Accurate analysis of mechanical stress in dielectric multilayers

Abstract

We present a systematic study of a stress coefficient of dielectric materials (SiO, NbO, and HfO). In particular, we show a thickness dependence of the stress coefficient on layer thickness, which shows that the determination of this coefficient is complex and requires careful analysis. We then apply the different models of the stress coefficient to multilayer structures and show that stress-induced deformation can be precisely predicted in final components with a few percent accuracy.

Coating stress analysis and compensation for iridium-based x-ray mirrors

“…Investigations of the coating stress were performed using a similar approach than the one that was recently developed for oxyde layers [10]. Two-side polished thin fused silica substrates (diameter: 25 mm, thickness: 1.07 ± 0.02 mm) with a deviation from flatness of λ/4 at 633 nm were used for the experiments.…”

“…Stress determination of Cr and Ir-layers relied on the deposition of layers with different thicknesses on fused silica substrates and measuring the flatness of the substrates before and after coatings [10]. Let us define the substrate thickness t S , the radius of curvature of the substrate before deposition R S , the radius of curvature of the substrate after deposition R S+f , the layer thickness t f and E S and ν s the Young modulus and the Poisson coefficient of the substrate, in our case fused silica (E s = 73 GPa and ν s = 0.16).…”

“…Let us define the substrate thickness t S , the radius of curvature of the substrate before deposition R S , the radius of curvature of the substrate after deposition R S+f , the layer thickness t f and E S and ν s the Young modulus and the Poisson coefficient of the substrate, in our case fused silica (E s = 73 GPa and ν s = 0.16). By applying Stoney equation [11], it is then possible to extract the following equation [10]:…”

High-performance thin-film optical filters with stress compensation

“…: (4) In other words, when designing the structures that will be coated on each face of the substrates, we did not only consider spectral performances of the components but also stressinduced deformation. The stress coefficient values that were determined previously [12] were directly implemented for this work. These stress coefficients are equal to: and were determined with a precision within ± 5 MPa (d HfO2 , d Nb2O5 and d SiO2 stands respectively for the thickness of HfO 2 , Nb 2 O 5 and SiO 2 layers and are given in nanometers).…”

“…In this paper, we thus provide a complete description of the fabrication of various kinds of optical elements with stress compensation. These results rely on the repeatable and accurately determined stress coefficients of Nb 2 O 5 , HfO 2 and SiO 2 [12] as obtained with plasma assisted reactive magnetron sputtering. Highly reflecting mirrors at 515 nm with 15 nm flatness peak-to-valley over up to 75 mm diameter aperture that were fabricated for integration on the laser beam circulator of the ELI-NP (Extreme Light Infrastructure -Nuclear Physics) are first presented.…”