Study of potential quantization effects in designs for 12.4 nm mirrors

Mirrors at normal incidence have been successfully made for the 12.4 nm spectral region using molybdenum (Mo), silicon (Si), and other materials. At these wavelengths, a typical layer is of the order of 3 nm in physical thickness, and the atomic diameters of the materials are of the order of 0.3 nm. The implication is that the layers are of the order of 10 atomic layers thick. If the deposition of such films were done by atomic layer epitaxy (ALE) or other atomic layer deposition (ALD) techniques, the spectral results would fall in discrete patterns that could limit the potential design choices. The problem would be even more severe at shorter wavelengths. This work reports on the study of some of those possibilities and limitations.