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Low stress W/Si multilayer mirrors are demanded in the hard X-ray telescopes to achieve the high angular resolution. To reduce the stress of the as-deposited multilayer and maintain a high reflectivity, two groups of low-temperature annealing experiments were performed on the periodic multilayers with a d-spacing of ~3.8 nm. The temperature-dependent experiments show that the 150 °C annealing can slightly increase the reflectivity while the stress reduced only by 24%. Higher temperature annealing induced a larger reduction of the stress and the multilayer reached an almost zero stress state at 250 °C. The stress relaxation was accompanied by a small drop of reflectivity of ≤5% and a period compaction of <0.02 nm. The time-dependent experiments indicate that most of the stress changes occurred within the first 10 minutes while a prolonged annealing is not useful. The X-ray scattering and transmission electron microscopy were further used to study the microstructure changes of the multilayers. It is found that the W/Si multilayer exhibits an amorphous structure before and after annealing, while an enhanced diffusion and intermixing is the main reason for the stress relaxation and structure changes.
© 2016 Optical Society of America
1. Introduction
X-ray Timing and Polarization (XTP) is a hard X-ray focusing telescope mission initiated in China, which is dedicated to the study of 1-singularity (black hole), 2-stars (neutron star and quark star) and 3-extremes (the physics under extreme gravity, density and magnetism) in astronomy. It is expected to make a highly sensitive temporal and polarization observations in the energy region of 1-30 keV [1]. As a nested Wolter-I optics system is used in the XTP telescopes, thousands of thin cylindrical mirrors with the thickness of only 0.3 mm are required [2]. These thin mirrors will be further coated with over a hundred layers of depth-graded multilayer in order to realize the high energy response. W/Si multilayers are used as the coatings in XTP, due to their high theoretical reflectivity and the relatively sharp interfaces. However, the intrinsic stress accumulated in the multilayer deposition is not negligible as seen in other applications [3]. It can cause an obvious figure distortion of the thin mirrors and deteriorate the focusing properties of the telescope.
Annealing process is a common method to reduce the post-deposition film stress. Many experimental works [4–7] have been performed to study the stress relaxation and the related changes of microstructure in the annealing process on different multilayers including W/Si. Windt [8] studied the W/Si multilayers with different layer thickness under annealing at 300 °C. A maximum reduction of the stress in excess of 400 MPa was found which can be attributed to the changes of the crystalline structure. Dupuis et al. [9] studied the thermal stability of W/Si multilayers under the furnace annealing from 250 °C to 1000 °C and a period compaction of about 5%-10% with a large drop of reflectivity was found. Molarius et al. [10] and Brunei et al. [11] performed high temperature annealing on W/Si multilayers at from 500 °C to 1000 °C while the tungsten silicide formation were observed in both works. Kortright et al. [12] performed the annealing process at 400 °C on W/Si and an absolute reflectivity drop from 68% to 53% at 8.04 keV together with a period compaction of 2.5% was reported. It can be seen that, although the stress can be completely relaxed after the high temperature annealing, it is usually accompanied with significant structure changes and a large decrease of the reflectivity. This will cause an obvious deterioration of the experimental performance which is not acceptable for the telescope mission.
On the other hand, low temperature annealing was developed for different multilayer systems. It can provide an obvious stress reduction and minimum changes of the structure. For instance, Montcalm et al. [13] annealed the Mo/Si multilayers at ~220°C for 6 hours which reduced the stress by 85%, with a reflectance loss of only 1.5% (absolutely). Barthelmess and Bajt [14] studied the stress change of Mo/B4C multilayers as a function of annealing temperature which proves that annealing at <200 °C for 1 hour was sufficient to reduce the stress by ~40%. This stress relaxation was accompanied by only a minor expansion of the multilayer period of ~0.02 nm and <0.5% decrease in reflectivity. Low temperature annealing process has also been explored on the W/Si multilayers. Platonov et al. studied the stress and reflectivity changes of the short period (d = 2.8 nm) W/Si multilayers annealed from 100 °C to 200 °C and the stress was reduced from ~-100 MPa to zero after 150 °C annealing [15]. Christensen et al. briefly reported that a 3 hours annealing at 130 °C can be an optimum process to achieve the zero stress state for certain W/Si multilayers [3]. However, these works reported before were non-systematic while the temperature-time dependence of the annealing effects, the microstructure changes and the temporal stability of the stress were not fully studied. Thus, these works provide limited guidance for the development of low-stress W/Si multilayers for the XTP mission and other forthcoming X-ray telescope projects using the similar coatings.
In this paper, we will report a systematic investigation of the stress, reflectivity, and structure changes of the periodic W/Si multilayers under the low temperature annealing from 150 °C to 250 °C, and with different annealing time from 10 minutes to 5 hours. The microstructure evolutions were further studied using the X-ray scattering measurements and high resolution transmission electron microscopy (TEM). It is found that the stress reduction is more sensitive on temperature instead of time. A 10 minutes annealing at 200 °C can already reduce the compressive stress by 55% with almost unchanged reflectance. The enhanced diffusion and intermixing is the main reason for the stress reduction and structure changes of the amorphous W/Si multilayers.
2. Experiments
The multilayers used in the X-ray telescope consist of a depth-graded structure with the d-spacing varied from 2.5 nm to ~6 nm, according to the power law design [16]. However, to study the effects of different low temperature annealing process on the multilayer with easy comparison of the structure and reflectivity changes, a single d-spacing periodic multilayer with d = 3.8 nm was used in this work as a first step. This d-spacing corresponds to the thickness of a major part of the layers in the depth-graded structure. The W/Si multilayers were fabricated using direct current magnetron sputtering technique. The base pressure was 8 × 10−5 Pa prior to deposition. High purity argon (99.999%) was used as the working gas and the argon pressure was fixed at 0.4 Pa during deposition. The multilayers were deposited both on thin quartz substrates and super-polished silicon wafers, while the former ones were used for stress measurements and the latter ones were used for structure characterizations. The quartz substrates are 1 mm-thick with a diameter of 30 mm. The thickness ratio of tungsten within each period is γ ≈0.45 and the number of bilayers is N = 120. The multilayer d-spacing was determined based on the angular positions of the Bragg peaks according to the modified Bragg equation and the thickness of each layer is obtained by the fitting results of the grazing incidence reflectivity curves.
Two groups of annealing experiments were performed in a high vacuum environment with a pressure lower than 5 × 10−4 Pa. The first group is to study the temperature-dependence effects, and the samples were annealed at 150°C, 175°C, 200°C, 225°C and 250°C for a constant time of 1hour. The second group is to study the time dependence effects, and the samples were annealed at 200°C for a time interval of 10mins, 1h, 3h and 5h, respectively. All the annealing processes were performed with a heating rate of 5 °C/min. After annealing, the samples were cooled down to the room temperature naturally. The annealing temperature was measured by a thermocouple and temperature monitoring labels with an accuracy of ± 5 °C.
The multilayer structure before and after annealing were characterized by grazing incidence X-ray reflectometry (GIXR) at Cu-Kα emission line (λ = 0.154nm). The measurements were performed with collection time of 2s per 0.005° step. Detector scans were performed around the 1st Bragg peak of the multilayers to measure the X-ray scattering from the interface roughness.
The stress of the multilayer as-deposited and after annealing is determined by wafer-curvature measurements. A Fizeau phase-shifting interferometer (λ = 632.8nm) is used to measure the surface contour and the radius of curvature of the substrates before and after the deposition and after annealing. Then, the multilayer stress σf is determined from the change of radius of curvature according to Stoney’s equation [17].
Where ts is the substrate thickness, tf the film thickness and Rpre and Rpost represent radius of curvature of the pre-deposited and post-deposited samples or samples before and after annealing, respectively. Es is Young’s modulus and Vs is Poisson’s ratio for the substrate. The value of Es = 72 GPa and Vs = 0.2 are used for the quartz substrate [18, 19]. For each annealing process, two samples were tested and the average stress value was calculated to represent the stress state.
The microstructure of the multilayers before annealing and after 1 h annealing at 150 °C and 250 °C are characterized by TEM. The samples were prepared by using focused ion beam technique and the measurements were performed with an FEI Tecnai G2 F20 equipment of Materials Analysis Technology Inc.. Both the high resolution images and selected area electron diffraction (SAED) patterns were taken to study the layer morphology and crystallization. The energy dispersive X-ray spectroscopy (EDX) was used for analyzing the elemental distribution of W, Si and O in the multilayer before and after annealing.
3. Results and discussion
3.1 Post-deposition annealing at different temperatures (1st group)
The GIXR curves of the 3 samples before and after annealing at 150 °C, 200 °C and 250 °C are shown in Fig. 1. The relative changes of the 1st order Bragg peak reflectivity, (Rafter-Rbefore)/Rbefore, and the d-spacing, dafter-dbefore, are calculated and shown in Fig. 2(a) and (b), respectively. An error bar is added for the determined reflectivity and d-spacing changes given to the measurement accuracy. The as-deposited W/Si multilayers exhibited a good layer structure with the 1st order reflectivity of 67%-71% at 8.04 keV, and the interface widths of 0.35-0.38 nm (according to the fitting results). The interface width means a sum of the interface roughness and interdiffusion. After annealing at 150°C, the intensity of all Bragg peaks was enhanced compared to the as-deposited sample, and the 1st order reflectivity was increased by about 3%, relatively. It is indicating that the layer structure was a little improved by the annealing. The peak positions of different orders are slightly shifted toward the large angle, which implies a small compaction of the period. With a higher temperature, the structural improvement was reduced while the reflectance after 200 °C annealing was almost the same as the as-deposited one. Further increasing the temperature leads to a decrease of the reflectance and about 5% drop was observed after 250 °C annealing. The period compaction enlarged with higher temperature that reached to around 0.018 nm at 250 °C. The reflectance drop and period compaction of W/Si is also observed in the high temperature annealing that can be caused by the enhanced inter-diffusion and formation of tungsten silicide [12]. These changes are much smaller in our experiments due to the low temperature applied. Besides the decreased 1st order reflectance, the intensity ratio among the high orders is also changed after 250 °C annealing, indicating a different layer thickness ratio or interface structure than before. This can distort the broadband reflectivity profile of the depth-graded multilayer in application and should be avoided.
Fig. 1 Grazing incidence X-ray reflectivity curves of the multilayers before and after annealing at 150 °C (a), 200 °C (b), and 250 °C (c).
Fig. 2 Relative changes of the 1st order reflectivity (a) and period (b) of the multilayer after annealing at different temperatures for 1 h.
The stress reduction of the multilayer under different annealing temperature is shown in Fig. 3. The as-deposited samples have a compressive stress of about −270 MPa. After 150 °C annealing, the initial stress decreases by 60 MPa (24% relatively). As the temperature increases from 150 °C to 250°C, the stress decreases linearly and it reaches an almost zero stress state after 250 °C annealing. The linear relaxation behavior of the stress with temperature is also reported in other multilayer systems [13, 14]. The stress stability of the multilayer is another important property which ensures that the mirror figure will not change over the operation period. Thus, the stress of the annealed multilayers was measured again after 11 months storage in the dry cabinet. The stress change between the stored multilayers and the as-deposited one was also shown in Fig. 3. The multilayers annealed at different temperatures maintained almost the same stress states after 11 months which indicate a good temporal stability.
Fig. 3 Stress reduction of the multilayers after annealing at different temperatures and after 11 months further storage.
3.2 Post-deposition annealing with different time (2nd group)
The GIXR curves of the multilayers annealed for 10 mins, 3 h, and 5 h at 200 °C are shown in Fig. 4. The small peak split in the 3rd diffraction order of the multilayers both as-deposited and annealed for 3 h is caused by an imperfection of the periodicity of the multilayer introduced in the deposition process. The relative change of reflectance and period are shown in Fig. 5(a) and 5(b), respectively. It can be seen that, after annealing at 200 °C for 10 mins, the 1st order peak reflectance slightly increased by ~1% compared to the as-deposited sample, and the multilayer period compaction was marginal. The prolonged annealing time slowly changed the layer structure and ~2.5% drop of the 1st order reflectance was observed after 5 h. The multilayer period compaction only reaches to ~0.01 nm after 5h. It is worth noting that the angular bandwidth of the 1st Bragg peak of all annealed samples (in the 1st and 2nd groups) decreased a bit as compared to the as-deposited one. The slightly decrease of the bandwidth can be caused by an enlarged interface width and a reduced optical contrast between the layers after annealing.
Fig. 4 Grazing incidence X-ray reflectivity curves before and after annealing at 200 °C for 10 minutes (a), 3 hours (b) and 5 hours (c).
Fig. 5 Relative changes of the 1st order reflectivity (a) and period (b) of the multilayer after annealing at 200 °C for different time.
The stress changes as a function of different annealing time are shown in Fig. 6. For the 10 minutes annealing, the stress reduces significantly by 113 MPa (43% relatively). Further increasing the annealing time from 1 h to 5 h only reduced the stress by 55% to 64%, respectively. It is evident that the stress relaxation occurs rapidly during the first 10 minutes annealing and probably also during the heating process. This trend was also found in the Mo/B4C multilayer [14]. Compared to the temperature-dependent reduction of the stress, long annealing time is much less effective which still induces a further drop of the reflectance. The stress of the multilayers was also measured 11 months after annealing as shown in Fig. 6. After long-term annealing, the temporal stability of the stress is still good.
Fig. 6 Stress reduction of the multilayers after annealing at 200 °C for different time and after 11 months further storage
Based on the results of all annealing experiments, the 1st order reflectance and stress changes of the ~3.8 nm-period W/Si multilayers are summarized in Table 1. Although the 150 °C annealing process can increase the reflectance, the stress relaxation is too small. In contrary, the relatively high temperature annealing at 250 °C produced a zero stress state while the structure change is significant. The annealing process performed at 200 °C for 10 minutes to 1 hour seems to be a good option while half of stress is relaxed and the structure change is negligible.
Table 1. Overview of the relative change of the 1st order reflectance (with brackets) and the stress reduction (without brackets in the unit of MPa) of the W/Si multilayer under different annealing processes
3.3 Micro-structure analysis before and after annealing
To better understand the physics for the changes of the reflectance, period and stress during annealing, the microstructure of the multilayer before and after annealing are characterized. The X-ray reflectivity changes can be caused by two effects, the different interface roughness or interdiffusion inside the multilayer. X-ray scattering measurements, the detector scans, are typically used to analyze the scattering signal from the interface roughness. The scattering curves of the as-deposited multilayer, and the multilayers after annealing at 150 °C and 250 °C are shown in Fig. 7. The curves were shifted slightly along the x axis for comparison, since the three samples have a little different d-spacing. The small peaks on the right side correspond to the resonant non-specular scattering (RNS) which arise from the interference of the scattering from the conformal roughness partially replicated through the interfaces. The wings between the specular position and the RNS peak correspond to the scattering from the non-conformal roughness. It can be seen that after annealing at 150 °C and 250 °C for 1 hour, the intensity of both the conformal and non-conformal scattering remain similar (within the detection limit). No obvious change of the roughness was found.
Fig. 7 Detector scans around the 1st Bragg peak of the as-deposited multilayer and the one annealed at 150 °C and 250 °C
The high resolution TEM images and SAED patterns of the three W/Si samples are shown in Fig. 8. In the TEM images, the white stripes are silicon and the black stripes are tungsten. For the as-deposited sample (Fig. 8(a) and 8(d)), a periodic layer structure with sharp interfaces was clearly observed. The d-spacing is measured to be 3.7 nm and the interface area is only ~0.4 nm in width for both interfaces which is similar to the fitted values of the GIXR results qualitatively. The layer thickness ratio is different from the designed value which can be caused by the imaging contrast during the measurement. The SAED image exhibits very faint and broadened diffraction rings which indicate a mainly amorphous state of the as-deposited W/Si multilayer, with a few nanoscale short-range order structures in the layers. After annealing at 150 °C for 1h, as shown in Fig. 8(b) and 8(e), the multilayer maintains a sharp interface structure with an interface width similar to the as-deposited one. Although the X-ray reflectivity slightly increased as mentioned above, the related interface improvement may be very small that cannot be clearly resolved by TEM. The SAED result exhibits a similar amorphous structure of the 150 °C annealed multilayer like the as-deposited one. As the annealing temperature reach to 250 °C, as shown in Fig. 8(c) and 8(f), the interface area of the multilayer enlarges significantly especially at the Si-on-W interface. The interface width of W-on-Si and Si-on-W is 0.4 nm and 0.6 nm, respectively. Nevertheless, the SAED results remain the same as the as-deposited sample indicating a mainly amorphous structure.
Fig. 8 TEM images and the SAED patterns of the as-deposited W/Si multilayer (a) (d), after 150 °C annealing for 1 h (b) (e), and after 250 °C annealing for 1 h (c) (f).
The EDX line scans performed at the cross-sections of the three samples are shown in Fig. 9. A periodic variation of the elemental concentration of W and Si is observed for all three samples. The elemental contrast between W and Si is similar for the as-deposited and 150 °C annealed samples, while it becomes smaller for the 250 °C case. It is evident that more inter-diffusion of Si and W atoms occurred at the interfaces of the 250 °C annealed sample that is consistent with the high resolution TEM result. Considering both the scattering and TEM results, the reflectance drop after annealing is mainly caused by the large inter-diffusion. The oxygen concentration also increases from ~4% to ~7% (in average) with higher temperatures. The presence of oxygen can come from the deposition, annealing, and the sample preparation process for TEM, while the increased concentration indicate a slightly enhanced oxidation during the 250 °C annealing process.
Fig. 9 EDX line scans of the W, Si and O elements along the depth position of the multilayer before and after annealing.
3.4 Discussion
The structure and stress changes of the amorphous W/Si multilayers can be explained by the “free-volume model” [20, 21]. The sputtering deposition is a strong non-equilibrium process which can cause a large amount of defects and vacancies in the layers, and the formed free-volume is larger than the one in the equilibrium state. Meanwhile, the energetic bombardment of particles on the layers and the mismatched atomic structure cause the large compressive stress of the multilayer [17]. During the annealing, the intermixing at the interface area is enhanced, especially due to the low activation energy of Si diffusion. This was clearly observed in the TEM image of the 250 °C annealing while the Si atoms played the dominant role. The enhanced inter-diffusion can partially annihilate the excess free volume induced during the deposition. Moreover, amorphous silicide can form at the interface which was found in many other works under the temperature of 210 °C −250 °C [22]. The formation of relatively high density interlayers will reduce the layer thicknesses as compared to the as-deposited structure [23]. The free volume annihilation and compound formation together brought the period compaction of the annealed W/Si multilayers. With higher temperature, both the diffusion and intermixing are further enhanced which result in the larger interface widths and the continuous drop of the reflectance and period compaction. The annihilation of free volume and the decreased average atomic volume are part of the process of structural relaxation which can lead to the stress reduction of the amorphous layers [20]. On the other hand, the structural and stress change of the multilayer was most prominent within the first 10 minutes while longer annealing time induced little changes, especially on the stress. This can be explained by the time-dependence of the diffusion coefficient [20]. With longer annealing time at 200 °C, the defect concentration in the multilayer is reduced that can slow down inter-diffusion and less changes compared to the beginning stage of the annealing.
4. Summary
The hard X-ray reflectivity, structure, and stress changes of the periodic W/Si multilayer after low temperature annealing were studied systematically. With the increased annealing temperature from 150 °C to 250 °C, the compressive stress decreased linearly and it almost reached a zero stress state at 250 °C. Meanwhile, the reflectivity and layer structure degraded gradually with higher temperature. The time-dependence experiments indicate that the stress relaxation mostly occurred at the first 10 minutes during the annealing process and a long-term annealing is not necessary. The X-ray scattering and TEM results show that the structure and stress changes are mainly caused by the enhanced inter-diffusion during the annealing. The present work is performed on a periodic multilayer with a d-spacing of ~3.8 nm, which helps to understand the changes induced by the low temperature annealing on a fixed W/Si layer structure. For the multilayers with smaller d-spacing, the layers will also be amorphous and a similar stress relaxation may be expected with annealing. For the thicker multilayers, the tungsten layers will start to crystallize and the polycrystalline structure can exhibit different relaxation under the annealing process. Thus, further work on the stress characterization of W/Si multilayers with different d-spacing and the depth-graded structure, on the flat and cylindrical glass substrate is underway. These different works together will provide a more comprehensive understanding of the stress and structural properties of the W/Si multilayer mirror for the X-ray telescope mission.
5. Funding
NSAF (No. U1430131), National Natural Science Foundation of China (No.11443007, No. 11505129), National Key Scientific Instrument and Equipment Development Project (No. 2012YQ13012505, 2012YQ24026402), Shanghai Pujiang Program (No. 15PJ1408000).
References
1. Y. Dong, “The X-ray Timing and Polarization Satellite - 1, 2, 3: Uncovering the mysteries of black holes and extreme physics in the universe,” Proc. SPIE 9144, 91443O (2014).
2. B. Z. Mu, H. Y. Liu, H. J. Jin, X. J. Yang, F. F. Wang, W. B. Li, H. Chen, and Z. S. Wang, “Optimization of geometrical design of nested conical Wolter-I X-ray telescope,” Chin. Opt. Lett. 10(10), 103401 (2012). [CrossRef]
3. C. J. Hailey, H. J. An, K. L. Blaedel, N. F. Brejnholt, F. E. Christensen, W. W. Craig, T. A. Decker, M. Doll, J. Gum, J. E. Koglin, C. P. Jensen, L. Hale, K. Mori, M. J. Pivovaroff, M. Sharpe, M. Stern, G. Tajiri, and W. W. Zhang, “The nuclear spectroscopic telescope array (NuSTAR): optics overview and current status,” Proc. SPIE 7732, 77320T (2010). [CrossRef]
4. M. H. Modi, S. K. Rai, M. Idir, F. Schaefers, and G. S. Lodha, “NbC/Si multilayer mirror for next generation EUV light sources,” Opt. Express 20(14), 15114–15120 (2012). [CrossRef] [PubMed]
5. P. N. Rao, S. K. Rai, M. Nayak, and G. S. Lodha, “Stability and normal incidence reflectivity of W/B4C multilayer mirror near the boron K absorption edge,” Appl. Opt. 52(25), 6126–6130 (2013). [CrossRef] [PubMed]
6. J. H. Lee, K. Y. Woo, K. H. Kim, H. D. Kim, and T. G. Kim, “ITO/Ag/ITO multilayer-based transparent conductive electrodes for ultraviolet light-emitting diodes,” Opt. Lett. 38(23), 5055–5058 (2013). [CrossRef] [PubMed]
7. A. Najar, H. Omi, and T. Tawara, “Effect of structure and composition on optical properties of Er-Sc silicates prepared from multi-nanolayer films,” Opt. Express 23(6), 7021–7030 (2015). [CrossRef] [PubMed]
8. D. L. Windt, “Stress, microstructure, and stability of Mo/Si, W/Si, and Mo/C multilayer films,” J. Vac. Sci. Technol. A 18(3), 980–991 (2000). [CrossRef]
9. V. Dupuis, M. F. Ravet, C. Tête, M. Piecuch, and B. Vidal, “Characteristics and thermal behavior of W/Si multilayers with well-defined interfaces,” J. Appl. Phys. 68(7), 3348–3355 (1990). [CrossRef]
10. J. M. Molarius, S. Franssila, G. Drozdy, and J. Saarilahti, “Tungsten silicide formation from sequentially sputtered tungsten and silicon films,” Appl. Surf. Sci. 53, 383–390 (1991). [CrossRef]
11. M. Brunel, S. Enzo, M. Jergel, S. Luby, E. Majkova, and I. Vavra, “Structural characterization and thermal stability of W/Si multilayers,” J. Mater. Res. 8(10), 2600–2607 (1993). [CrossRef]
12. J. B. Kortright and E. Ziegler, “Stability of tungsten/carbon and tungsten/silicon multilayer x-ray mirrors under thermal annealing and x-radiation exposure,” J. Appl. Phys. 69(1), 168–174 (1991). [CrossRef]
13. C. Montcalm, “Reduction of residual stress in extreme ultraviolet Mo/Si multilayer mirrors with postdeposition thermal treatments,” Opt. Eng. 40(3), 469–477 (2001). [CrossRef]
14. M. Barthelmess and S. Bajt, “Thermal and stress studies of normal incidence Mo/B4C multilayers for a 6.7 nm wavelength,” Appl. Opt. 50(11), 1610–1619 (2011). [CrossRef] [PubMed]
15. Y. Y. Platonov, D. M. Broadway, B. DeGroot, P. H. Mao, F. A. Harrison, G. Gutman, and J. Rodriguez, “X-ray reflectivity and mechanical stress in W/Si multilayers deposited on thin substrates of glass, epoxy-replicated aluminum foil, and Si wafer,” Proc. SPIE 3133, 469–475 (1997). [CrossRef]
16. K. D. Joensen, P. Voutov, A. Szentgyorgyi, J. Roll, P. Gorenstein, P. Høghøj, and F. E. Christensen, “Design of grazing-incidence multilayer supermirrors for hard-x-ray reflectors,” Appl. Opt. 34(34), 7935–7944 (1995). [CrossRef] [PubMed]
17. L. B. Freund and S. Suresh, Thin film materials-stress, defect formation and surface evolution (Cambridge University, 2003)
18. J. F. Shackelford, W. Alexander, and J. S. Park, CRC materials science and engineering handbook (CRC, 1994).
19. MEMSnet [DB/OL].MNX, http://www. Memsnet. org/material/.
20. O. B. Loopstra, E. R. van Snek, T. H. de Keijser, and E. H. Mittemeijer, “Model for stress and volume changes of a thin film on a substrate upon annealing: Application to amorphous Mo/Si multilayers,” Phys. Rev. B Condens. Matter 44(24), 13519–13533 (1991). [CrossRef] [PubMed]
21. E. N. Zubarev, “Reactive diffusion in multilayer metal/silicon nanostructures,” Phys. Uspekhi 54(5), 473–498 (2011). [CrossRef]
22. D. L. Voronov, E. N. Zubarev, V. V. Kondratenko, A. V. Penkov, Y. P. Pershin, A. G. Ponomarenko, I. A. Artioukov, A. V. Vinogradov, Y. A. Uspenskii, and J. F. Seely, “Thermoresistive multilayer mirrors with antidiffusion barriers for work at the wavelengths 40–50 nm,” 8th International Conference on X-Ray Lasers, Aspen, U.S.A., AIP Conf. Proc. 641, 575–582 (2002). [CrossRef]
23. S. L. Nyabero, R. W. E. van de Kruijs, A. E. Yakshin, E. Zoethout, G. von Blanckenhagen, J. Bosgra, R. A. Loch, and F. Bijkerk, “Interlayer growth in Mo/B4C multilayered structures upon thermal annealing,” J. Appl. Phys. 113(14), 144310 (2013). [CrossRef]
