# On the Properties of WC/SiC Multilayers
## 1 Introduction  
Multilayers are \"artificial crystals\" that can be designed and optimized for specific X-ray optical applications. They are often used when reflectivity, bandwidth, operating angle or some other property has to be optimized beyond the range afforded by natural crystal optics. X-rays interact very weakly with materials, so the scattering efficiency of most structures is very low except under specific circumstances such as those giving rise to constructive interference. This is the case for multilayer films with a period \(d\) comparable to the wavelength, \(\lambda\), of X-rays scattering by an angle \(2\theta\) that satisfies Bragg's condition of \(\lambda=2d\) sin \(\theta\). Advances in thin film technology including interface engineering, novel materials and material combinations enabled the manufacture of high quality multilayer structures for X-ray applications [1]. In this paper, we explore the properties of the tungsten carbide/silicon carbide (WC/SiC) multilayer system, which has remarkably low interfacial roughness and can form nanometer or even sub-nanometer period multilayers [2; 3]. Originally this material pair was investigated as a potential coating for hard X-ray telescopes, which require ultra-thin periods. Here we are particularly interested in other applications such as multilayer-based gratings and multilayer Laue lenses (MLLs) [4]. A MLL [5] is a zone plate or a variable-period transmission grating that diffracts X-rays to a common focus. The resolution of the lens, which is inversely proportional to its numerical aperture (NA), is proportional to the smallest zone width. Hence, multilayers that can form sharp and smooth interfaces at nanometer and sub-nanometer layer thicknesses are of high interest for these novel optics. A MLL is prepared by sputtering a multilayer on a flat substrate, which is then sliced in a direction perpendicular to the layers to create a block of a desired depth, and which is typically several microns thick for hard X-ray lenses. The multilayer periods follow the Fresnel zone plate law [6]:\[r_{\rm n}=(n\lambda f+n^{2}\lambda^{2}/4)^{1/2}, \tag{1}\]  
where \(n\) is an integer, \(\lambda\) is the wavelength and \(f\) is the focal length and whereby the bi-layer spacing varies inversely with the square root of the layer number. To take advantage of smooth Si wafer substrates (surface roughness of 0.1-0.2 nm) the MLL deposition starts with the thinnest and ends with the thickest period. Unlike a zone plate, a MLL focuses X-rays only in one direction so two MLLs with slightly different focal lengths are needed to produce a focused spot, analogous to two crossed cylindrical lenses. Usually these two MLLs are produced from multilayers made in two separate deposition runs. The depositions can take several days or even longer to prepare multilayers with a total thickness exceeding 100 \(\upmu\)m. This requires extreme stability and reproducibility of the sputter deposition process. Of course, due to sputter target consumption, the sputter rate changes over time, which has to be taken into account as well. Since MLLs consist of layers spanning over a wide range of thicknesses it is of interest to know how the material properties of WC and SiC change as a function of layer thickness. For example, an abrupt amorphous-to-crystalline transition first observed in Mo layers at 2 nm [7] was also noticed in W layers [8]. This transition caused a phase error [9] in a high numerical aperture wedged MLL [10] fabricated from a W/SiC multilayer. It has been shown that presence of carbon delays this transition. For example, in Mo, where this transition occurs at 2.0 nm, it is shifted to 2.6 nm when Mo is in the vicinity of carbon such as in Mo/B\({}_{4}\)C/Si multilayers [11]. Replacing pure metal with its carbide is another way to prevent nucleation of crystals. In the aforementioned case we replaced W with WC. The new WC/SiC multilayer had no crystalline layers in the whole range of layer thicknesses (3.86 to 21.70 nm) used in these MLLs [8].