Introduction

Highly reflective multilayer optics in the extreme ultraviolet (EUV) have enabled many areas of scientific study. Specifically, in the wavelength range of 25 to 50 nm multilayers are used as focusing and imaging elements for research in high harmonic femtosecond chemistry [1] and solar astrophysics imaging [2] such as the He II 30.4nm line. Currently the highest published results on reflectivity in this region are obtained from Magnesium /Silicon Carbide (Mg/SiC) multilayers and are around 40% to 50% [3].

The relatively high reflectivity of these mirrors comes with a drawback of reduced bandwidth. In femtosecond/attosecond applications a large bandwidth is very important to maintain short pulses. In many applications integrated reflectivity is more desirable as a merit function for mirror performance than peak reflectivity. For example the odd harmonics of a Ti-sapphire high harmonic generator are separated by 2 nm in the vicinity of the 27th harmonic (~30 nm). The typical bandwidth of an optically thick (highest obtainable reflectivity) Mg/SiC multilayer is 2.9 nm limiting their use to a single harmonic.

Several methods have been implemented to increase the bandwidth of multilayer coatings. The simplest method to increase bandwidth is to use fewer periods in the multilayer stack. Multilayers are artificial Bragg crystals; they use temporal coherence to obtain high reflectivity. In other words each reflective interface adds coherently with the one next to it. For an optically thin stack the temporal/longitude coherence length is proportional to the thickness of the multilayer:

The second method implemented is to make the multilayer aperiodic [4, 5]. This method also trades off peak reflectivity for larger bandwidth, however the integrated reflectivity is often higher than it is by just reducing the number of layers. However the aperiodic structure can introduce non-uniform phase response and affect the temporal structure of the reflected radiation. Although this provides a mechanism for pulse compression [6], in general the use of aperiodic optics with high harmonic sources in femtosecond dynamic studies requires full characterization of the source, as well as the optics, to insure that the femtosecond pulses are not inadvertently broadened.

An alternative solution that has been used at longer wavelength (>50 nm) [7, 8] is to use more than two materials in each repeating period of the stack. This allows for higher reflectivity per period in the multilayer stack. Thus higher reflectivity is obtained in fewer periods, therefore increasing the bandwidth. Three material multilayers have also been proposed and measured for use in both the extreme ultraviolet and the soft x-ray regime of the spectrum [9–11]. At 25-50 nm, previous research using tri-material multilayers did not demonstrate improvement over standard bilayer Mg/SiC due to the materials chosen in the study [11]. Here, we report the design and fabrication of a tri-material multilayer that shows good improvements in both the reflectivity and bandwidth.

Material selection, optimization, and fabrication

The three materials chosen for improving multilayer bandwidth and maintaining high reflectivity in the 25 to 50 nm range were Mg, SiC, and Sc. Mg was chosen as the low Z element, because the L3 absorption edge is located at 25.0 nm. This makes Mg optically transparent, and it is typically used as a spacer for multilayers in this wavelength range. SiC is usually chosen as the high Z compound (absorber) in Mg based multilayer due to its low interdiffusion and roughness. In this work the authors chose Scandium to be a second high Z material. Sc was chosen because of its M2,3 absorption edge at 43.8 nm makes the real part of its index of refraction greater than one and it is also used in multilayers between 35 and 50 nm [12]. It is expected that the reflection from the Sc/SiC interface is strong, since the Fresnel reflectivity scales with the difference in the index of refraction. The optical constants [13–15] of the 3 materials are shown in Fig. 1 .

 

Fig. 1 This graph shows the optical constants for Mg, Sc, and SiC. The solid line represents delta while the doted lines represent beta. The index of refraction uses the standard convention: n = 1-δ+iβ.

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Four samples were made for this experiment: 2 Mg/SiC multilayers and 2 Mg/Sc/SiC. One set (1 Mg/SiC and 1 Mg/Sc/SiC) was designed for a peak reflectivity at 37 nm near the optimal location for the optical constants. The optimal is the wavelength that maximizes the difference in the real parts of the index of refraction and minimizes the complex or absorptive part for the materials. A larger difference in the real parts increases reflectivity at each interface, and the lower absorption allows for more layer also increasing reflectivity. The other set was designed for a reflectivity peak at 28 nm to be away from the optimal difference in optical constants. For the 28 nm samples we used non-optically thick stacks for both samples in an attempt to produce the same reflectivity for both multilayer thus allowing for a direct comparison of the bandwidth. A brute force reflectivity simulation was performed to optimize the material thickness of each sample by simulating the peak reflectivity, at a chosen wavelength, as a function of the thickness of the three materials. The brute force multilayers simulation was preformed on optically thick stacks and for thickness of the 3 materials ranging from 0 nm to half of the chosen wavelength in 0.1 nm steps for all combinations of thicknesses. The thickness parameters that created the global maximum reflectivity were chosen. As predicted by the theory [8, 9] the order of the materials is critical when three or more materials are used.

For the 37 nm samples, the optimal parameters for the Mg/Sc/SiC were: d = 19 nm, γ1 = 0.2 (SiC thickness / d), γ2 = 0.13 (Sc thickness / d), N = 35 tri-layers. The Mg/SiC sample d = 19.5 nm, γ1 = 0.33, N = 35 bi-layers. For the 28 nm samples, the optimal parameters for the Mg/Sc/SiC were: d = 15.4 nm, γ1 = 0.2, γ2 = 0.07, N = 30 tri-layers. The Mg/SiC sample d = 14.0 nm, γ1 = 0.3, N = 40 bi-layers.

The samples were fabricated on polished silicon wafers using magnetron sputtering. DC sputtering was used for Mg and Sc targets at 100 W. While RF sputtering was used SiC, at 275 W. The samples were fabricated under a 1.0 mTorr argon pressure during the deposition. The top layer of each sample is SiC to prevent oxidation.

Reflectivity measurements

The samples were measured at the Advanced Light Source beamline 6.3.2. The beamline is designed for EUV optical metrology and reflectivity measurements [16]. The beamline has high spectral purity, and a spectral resolving power (Δλ/λ) of up to 7000, a wavelength accuracy of 2x10⁻³ nm, and a reflectivity accuracy of 0.1% (absolute). The samples were measured at 5 degrees from normal incidence. The reflectivity for the 37 nm samples is shown in Fig. 2 , while the reflectivity for the 28 nm samples is shown in Fig. 3 .

 

Fig. 2 The reflectivity of optimized, optically thick Mg/SiC and Mg/Sc/SiC multilayers is shown for the samples optimize for 37 nm. The tri-material multilayer has a FWHM bandwidth of 3.2 nm and a peak reflectivity of 48.7% at 36.8 nm., while the bi-layer Mg/SiC has a FWHM bandwidth of 3 nm and a peak reflectivity of 42.5% at 37.1 nm. The solid lines represent numerical fits to the measured reflectivity curves.

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Fig. 3 The reflectivity of optimized, 30 period Mg/SiC and Mg/Sc/SiC multilayers is shown for the samples optimized for 28 nm. The tri-material multilayer has a FWHM bandwidth of 1.6 nm and a peak reflectivity of 52.8% at 28.4 nm, while the bi-layer Mg/SiC has a FWHM bandwidth of 1.2 nm and a peak reflectivity of 46.5% at 27.8 nm. The solid lines represent numerical fits to the measured reflectivity curves

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Results and conclusion

As shown in Figs. 2 and 3 the reflectivity of the tri-material multilayer is an improvement over the Mg/SiC multilayers. In Figs. 2 and 3 the reflectivity of the optimized tri-material multilayer stack is even higher than the optimized bi-material multilayer stack. Looking at the reflectivity curves one also notices the asymmetry about the peak in the tri-material multilayers. There is an increased reflectivity on the higher wavelength side for the 28 nm multilayer optic, and also increased reflectivity on the short wavelength side for the 37 nm multilayer optic. The reason is the near linear change in optical properties of Sc between 27 and 35 nm as seen in Fig. 1. This change in index of refraction as a function of wavelength leads to higher reflectivity causing the asymmetry and increasing the multilayer’s bandwidth. If the index of refraction follows the relation:

As the tri-material stack uses fewer periods the integrated reflectivity and bandwidth are larger. To determine the usable bandwidth often the full width at half maximum (FWHM) reflectivity is given. However, this is not a good comparison as the FWHM values occur at different reflectivity levels. For example in the tri-material multilayer for 37 nm the FWHM level would be located at 25% reflectivity while the bi-material multilayer the FWHM level would be located at 21% reflectivity thus giving comparable FWHM bandwidths of 3.2 nm and 3 nm respectively. This makes a fair comparison difficult if FWHM bandwidth values alone are used for comparison. Also as the shape of the tri-material multilayer is asymmetric calculating the integrated reflectivity gives a better comparison of usable bandwidth. The integrated reflectivity is 40% higher for the 37 nm sample and 47% higher for the 28 nm sample giving a better comparison of the bandwidth and reflectivity. The limits of the integration were chosen to be the wavelengths giving 5% absolute reflectivity.

The optical properties of the materials alone do not determine if a multilayer is practical. Various considerations such as interface roughness and interdiffusion (σ) when depositing the multilayer, temporal stability, and environmental degradation are all factors. To obtain a comparison of the interface roughness and interdiffusion for the bi-material and tri-material multilayers, numerical fitting of the material thickness and σ interdiffusion parameter were conducted to compare with the deposition parameters. The standard recursive formula [17] for dynamical diffraction of multilayers was used in conjunction with a downhill simplex optimization algorithm [18] to minimize the root mean squared difference in the calculated verses measured reflectivity curves as a function of the three material thickness and σ interdiffusion parameter. The solid curves in Figs. 2 and 3 show the numerical fits. For the tri-material multilayers the 37 nm sample the numerical parameters obtained by fitting were d = 19.1 nm, γ1 = 0.19, γ2 = 0.18, and σ = 1.3 nm. For the 28 nm sample the fitted parameters were d = 14.5 nm, γ1 = 0.20, γ2 = 0.07, and σ = 1.0 nm. The fittings are comparable to the deposition parameters with the difference in σ possibly being caused by the thinness of the Scandium layer in the 28 nm sample. For the bi-material multilayer the numerical fit of the 37 nm multilayer yielded d = 19.9 nm γ1 = 0.34, and σ = 1.7 nm, and d = 14.3 nm γ1 = 0.34, and σ = 1.7 nm for the 28 nm sample. The d-spacing and γ values obtained for all samples are with in the reproducibility of the magnetron deposition system used. The comparison of the derived σ parameters for the tri-material multilayers to the bi-material multilayers suggests that interdiffusion is either less or comparable.

However more studies are needed to determine the accuracy of the fittings to actual measurements on interdiffusion roughness. Also thermo-annealing and lifetime studies will be conducted in future work. These are needed to determine the applicability to astrophysics application, which require optics that are stable with time and temperature.

We have optimized tri-material multilayers for use in the range of 25 to 40 nm EUV light. The tri-materials allows for larger bandwidths without sacrificing peak reflectivity. These tri-material multilayers suggest a method for obtaining higher reflectivity and larger bandwidths over the entire EUV wavelength range if the proper material combinations are chosen.