research papers
Interface characterization of B_{4}Cbased multilayers by Xray grazingincidence reflectivity and diffuse scattering
^{a}Shanghai Synchrotron Radiation Facility, Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Zhangheng Road 239, Pudong District, Shanghai 201204, People's Republic of China, and ^{b}Institute of Precision Optical Engineering, Department of Physics, Tongji University, Shanghai 200092, People's Republic of China
^{*}Correspondence email: jianghui@sinap.ac.cn
B_{4}Cbased multilayers have important applications for soft to hard Xrays. In this paper, Xray grazingincidence reflectivity and diffuse scattering, combining various analysis methods, were used to characterize the structure of B_{4}Cbased multilayers including layer thickness, density, interfacial roughness, interdiffusion, correlation length, etc. Quantitative results for W/B_{4}C, Mo/B_{4}C and La/B_{4}C multilayers were compared. W/B_{4}C multilayers show the sharpest interfaces and most stable structures. The roughness replications of La/B_{4}C and Mo/B_{4}C multilayers are not strong, and oxidations and structure expansions are found in the aging process. This work provides guidance for future fabrication and characterization of B_{4}Cbased multilayers.
Keywords: boron carbide; multilayer; Xray reflectivity; diffuse scattering; interface; aging.
1. Introduction
Multilayer mirrors are artificial onedimensional crystals with wide applications in the Xray and extreme ultraviolet regime. For synchrotron radiation science they are considered key components for reflection (Windt et al., 2002), polarization (Wang et al., 2011), focusing (Mimura et al., 2010) and monochromatization (Rack et al., 2010). Compared with transmission focusing optics, they provide higher efficiency and realise nanofocusing more easily. Compared with a doublecrystal monochromator, they provide more due to a wider bandpass and their large dspacing extends their ranges to the soft Xray region. Boron carbide (B_{4}C) based multilayers have valuable applications in synchronization radiation (Rack et al., 2010), space observation (Joensen et al., 1995), biological microscopy (Gutman, 1994), etc. The stable capping or barrier layer of B_{4}C multilayers (Bottger et al., 2003) expands application opportunities.
Each layer in a multilayer mirror is very thin, typically several nanometers to less than 1 nm, and mirror performance depends on the quality of the layer interfaces. The most effective methods of characterizing multilayers are hard Xray grazingincidence reflectivity and diffuse scattering measurements. Detailed characterization can estimate defects introduced during fabrication, and offers feedback for improving the manufacture technology. Characterization also allows inspection of component quality in storage or during service to estimate their lifetime.
In this paper, various B_{4}Cbased multilayers were fabricated and investigated by Xray reflectivity and diffuse scattering techniques. Interfacial roughnesses, roughness correlations, interdiffusion, layer densities and their aging effects were characterized and compared systematically.
2. Experiment and method
2.1. Fabrication
All multilayer samples were deposited by DC magnetron sputtering on silicon substrates with a RMS roughness of ∼0.3 nm at room temperature. For W/B_{4}C multilayers the base vacuum was 1.2 × 10^{−4} Pa and the argon gas pressure (purity 99.999%) was 0.667 Pa. The sputtering powers for the W (purity 99.95%) and B_{4}C (purity 99.50%) targets were 20 W and 150 W, respectively. For Mo/B_{4}C and La/B_{4}C multilayers the base vacuum was 1 × 10^{−4} Pa and the argon gas pressure was 0.18 Pa. The sputtering powers for the Mo, La (purity 99.95%) and B_{4}C targets were 10 W, 10 W and 80 W, respectively. The distance between substrate and targets was 8 cm. All samples were measured using a highresolution Xray diffractometer (BEDE D1) at the Cu K_{α} line. The Xray reflectivity measurement was run using only the second channelcut crystal with a divergence angle of 0.007°, and the nonspecular diffusescattering measurement was run in directbeam mode to increase the Xray intensity.
2.2. Xray reflectivity and diffuse scattering
Xray grazingincidence reflectivity is an effective, simple and nondestructive technique for characterizing the structure parameters in a multilayer (Gibaud & Hazra, 2000). For periodic multilayers the behavior is described by a corrected Bragg equation with constant periodic thickness D, fractional thicknesses of absorber (scattering) layers d_{a} and spacer layers d_{s}, and complex refractive indices n_{a} = 1 − δ_{a} + iβ_{a} and n_{s} = 1 − δ_{s} + iβ_{s},
where m is the reflection order, λ is the wavelength and θ is the grazingincidence angle. This equation relates the periodic thickness and the grazingincidence angles. According to the positions of different sharp Bragg reflection maximums, based on the method of least squares, the periodic thickness can be calculated. The thickness ratio Γ = d_{a}/D is related to the distribution of peak intensities. When mΓ is a positive integer, the mth (m = 1, 2, 3…) Bragg maximum disappears.
Another effective method of obtaining information about layer thickness is based on the Fourier transform. Parratt's recurrence formula (Parratt, 1954) can be kinetically approximated and the reflectivity is related to an autocorrelation function (ACF) (Bridou et al., 2006),
where k_{0} is the modulus of the incident wavevector, δχ is the polarizability change, Z_{ij} = Z_{i} − Z_{j} is the distance between the jth and ith interfaces, and the interfacial width = + . According to the positions and widths of the ACF maxima, the layer thickness and interfacial width can be obtained.
More accurate structure parameters need to be estimated by fitting the reflectivity curve. In order to realise good agreement between the experimental and theoretical curves of Parratt's model, global optimization (Wormington et al., 1999) can be used to search for the optimum simulated structure in a given constraint.
Xray reflectivity is unable to distinguish between interfacial roughness and interdiffusion because both deteriorate the reflectivity in a similar way. Xray diffuse scattering is one of the most direct techniques for determining interfacial roughnesses in a complicated multilayer structure. A distortedwave Born approximation (DWBA) model (Holý et al., 1993) is suitable for slightly rough interfaces. The scattering potential is divided into a nondisturbed part and a disturbance. Interferences of reflected and transmitted waves have four types of interaction based on the dynamic scattering process (Stepanov et al., 1996). The whole diffuse scattering signal (Stoev & Sakurai, 1997) is represented by
where ΔΩ is the detector acceptance angle, A_{s}/A_{b} is the area ratio of the radiation on the sample to the beam spot, G_{j}^{m} are the four mutual products of T_{i} (or R_{i}) and T_{s} (or R_{s}), and S(q_{x}) is the structure factor
where ξ_{⊥} is the vertical correlation length (Pape et al., 1998) and C(x) is the lateral correlation function which is based on the selfaffine characteristic of the rough interface (Sinha et al., 1988),
where ξ_{∥} is the lateral correlation length and h is the fractal exponent.
The diffuse scattering signals are distributed around the reflection direction. Common scan methods include rocking curve scans (ω scan), offset scans, detector 2θ scans and full reciprocalspace scans. Rocking curve scans are performed by fixing the detector and scanning the incidence angle, whose track is parallel to the q_{x} direction. Owing to the proportional relationship between q_{x} and the roughness frequency, this method is very sensitive in determining roughness information. The method of scattering curve fitting is also based on global optimization to approach the real multilayer structure.
3. Result and discussion
Eight multilayers were measured using the Xray grazingincidence reflectivity technique including three W/B_{4}C, three Mo/B_{4}C and two La/B_{4}C multilayers. Three methods were used to analyze the reflectivity curves. As can be seen from Fig. 1 and Table 1, by using not only the corrected Bragg equation calculation but also the Fourier transform method, the periodic thickness is very accurate because almost no assumptions were introduced into the calculation. The curvefitting method provides more comprehensive structure information but a more reasonable initial structure model is necessary. This model was based on the preanalyses of the two methods mentioned above in this paper or even the fabrication goals.

The interface situations are different for different metal choice. In general the interfacial width of the metalonB_{4}C interface is smaller than that of the B_{4}Conmetal interface. The metalonB_{4}C interfaces are produced by the impact of highenergy metal atoms on the B_{4}C surface during deposition. An exception is La/B_{4}C multilayers because lanthanum may be more chemically active and has a larger atom size. The B_{4}Conmetal interface mainly embodies the characteristics of a rougher metal surface, and smaller boron and carbon atoms enable them to diffuse to the metal layer so that the B_{4}Conmetal interlayer becomes thicker, normally beyond 0.4 nm. Comparing various multilayers, the W/B_{4}C multilayer has the best interface characteristics and La/B_{4}C has the worst, and can be compared with previous records (Andreev et al., 2010). Keissig fringes disappear in the reflectivity curve of the La/B_{4}C multilayers because longrange disorder of the large interfacial width (Jiang et al., 2011a) degrades the whole periodicity. Highangle reflectivity was measured as well. Apart from ultrathinperiod W/B_{4}C multilayers, slight crystallizations were found in other multilayers including the Mo(110), La(100) and Cr(110) crystallographic planes. It is clear that the deposition environments of these multilayers were not the same in this paper and changes of environments may produce slightly different multilayer performances.
As a consumable optics, multilayer structures are not always stable. Aging effects related to the inherent characteristics of the materials deserve to be studied. Three multilayer samples, W/B_{4}C, Mo/B_{4}C and La/B_{4}C (Fig. 2), were measured justprepared and after longtime storage in a dry atmosphere environment (296 K). As can be seen from Table 2, the periodic thickness increased by 0.38% for the La/B_{4}C multilayer and by 0.24% for the Mo/B_{4}C multilayer after one year, but decreased by 0.05% for the W/B_{4}C multilayer after two years. The changes may result from interdiffusion mechanisms and stress release. Surface oxidation increased the stress and the changes of the layer thickness balanced the whole stress of the multilayer. The outermost layer thickness increases apparently by over 10% for the La/B_{4}C and Mo/B_{4}C multilayers because lanthanum and molybdenum have stronger oxidation capabilities than tungsten so that oxygen atoms penetrate through the B_{4}C layer gradually and react with metal atoms. The surface B_{4}C layer was also determined to absorb oxygen (Jiang et al., 2011b). Thus it is important to deposit a stable capping layer to protect the multilayer structure.

The reciprocalspace map shown in Fig. 3 presents comprehensive scattering information for the Mo/B_{4}C multilayer (sample 6). The first five Bragg maxima were determined. Along their lateral directions, clear and narrow crescentshaped fringes can be seen owing to a good replication of the periodicity and roughness. Near the critical reflection area, the strong scattering signal means that the surface structure was oxide and sparse but did not influence the inner periodicity.
Three metal/B_{4}C multilayers were chosen to measure the Xray diffuse scattering. In order to improve the precision of the analysis, rocking curve scans near different Bragg maximums were simultaneously fit based on equation (3), as shown in Fig. 4. According to the fitted interfacial roughness σ_{r} and the interfacial width σ obtained by Xray reflectivity measurement, the interdiffusion σ_{d} can be calculated by the equation = . As can be seen from Table 3, the RMS roughnesses for the three multilayers are almost the same but the Mo/B_{4}C and La/B_{4}C multilayers have larger interdiffusions. Comparing the lateral correlation length ξ_{∥} and fractal exponent h, the Mo/B_{4}C and La/B_{4}C multilayers have a stronger lateral correlation and more apparent island growth features than the W/B_{4}C multilayer. Owing to the weak interdiffusion and small layer thickness, the vertical correlation length in the W/B_{4}C multilayer is over 100 times the periodic thickness. In contrast, the replication capability is very weak for La/B_{4}C multilayers. The vertical correlation length is only about four times the periodic thickness. The fractal model (Sinha et al., 1988) was also used to fit the twodimensional power spectral density curve calculated from various atomic force microscopy measurements (Bioscope BS2Z, 256 × 256 pixels) of the W/B_{4}C multilayer (S11) at different scan scales from 10 µm × 10 µm to 0.5 µm × 0.5 µm. The result shows that the RMS roughness is 0.31 nm, the lateral correlation length is 63.63 nm and the fractal exponent is 0.06. The result is comparable with the characterization by Xray diffuse scattering.

All measurements and relevant analyses mentioned above are suitable for all multilayer structures. The characteristics of the metal/B_{4}C multilayer structures (metal = W, Mo, La, Cr, Pt, Ni, Ti, Ru, Pd, etc.) can be extended to other typical material pairs such as Bbased, Cbased, Sibased and Ybased multilayers. The optical constants of the scattering layers (highZ metal material) are the decisive factor regarding the reflectivity so that near bulk densities are required. Smooth and stable interfaces of the spacer layers (lowZ material) keep whole multilayers stable and further improve the optical performance. By the characterization of metal layers in this paper, other corresponding multilayer structures such as W/C, Mo/Si, Mo/Y and Mo/B_{4}C/Si/B_{4}C can be estimated. Accurate determination of the B_{4}C layers is also useful for more complicated characterization of multilayers which use B_{4}C as capping layers or barrier layers. Aging effects were also observed in this study. In the application, other environmental influences need to be considered as well. For example, heat load and may be very serious problems when the multilayers are radiated by highflux synchrotron Xrays. Related studies will be carried out in the future.
4. Conclusion
In order to study the properties of key B_{4}Cbased multilayers, Xray grazingincidence reflectivity and diffuse scattering were used to characterize multilayer structures synthetically, including information of the thickness, density, interfacial roughness, interdiffusion, surface state, correlation length, etc. Corrected Bragg equation calculations, Fourier transform methods and curve fitting were combined to obtain accurate structure parameters, and the diffuse scattering technique distinguished interfacial roughness and interdiffusion well. The results show that the interfacial width of the metalonB_{4}C interface is about 0.2–0.3 nm, and that of the B_{4}Conmetal is >0.4 nm. The interfaces in W/B_{4}C multilayers are sharpest, while the interfacial widths in La/B_{4}C multilayers are largest. Large interdiffusion occurs in the Mo/B_{4}C and La/B_{4}C multilayers, based on scattering measurements, while the interfaces in the W/B_{4}C multilayers are simple roughness states and have a smaller lateral and larger vertical correlation length. The main changes of the metal/B_{4}C multilayers aged in a dry atmosphere are surface oxidation and increase in period thickness. W/B_{4}C multilayers are stable enough so that no obvious oxidation appears at the surface and the period thickness keeps almost constant. All quantitative characterizations and comparisons will be useful to further improve the fabrication technology.
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