Interfacial structure of Mg/SiC multilayers as extreme ultra-violet reflectors was studied along with Mg/Si and Mg/C multilayers by means of x-ray reflectometry, x-ray diffraction, x-ray photoemission spectroscopy, and transmission electron microscopy. The interfacial diffusion in the Mg/SiC multilayer is found asymmetrical as the interlayers formed at SiC-on-Mg interfaces (2.5 nm) are much thicker than those at Mg-on-SiC interfaces (1.0 nm). Contrary asymmetry is found in the Mg/Si and Mg/C multilayers. An explanation of this phenomenon is suggested based on the investigation results. Our findings may result in improved reflectance of Mg/SiC multilayers by inserting diffusion barriers at the more diffused interfaces.
© 2013 OSA
Multilayer mirrors are widely used as reflective elements in the extreme ultra-violet (EUV) and x-ray region. Interfacial diffusion between the constituent layers in the multilayer is one of the primary defects that will reduce the reflectance. Interfacial diffusion in these nanoscale multilayers is a phenomenon not as well understood as diffusion in bulk materials. It attracts considerable research interest, not only in fundamental understanding of the phenomenon itself, but also in controlling physical properties of multilayers in practical applications [1–4]. One interesting finding about interfacial diffusion in particular multilayers [5–7] is asymmetry at different interfaces, i.e., the diffusion at A-on-B interfaces and B-on-A interfaces differ in an A/B multilayer. In Mo/Si multilayers, diffusion at Mo-on-Si interface was found to be much larger than that at Si-on-Mo interface. This is because it is easier for Si to penetrate into the amorphous growing Mo layer at Mo-on-Si interface than to penetrate into textured Mo grains at Si-on-Mo interface [8–10]. In Fe/Si multilayers, similar asymmetry was also found and is explained by the lower surface free energy of Si, which provides an additional driving force for Si diffusion at Fe-on-Si interface .
Mg/SiC multilayers are important for wavelengths λ = 25–40 nm in the EUV region. They have been investigated in terms of optical performance, temporal and thermal stability [12–16]. Although detailed investigation on the interfacial structure has not been reported, the roughness value listed in [12–15] shows that interface width of SiC-on-Mg (1.4–2.6 nm) is much larger than that of Mg-on-SiC (0.6–1.6 nm). However the authors of these literatures have not discussed this large asymmetry. Furthermore this asymmetry is contrary to the Mo/Si one and thus cannot be explained by the crystallization of Mg. And it cannot be explained by surface free energy either because of the small difference in the surface energies of SiC (1.3 J/m2, amorphous ) and Mg (1.0 J/m2, hcp (001) plane ).
Here we intend to verify whether this asymmetry exists in Mg/SiC multilayers and to find the origin of the asymmetry if it does. The Mg/SiC system is more complicated than Mo/Si or Fe/Si because SiC is a compound material. Thus we studied the Mg/SiC multilayers along with Mg/Si and Mg/C multilayers by means of low-angle x-ray reflectometry (XRR), depth-profile x-ray photoelectron spectroscopy (XPS), cross-section transmission electron microscopy (TEM), and wide-angle x-ray diffraction (XRD).
2. Experimental details
To compare Mg/SiC interfaces with Mg/Si and Mg/C interfaces, we deposited a series of multilayers with the structure of [X1/Mg/X2]×5 (X1,2 = SiC, Si, and C). The symbol on the left side of the formula represents layer close to the substrate. The nominal thickness of Mg is 5.0 nm and that of X1,2 is 2.5 nm. For the X1 = X2 case, [X/Mg/X] is actually a [Mg/X] multilayer with nominal thickness of X being 5.0 nm.
All multilayers were deposited onto polished Si (001) wafer at ambient temperature using dc magnetron sputtering. The pressure of residual gas before deposition was 5.0 × 10−5 Pa and that of Ar sputtering gas was 0.13 Pa. The deposition rates for Mg, SiC, Si, and C were 0.45, 0.08, 0.12, and 0.05 nm/s, respectively.
XRR measurements were made for each sample using a Bede D1 x-ray diffractometer with a Cu Kα source (λ = 0.154 nm) to determine the multilayer structure. The measured curves were fitted to obtain the interface width. The fitting process utilizes the well-known recursive formula  for calculating the reflection curve and genetic algorithm for optimization. The interfaces were modeled by introducing both Debye-Waller factors and intermixed interlayers. XPS measurements were carried out for the three [X/Mg/X] multilayer samples. The measurements were done on a Thermo Scientific K-Alpha system with an Al Kα source. Depth-profiles were obtained by Ar+ (3 keV) etching. The binding energy scale was calibrated from hydrocarbon contamination using the C 1s peak at 285.0 eV. Core peaks were analyzed using a nonlinear Shirley-type background. The peak positions and areas were optimized by a weighted least-squares fitting method using 70% Gaussian, 30% Lorentzian lineshapes. Quantification was performed on the basis of Scofield’s relative sensitivity factors. TEM measurements were carried out on an FEI microscope (Tecnai G2 F20) for another three [X/Mg/X] multilayer samples having the same structure with the ones for XPS measurements except that the period repeat number is 80. The cross-section samples for TEM were prepared by focused ion beam etching. XRD measurements in the symmetric (θ–2θ) geometry were performed on a Rigaku-Dmax-2550V powder diffractometer (λ = 0.154 nm).
XRR results for the [X1/Mg/X2]×5 multilayers are shown in Fig. 1 as black thick line. The curves have been shifted vertically for clarity. As can be seen, [SiC/Mg/SiC] has the most intense Bragg peaks among all the seven multilayers, showing best interface quality. [Si/Mg/Si] and [C/Mg/C] have the worst interface quality as only one Bragg peak can be observed. Generally the Si series and the C series have a similar pattern. [SiC/Mg/Si] and [SiC/Mg/C] are slightly worse than [SiC/Mg/SiC] which indicates the diffusion at SiC-on-Mg, Si-on-Mg, and C-on-Mg interfaces are similar. However [Si/Mg/SiC] and [C/Mg/SiC] are much worse than [SiC/Mg/SiC] and resemble [Si/Mg/Si] and [C/Mg/C], respectively. This reveals essential distinction between Mg-on-SiC and Mg-on-Si(or C). Some differences can be found between the Si series and the C series. The [SiC/Mg/Si] is slightly worse than [SiC/Mg/C] while [Si/Mg/SiC] is much better than [C/Mg/SiC]. We will discuss the difference in the following sections. All the XRR curves were fitted to obtain the interlayer thickness. The fitted curves are plotted in Fig. 1 as red thin line. The fitted values for the interlayer thicknesses are listed in Table 1 . The thickness of Mg-on-SiC interlayer is the smallest and of the value 0.7 nm. The values for SiC-on-Mg, Si-on-Mg, and C-on-Mg interlayers are very close and in the 1.8–2.4 nm range. Mg-on-Si and Mg-on-C interlayers have the largest thicknesses of about 3.3–3.5 nm.
3.2 TEM and XRD
The measured TEM microphotographs of the three [X/Mg/X] multilayers are shown in Fig. 2 . Figure 2(a) is the bright field (BF) image of [SiC/Mg/SiC]. Clear boundary of Mg and SiC at the Mg-on-SiC interfaces can be observed. On the contrary, Mg and SiC are separated by gradient interlayers at the SiC-on-Mg interfaces. The thickness of the SiC-on-Mg interlayer is measured to be about 2.5 nm while that of Mg-on-SiC interlayer is less than 1.0 nm. The high resolution (HR) image in Fig. 2(b) reveals the nanocrystalline nature of Mg which can be confirmed by the selected-area electron diffraction (SAED) pattern in Fig. 2(c). The blurred spots in the diffraction pattern are associated with d-spacing of 0.255, 0.243, 0.276, 0.159, and 0.128 nm, which are consistent with (002), (101), (100), (110), and (004) planes of hcp Mg, respectively. The position of the (002) diffraction spot shows that the nanocrystal is oriented with (002) plane parallel to the film surface.
Figure 2(d) is the BF image of [Si/Mg/Si]. The layers are very rough and some layers are discontinuous. From the HR image in Fig. 2(e) and dark field (DF) image in Fig. 2(f) it can be found that most parts of the film is crystalline. The SAED pattern in Fig. 2(f) reveals that the layers are polycrystalline as ring-like pattern was observed. The two rings are associated with d-spacing of 0.372 and 0.222 nm, which are not consistent with any Mg lattice plane. Actually they are the (111) and (220) planes of fcc Mg2Si, respectively. This fact demonstrates that all the Mg reacts with Si and forms crystalline disilicide in [Si/Mg/Si]. To verify at which interface this occurs, we performed XRD measurements on the [SiC/Mg/Si] and [Si/Mg/SiC] multilayers. The results are shown in Fig. 3 . [SiC/Mg/Si] shows only one diffraction peak at 34.55° which is associated with hcp Mg (002) plane while [Si/Mg/SiC] shows a peak at 24.57° which is associated with fcc Mg2Si (111) plane. No crystalline Mg phase has been observed in the [Si/Mg/SiC] multilayer suggesting that all the Mg (5nm thick) deposited onto Si forms crystalline silicide at Mg-on-Si interface. The thickness of the silicide interlayer (formed from 5 nm thick Mg) at Mg-on-Si interface is calculated to be 7 nm using the formula and bulk material density. The thickness of the Si-on-Mg interlayer can be estimated by comparing the average Mg grain size of the [SiC/Mg/Si] and [SiC/Mg/SiC] multilayers along the growth direction, which is associated with the full-width at half maximum (FWHM) of the diffraction peak via Scherrer equation. The grain size for [SiC/Mg/Si] and [SiC/Mg/SiC] are calculated to be 3.2 nm and 3.5 nm, respectively, which implies the amount (in thickness) of reacted Mg in [SiC/Mg/Si] is 0.3 nm larger than in the [SiC/Mg/SiC] as the amount of deposited Mg in the two cases is the same. Consequentially the formed silicide at Si-on-Mg interface is about 0.5 nm thicker than at SiC-on-Mg interface and approaches about 3.0 nm in thickness.
Figure 2(g) is the BF image of [C/Mg/C]. The layers are greatly intermixed and almost indistinguishable. The HR image in Fig. 2(h) and the DF image in Fig. 2(i) show that the Mg layer consists of discontinuous small polycrystalline islands. The ringed SAED pattern in Fig. 2(i) confirms that Mg is polycrystalline. The two diffraction rings have a d-spacing of 0.269 and 0.243 nm and can be attributed to (002) and (101) planes of hcp Mg, respectively. The orientation of Mg polycrystallites is mostly random. XRD measurements for the [C/Mg/SiC] and [SiC/Mg/C] multilayers are also shown in Fig. 3. The curve for [SiC/Mg/C] exhibits a peak at 34.58° associated with Mg (002) plane while the curve for [C/Mg/SiC] only show a small bump at 34.65°. This demonstrates that almost all 5 nm Mg intermixed with C at Mg-on-C interface. At C-on-Mg interface, the amount of intermixed Mg can also be estimated by the average grain size along the growth direction. The grain size in [SiC/Mg/C] is about 3.2 nm, which is 0.3 nm smaller than in [SiC/Mg/SiC]. However the thickness of formed interlayer cannot be calculated as its density is unknown. Taking the XRR results, which shows the interface quality of [SiC/Mg/C] is better than [SiC/Mg/Si] and worse than [SiC/Mg/SiC], into consideration we conclude that the interlayer at C-on-Mg interface is about 2.5–3.0 nm thick.
The interlayer thicknesses deduced from the TEM and XRD combination are also listed in Table 1. Although a similar pattern is found in the two sets of values, the absolute values deviate from those deduced from XRR. We think that the values deduced from TEM and XRD combination are more practical because the resolving power of XRR on these structures is relatively weak due to the small optical contrast among Mg, SiC, Si and C at λ = 0.154 nm.
Depth-profile XPS measurements were performed over the first bilayer in the three [X/Mg/X] multilayers. The depth profile of atomic concentration is shown in Fig. 4 . The result of [SiC/Mg/SiC] in Fig. 4(a) exhibits typical bilayer profile with Mg and SiC layers clearly resolved. The high concentration (20–25%) of Si and C at the positions of Mg layer is due to preferential sputtering of Mg in Ar+ etching process. The concentration changes slower at SiC-on-Mg interface than that at Mg-on-SiC interface, which is consistent with the conclusion that the interfacial diffusion at SiC-on-Mg interface is larger at the Mg-on-SiC interface. For [Si/Mg/Si] shown in Fig. 4(b), the bilayer structure consisted of a thick layer, which is determined to be Mg2Si by SAED, and a thin layer is resolved. For [C/Mg/C] shown in Fig. 4(c), the concentration of C and Mg stays almost unchanged after the first C layer is sputtered (after etching time of 60s). This means that the Mg layers are almost intermixed with C. The oxygen concentration in [C/Mg/C] is very high and the Mg:O ratio is near 1:1. This fact suggests that Mg in [C/Mg/C] is almost oxidized and can be explained by that the intermixed Mg:C layer is porous and with considerable defects to allow oxygen or water vapor to penetrate in. This porous Mg:C layer assumption can also explain why the interface quality of [C/Mg/SiC] is much poorer than [Si/Mg/SiC] which is observed in XRR. This porous Mg:C layer promotes Si diffusion when Si and C deposits onto it in the [C/Mg/SiC] case. While in the [Si/Mg/SiC] case, formation of polycrystalline Mg2Si prevents further C diffusion from the upper SiC layer.
During XPS measurement, narrow scans of Mg 1s, Si 2p, and C 1s spectra were obtained after each etching. In the [Si/Mg/Si] and [C/Mg/C] sample, all the spectra in different etching level (except for the first 2 nm from the surface) are similar in peak position and peak shape while a little difference is presented in the [SiC/Mg/SiC] sample. Thus we discuss the spectra in details at four etching levels. Two levels are chosen for [SiC/Mg/SiC] representing the position at SiC-on-Mg (etching time of 48 s) and Mg-on-SiC (etching time of 120 s) interfaces. For [Si/Mg/Si] and [C/Mg/C], etching time of 108 s is chosen. The measured spectra (subtracted by Shirley type background) are shown as open symbols in Fig. 5 . The spectra are all fitted and the fitted peaks are shown as solid lines. If the fitting involves superposition of more-than-one peaks, the peaks used will be shown as dashed lines. In Fig. 5(a), the Mg 1s spectra of SiC-on-Mg, Mg-on-SiC, and [Si/Mg/Si] can be fitted by a single peak. The peak position of SiC-on-Mg and Mg-on-SiC is 1304.5 eV which is attributed to metal Mg. The peak in [Si/Mg/Si] is located at 1304.8 eV and should be attributed to Mg2Si. No sign of Mg—Si bond is found in Mg 1s spectra at either Mg/SiC interface possibly due to the small chemical shift of about 0.3 eV. The Mg 1s spectrum in [C/Mg/C] is completely different. It consists of two peaks representing MgO (1303.9 eV) and Mg(OH)2 (1302.9 eV) which is consistent with conclusion that Mg in [C/Mg/C] is almost oxidized. In Fig. 5(b), the Si 2p spectra of SiC-on-Mg and Mg-on-SiC can be divided into two peaks. The main peak is at 100.1 eV corresponding to C—Si bond. A very weak peak is found at 98.2 eV which may be attributed to Mg2Si  as the Mg2Si peak is found to be at 98.5 eV in the [Si/Mg/Si] sample. The Mg2Si peak area at SiC-on-Mg is larger than at Mg-on-SiC implying more diffusion at SiC-on-Mg. In Fig. 5(c), the C 1s spectra can be divided into two peaks at SiC-on-Mg and Mg-on-SiC interfaces. One at 282.7 eV is of the C—Si bond. The other at 284.3 eV is of the C—C bond. The C—C peak area at SiC-on-Mg is also larger than at Mg-on-SiC which implies larger amount of Si is bonded with Mg at the SiC-on-Mg interface. The C 1s spectrum of [C/Mg/C] is a single peak at 284.3 eV of the C—C bond and shows no sign of Mg—C bond.
On the basis of the data presented here, different mechanisms for the interfacial diffusion at the Mg-on-X and X-on-Mg interfaces can be suggested. A simple illustration is shown in Fig. 6 .
Great asymmetry has been found at Mg/Si interfaces. At Si-on-Mg interface, amorphous Mg2Si interlayer formation is found and the thickness of the interlayer is about 3 nm. At Mg-on-Si interface, polycrystalline Mg2Si interlayer is formed and the thickness of the interlayer can be larger than 7 nm. This asymmetry is similar to that in Mo/Si multilayers [8–10] and can be explained by the crystallization of Mg. When Mg deposits onto amorphous Si, Si atoms diffuse along the growing Mg layer by surface diffusion, which can be enhanced by the nanoscale roughness. When the atomic ratio of Mg and Si reaches 2:1 at a local area, clusters of Mg2Si are formed. Nucleation around the Mg2Si clusters forms polycrystalline Mg2Si interlayer. Further Si diffusion across the interlayer can be possible by grain boundary diffusion. The eventual thickness of the interlayer at Mg-on-Si interface can exceed 7 nm. On the other hand, when Si deposits onto an Mg layer with good texture, the Si atoms can penetrate into the textured Mg grains chiefly by bulk diffusion whose diffusion coefficient is much lower than surface diffusion or grain boundary diffusion at low temperatures. As a result a thinner amorphous interlayer with the thickness of about 3 nm is formed at the Si-on-Mg interface.
The Mg/C interfaces are found with the similar asymmetry as Mg/Si. The same mechanism relating to Mg crystallinity can explain the diffusion phenomenon at Mg/C interfaces. The main difference with the Mg/Si case is that when Mg deposits onto C, nearly amorphous Mg:C mixed layer forms rather than polycrystalline layer. The amorphous Mg:C layer is highly porous and could not act as a barrier for further diffusion. Thus the eventual thickness of the interlayer at Mg-on-C interface can exceed 5 nm. The porous Mg:C layer is also the cause of further diffusion of Si if SiC is deposited onto it as observed in the [C/Mg/SiC] stack. Furthermore the porous Mg:C layer is easy for oxygen or water vapor to penetrate in and results almost fully oxidization of Mg in the [C/Mg/C].
The Mg/SiC interfaces are also found asymmetry. The thickness of interlayer at Mg-on-SiC and SiC-on-Mg interfaces are about 1.0 nm and 2.5 nm, respectively. As can be seen, this asymmetry is contrary to that of Mg/Si or Mg/C interfaces. The difference is due to different diffusion mechanism at Mg-on-SiC interface. The diffusion at SiC-on-Mg interface is similar to that at Si-on-Mg and C-on-Mg and forms an amorphous interlayer with the thickness of about 2.5 nm due to high crystallinity of Mg. The limited diffusion at Mg-on-SiC interface can be explained by the strong covalent bonds in SiC. The enthalpy of formation for SiC, Mg2Si, and Mg2C3 is −71.5, −77.8, and + 79.5 kJ/mol, respectively. At low temperatures it is hard for Si atoms to break the strong covalent bonds and diffuse into the growing Mg layer. Liu et al.  calculated the pressure-temperature phase diagram of Mg-SiC system and found that no reaction between Mg and SiC occurs if the temperature is below Mg melting point (650°C) or Mg partial pressure is below 95% of its vapor pressure. They also showed the successful deposition of MgB2 film on SiC substrate without reaction between Mg and SiC when the SiC substrate is subject to Mg vapor . Owning to the strong bonding in SiC and high crystallinity of Mg, both interfaces of Mg/SiC are with limited diffusion and thus good chemical modulated Mg/SiC multilayers can be formed.
Our current findings on asymmetrical diffusion can be beneficial for improving the reflectance or thermal stability of Mg/SiC multilayers by inserting barrier layers at the interfaces. Si, C, and B4C, which are commonly chosen as barrier layers for EUV multilayers due to the low absorption, are not suitable for the Mg/SiC multilayers because they cannot form sharp interfaces with Mg . On the other hand, some transition metals such as Co, Mo and Zr can form sharp interfaces with Mg [24,25]. Nevertheless, the absorption of these transition metals is relatively large, causing a decrease of the multilayer’s theoretical reflectance if they are inserted at the interfaces. To be more precisely, the decrease of reflectance happens when the absorptive layers are inserted at the Mg-on-SiC interfaces. Inserting thin absorptive layers at the SiC-on-Mg interfaces leads to almost no additional absorption because the SiC-on-Mg interfaces locate at the nodes (minimum electric field intensities) of the standing wave generated in the multilayer. The finding that the SiC-on-Mg interfaces, where inserting barrier layers lead to no decline of theoretical reflectance, are much more diffused provides an opportunity to insert barrier layers at only SiC-on-Mg interfaces with expected improvement in the reflectance of Mg/SiC multilayers.
Mg/SiC multilayers along with Mg/Si and Mg/C multilayers were studied by XRR, XRD, depth-profile XPS, and cross-section TEM. Asymmetry is found on the interlayer thickness at all three interfaces. The thickness of the interlayer at Mg-on-Si (>7 nm) and Mg-on-C (>5 nm) is larger than that at Si-on-Mg (3 nm) and C-on-Mg (2.5–3 nm). In the Mg/SiC multilayers, contrary asymmetry is found as the thickness of the interlayer at Mg-on-SiC (1 nm) is smaller than SiC-on-Mg (2.5 nm). Based on the XRD, XPS and TEM results, different mechanisms for interfacial diffusion are proposed. The asymmetry in Mg/Si and Mg/C is mainly caused by lower diffusion coefficient of Si and C to penetrate into highly textured Mg. In the Mg/SiC case, the much lower diffusion at Mg-on-SiC interface is explained by the strong covalent bonding in SiC. Besides being of fundamental importance in understanding the nanoscale interfacial diffusion, current results can be beneficial for improving the performance of Mg/SiC multilayers as EUV reflectors by inserting diffusion barriers at the more diffused interfaces.
This work is supported by National Basic Research Program of China (No. 2011CB922203) and National Natural Science Foundation of China (No. 10825521, 10905042, and 11027507).
References and links
1. D. Iuşan, M. Alouani, O. Bengone, and O. Eriksson, “Effect of diffusion and alloying on the magnetic and transport properties of Fe/V/Fe trilayers,” Phys. Rev. B 75(2), 024412 (2007). [CrossRef]
2. J. Jiang, D. G. Zeng, H. Ryu, K.-W. Chung, and S. Bae, “Effects of controlling Cu spacer inter-diffusion by diffusion barriers on the magnetic and electrical stability of GMR spin-valve devices,” J. Magn. Magn. Mater. 322(13), 1834–1840 (2010). [CrossRef]
3. N. Ghafoor, F. Eriksson, E. Gullikson, L. Hultman, and J. Birch, “Incorporation of nitrogen in Cr/Sc multilayers giving improved soft x-ray reflectivity,” Appl. Phys. Lett. 92(9), 091913 (2008). [CrossRef]
4. T. Tsarfati, R. W. E. van de Kruijs, E. Zoethout, E. Louis, and F. Bijkerk, “Nitridation and contrast of B4C/La interfaces and X-ray multilayer optics,” Thin Solid Films 518(24), 7249–7252 (2010). [CrossRef]
5. A. K. Petford-Long, M. B. Stearns, C.-H. Chang, S. R. Nutt, D. G. Stearns, N. M. Ceglio, and A. M. Hawryluk, “High-resolution electron microscopy study of x-ray multilayer structures,” J. Appl. Phys. 61(4), 1422–1428 (1987). [CrossRef]
6. T. Shinjo and W. Keune, “Mössbauer-effect studies of multilayers and interfaces,” J. Magn. Magn. Mater. 200(1-3), 598–615 (1999). [CrossRef]
7. V. M. Uzdin and L. Häggström, “Atomic-scale magnetic and chemical structure of Fe/V multilayers using Mössbauer spectroscopy,” Phys. Rev. B 72(2), 024407 (2005). [CrossRef]
8. S. Bajt, D. G. Stearns, and P. A. Kearney, “Investigation of the amorphous-to-crystalline transition in Mo/Si multilayers,” J. Appl. Phys. 90(2), 1017–1025 (2001). [CrossRef]
9. S. Yulin, T. Feigl, T. Kuhlmann, N. Kaiser, A. I. Fedorenko, V. V. Kondratenko, O. V. Poltseva, V. A. Sevryukova, A. Yu. Zolotaryov, and E. N. Zubarev, “Interlayer transition zones in Mo/Si superlattices,” J. Appl. Phys. 92(3), 1216–1220 (2002). [CrossRef]
10. S. Bruijn, R. W. E. van de Kruijs, A. E. Yakshin, and F. Bijkerk, “The effect of Mo crystallinity on diffusion through the Si-on-Mo interface in EUV multilayer systems,” Defect Diffus. Forum 283–286, 657–661 (2009). [CrossRef]
11. A. Gupta, D. Kumar, and V. Phatak, “Asymmetric diffusion at the interfaces in Fe/Si multilayers,” Phys. Rev. B 81(15), 155402 (2010). [CrossRef]
12. T. Ejima, A. Yamazaki, T. Banse, K. Saito, Y. Kondo, S. Ichimaru, and H. Takenaka, “Aging and thermal stability of Mg/SiC and Mg/Y2O3 reflection multilayers in the 25-35 nm region,” Appl. Opt. 44(26), 5446–5453 (2005). [CrossRef]
13. H. Maury, P. Jonnard, K. Le Guen, J.-M. André, Z. Wang, J. Zhu, J. Dong, Z. Zhang, F. Bridou, F. Delmotte, C. Hecquet, N. Mahne, A. Giglia, and S. Nannarone, “Thermal cycles, interface chemistry and optical performance of Mg/SiC multilayers,” Eur. Phys. J. B 64(2), 193–199 (2008). [CrossRef]
14. M. Fernández-Perea, R. Soufli, J. C. Robinson, L. R. De Marcos, J. A. Méndez, J. I. Larruquert, and E. M. Gullikson, “Triple-wavelength, narrowband Mg/SiC multilayers with corrosion barriers and high peak reflectance in the 25-80 nm wavelength region,” Opt. Express 20(21), 24018–24029 (2012). [CrossRef]
15. M. G. Pelizzo, S. Fineschi, A. J. Corso, P. Zuppella, P. Nicolosi, J. Seely, B. Kjornrattanawanich, and D. L. Windt, “Long-term stability of Mg/SiC multilayers,” Opt. Eng. 51(2), 023801 (2012). [CrossRef]
16. R. Soufli, M. Fernández-Perea, S. L. Baker, J. C. Robinson, J. Alameda, and C. C. Walton, “Spontaneously intermixed Al-Mg barriers enable corrosion-resistant Mg/SiC multilayer coatings,” Appl. Phys. Lett. 101(4), 043111 (2012). [CrossRef]
17. P. Vashishta, R. K. Kalia, A. Nakano, and J. P. Rino, “Interaction potential for silicon carbide: A molecular dynamics study of elastic constants and vibrational density of states for crystalline and amorphous silicon carbide,” J. Appl. Phys. 101(10), 103515 (2007). [CrossRef]
18. H. J. Gotsis, D. A. Papaconstantopoulos, and M. J. Mehl, “Tight-binding calculations of the band structure and total energies of the various phases of magnesium,” Phys. Rev. B 65(13), 134101 (2002). [CrossRef]
19. J. H. Underwood and T. W. Barbee Jr., “Layered synthetic microstructures as Bragg diffractors for X rays and extreme ultraviolet: theory and predicted performance,” Appl. Opt. 20(17), 3027–3034 (1981). [CrossRef]
20. M. R. J. van Buuren, F. Voermans, and H. van Kempen, “Bonding in Mg2Si studied with x-ray photoelectron spectroscopy,” J. Phys. Chem. 99(23), 9519–9522 (1995). [CrossRef]
21. Z.-J. Liu, S. H. Zhou, X. X. Xi, and Z.-K. Liu, “Thermodynamic reactivity of the magnesium vapor with substrate materials during MgB2 deposition,” Physica C 397(3-4), 87–94 (2003). [CrossRef]
22. X. H. Zeng, A. V. Pogrebnyakov, M. H. Zhu, J. E. Jones, X. X. Xi, S. Y. Xu, E. Wertz, Q. Li, J. M. Redwing, J. Lettieri, V. Vaithyanathan, D. G. Schlom, Z.-K. Liu, O. Trithaveesak, and J. Schubert, “Superconducting MgB2 thin films on silicon carbide substrates by hybrid physical–chemical vapor deposition,” Appl. Phys. Lett. 82(13), 2097–2099 (2003). [CrossRef]
23. J. Zhu, S. Zhou, H. Li, Q. Huang, Z. Wang, K. Le Guen, M.-H. Hu, J.-M. André, and P. Jonnard, “Comparison of Mg-based multilayers for solar He II radiation at 30.4 nm wavelength,” Appl. Opt. 49(20), 3922–3925 (2010). [CrossRef]
24. J. Zhu, S. Zhou, H. Li, Z. Wang, P. Jonnard, K. Le Guen, M.-H. Hu, J.-M. André, H. Zhou, and T. Huo, “Thermal stability of Mg/Co multilayer with B4C, Mo or Zr diffusion barrier layers,” Opt. Express 19(22), 21849–21854 (2011). [CrossRef]
25. H. Li, J. Zhu, S. Zhou, Z. Wang, H. Chen, P. Jonnard, K. Le Guen, and J.-M. André, “Zr/Mg multilayer mirror for extreme ultraviolet application and its thermal stability,” Appl. Phys. Lett. 102(11), 111103 (2013). [CrossRef]