Depth-Graded Multilayers

At X-ray energies above ~1 keV, multilayer coatings operate efficiently only at shallow graze angles (although these angles are nevertheless several times larger than the critical angle for total external reflection of the best single-layer materials). While periodic X-ray multilayer coatings can provide high reflectance over a narrow spectral band even in the hard X-ray, for many applications, such as X-ray astronomy, broad spectral response is required.

A “depth-graded multilayer” coating (DGML), illustrated conceptually in the figure at right, is a film stack containing a range of layer thicknesses so as to achieve high reflectance over a wide band of X-ray energies. One type of depth-graded multilayer uses a power-law distribution of layer thicknesses, as shown in Figure 1, for example. The theoretical response of a DGML comprising Si/W bilayers is shown in Figure 2, relative to the reflectance of single-layer Pt and Ir coatings.

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Figure 1. Left: layer thickness vs. layer index (counting from the top surface), for a Si/W depth-graded multilayer containing 300 bilayers with a power-law distribution of layer thicknesses so as to achieve broad spectral response. Right: a TEM image of the top few bilayers of a DGML coating similar to the design shown at left.

Figure 2. Theoretical grazing-incidence X-ray reflectance of a Si/W DGML, relative to Ir and Pt single-layer coatings.

The W-based DGML coating shown in Figure 2 is efficient up to the W K-edge near 70 keV. Other material combinations can be used for efficient operation at even higher energies, as illustrated in the next figure.

Figure 3. Theoretical grazing-incidence X-ray reflectance of W-, Pt-, and Co-based DGML coatings.

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Introduction Periodic Multilayers Normal-Incidence Multilayer Optics Depth-Graded Multilayers Grazing-Incidence Multilayer Optics Aperiodic and Laterally-Graded Multilayers