Development of an ultra-high resolution diffraction grating for soft x-rays Page: 4 of 12
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parameter s . Such a loss would make appearance of the optimal finite size of the lands (slits), similar to that was found
above.
The number of layers necessary for efficient diffraction has been also examined for the 9th order. From the simulation, it
was found that approximately 1000 layer pairs are necessary to get maximum efficiency, and about 350 bilayers for the
half of the maximum.
Concluding the discussion of possibility of use a lamellar ML grating in high order with soft x-rays, we should say that
the efficiency of 9th order at s/d 0.05 is rather high (Fig. 2), reaching close to the efficiency of the zero order. Small
land width at large effective number of bilayers results to the separation of the orders (preventing overlapping).
However, the reflectivity of a very narrow land is small, increasing the effective extinction length and demanding the
large number of ML bilayers to provide high ML reflectivity and grating efficiency. As a result of that the optimal
design has a very large aspect ratio that is a great challenge for existing lithographic technology.
Multilayer coated blaze (MLBG) grating"1 is another design of a low groove density grating, capable of providing high
efficiency of diffraction in high orders (Fig. 3). The high efficiency of a MLBG grating in the 1st order has been
demonstrated in EUV wavelength range.14 In order to provide high efficiency of the grating in higher orders, a
significantly larger blaze angle is required. This in turn has its limitations as the grating efficiency ultimately will be
decreased due to enhanced shadowing and losses on non-working facets of the grating grooves.p
a
Fig. 3. Design of a multilayer coated blaze
grating. d is the grating period, D is the
ML bilayer spacing, cp is the blaze
angle, c: is the incidence angle, f is the
diffraction angle, 20' is the scattering
angle, 0 is the Bragg angle.0.40
0.35
0.30
0.25
c
0.20
N 0.15
0.10
0.05
0.00
78.0
78.2 78.4 78.
a, degrees6 78.8 79.0
Fig. 4. Dependence of efficiency of 19th (the dotted line), 20th (the
solid line), and 21th (the dashed line) diffraction orders of a
MLCB grating on the incidence angle at 1.3 nm wavelength.
The grating with the period d=1 m and blaze angle =3.03
is optimized for 20th order. Parameters of W/B4C multilayer
are: DML=2.644 nm, F=0.2, N=100. 30 orders were used in
the calculation. The efficiency of the 20th order exceeds 30%,
whereas the adjacent orders are almost completely suppressed
due to high selectivity of the ML.According to the Maystre - Petit scalar model15, the resulting efficiency of a blaze grating is equal to the reflectivity of
working facet, R(0') multiplied by a geometry factor:'max = R(I ) xmi cos a .cos/p
Im cosp'cosa)(4)
The geometry factor increases at small scattering angle 20', and reaches one at the Littrow geometry, when 20' = 0 .
The Littrow geometry works well for EUV range, where the reflectivity of ML mirrors at normal incidence can be rather
high. In the soft x-ray range, the reflectivity of the ML mirrors rapidly decreases with increase of the grazing angle. In
this case, the maximum efficiency for the chosen l -th order is achieved at some optimal value of scattering angle. Using
the optimal scattering angle, grating equation, and Bragg equation, one can calculate all parameters of the grating,-19 order
- 20" order
----- 21f" order
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Voronov, Dmitriy L.; Cambie, Rossana; Feshchenko, Ruslan M.; Gullikson, Eric M.; Padmore, Howard A.; Vinogradov, Alexander V. et al. Development of an ultra-high resolution diffraction grating for soft x-rays, article, August 21, 2007; Berkeley, California. (https://digital.library.unt.edu/ark:/67531/metadc894637/m1/4/: accessed April 24, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.