# Periodic Multilayer for X-ray Spectroscopy in the Li K Range
## 1 Introduction  
Most chemical elements in inorganic samples can be quantitatively analyzed by X-ray microanalysis. This nondestructive technique, classically implemented on scanning electron microscopes (SEM) and electron probe microanalyzers (EPMA), is used to quantify (determine the weight fraction of) elements present in solid samples from the measurement of the characteristic X-ray intensities emitted by these elements under electron irradiation. However, lithium, despite its many applications, notably in the energy domain [1], is a light element that cannot currently be measured with this standard X-ray analytical technique. Today, lithium analysis thus requires the use of either synchrotron radiation facilities, not readily accessible, or destructive techniques such as laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS) [2] or laser induced breakdown spectroscopy (LIBS) [3]. Moreover, LIBS analysis is only semiquantitative due to major matrix effects, and LA-ICP-MS analysis requires analytical spots often larger than the size of many structures in materials, which are of micrometric size (batteries, ceramics, minerals). The K\(\alpha\) spectrum of lithium (in the 45-55 eV spectral range [4]) has been studied for a long time with high spectral resolution grating spectrometers [5; 6; 7; 8; 9]. However, there has been recent progress in equipping laboratory instruments with spectrometers dedicated to the ultrasoft X-ray range and particularly for the analysis of the Li K emission [10; 11]. To disperse the X-ray radiation, they rely on gratings or zone plates and thus should be used as accessories on SEM and EPMA, which come in addition to the standard bent crystal spectrometers. A much simpler and cheaper way would consist of using a periodic multilayer as a dispersive element, which can be set up in the crystal spectrometers of SEM or EPMA. In this case, the user can continue to work with his standard procedure to obtain the Li K spectrum necessary to perform quantification. Owing to the long wavelength of the Li K radiation (around 25 nm), there is no available crystal to perform spectroscopy, but nanoscale periodic multilayers, whose period can be suited to the desired spectral range, should be used, as this is commonly done to analyze low-Z elements [12; 13; 14; 15; 16; 17]. In order to perform a reliable and precise quantification, it is necessary to obtain the most intense possible spectrum, free of spectral interferences. This translates into the following requirements for the design of the multilayer, which should:  
* present a high reflectance in the Li K range;
* present a narrow bandwidth;
* minimize the contribution of the high diffraction orders;
* have a period leading to a Bragg angle at the center of the angular range spanned by standard spectrometers used in SEM and EPMA. In this context, Be-based periodic multilayers, i.e., multilayers in which one of the layers is a Be thin film, are of high interest [18; 19; 20]. In these works, the Be/Si/Al structures were studied for the 17-30 nm (40-75 eV) wavelength range. The combination of only weakly absorbing materials in the period allows one to increase the extinction depth in comparison with the case of materials with high absorption: for example, Mo/Si or B\({}_{4}\)C/Si [21]. This increases spectral selectivity (decreases bandwidth). The reflection coefficient remains high due to the fact that a larger number of periods of the structure diffract when the radiation is reflected than in the case of using strongly absorbing materials. It is important to note the role of the silicon layer as an element smoothing out the roughness. Theoretically, a two-component Be/Al structure should have a high reflection. However, it was shown in [18; 19; 20] that such a structure has a high (up to 2.3 nm) interfacial roughness. The introduction of a thin (1-2 nm) silicon layer reduces the roughness by a factor of 1.5 to 2.