Letters 58, 2059 (1987); S. John, ibid. 58, 2486 (1987).
[2] F. Kuchar, R. Meisels, P. Oberhumer, R. Gajic, Adv. Eng. Mat. 8, 11, 1156 (2006).
[3] R. Meisels, O. Glushko, F. Kuchar, Photonics and Nanostructures 10, 60 (2012).
[4] R. Meisels, R. Gajic, F. Kuchar, K. Hingerl, Optics Express 14, 6766 (2006).
[5] M. Campbell, et al., Nature 404, 53 (2000).
[6] V. Bakshi, ed., EUV Lithography, Wiley, 2009.