Numerical Simulation of C/C/C Planar X-ray Waveguides
A planar X-ray waveguide is generally considered to be a layer of light material sandwiched between metal layers. This simple structure allows an X-ray standing wave (XSW) field formation in the core layer. Jark et al. 1 have proposed that beryllium is the most promising alternative out of the possible light materials. Mo/Be/Mo waveguides were tested successfully and a guided beam of high intensity and high degree of coherence was detected at the waveguide exit. 1, 2 The problem is that
... lem is that beryllium is toxic. Workers exposed to beryllium are at risk of developing serious, debilitating diseases. Chronic beryllium disease (or berylliosis) is a painful scarring of the lung tissue. Less common, acute beryllium disease causes lung inflammation, resembling pneumonia. Several healthcare organizations consider beryllium to be carcinogenic. 3 Consequently, it is a good idea to revise the suitability of the other light materials, carbon for example, to be used as an X-ray waveguide core. Recently Menzel et al. 4 have reported a high-resolution carbon/carbon multilayer deposition. They were able to achieve the density contrast of the layers up to ∆ρ = 0.2 g/cm 3 for the multilayer with a period thickness d = 3.78 nm; the interface roughness was in the range of σc = 0.13 -0.19 nm. The parameters of the growing carbon film can be controlled with high precision 4 and single carbon layer density can be varied in the range ρ = 2.0 -2.7 g/cm 3 . Consequently, it is possible in principle to fabricate a structure that will consist of a lowdensity carbon core layer sandwiched between denser carbon cladding layers. At first sight, the C/C/C waveguide looks to be physically meaningless, since the density contrast, which can be ensured in that structure, does not seem to be enough for waveguide mode formation. Nevertheless, the energy losses in waveguides with low-Z cladding layers may decrease significantly due to low absorption in all layers. Consequently, these structures may turn out to be more promising compared with traditional ones. Jark and Di Fonzo, for example, have mentioned in their work that the C/Be/C X-ray waveguides were produced and tested successfully by Kovalenko and Chernov. 5 Here we present the results of a numerical simulation of a C/C/C planar X-ray waveguide. Two types of structures were under consideration. The first one has a density contrast of ∆ρ = 0.7 g/cm 3 and the other one has a density contrast ∆ρ = 0.2 g/cm 3 . For both types of waveguides, the substrate was chosen to be Si and the interface roughness was assumed to be σc = 0.2 nm. Core layer density was assumed to be the lowest achievable value, namely ρ = 0.2 g/cm 3 . Incident beam energy was fixed at 13 keV since at that energy the planar X-ray waveguides were used successfully for the microbeam formation. 1,2 The waveguide mode formation is characterized by resonant enhancement of XSW field intensity inside the structure. The degree of intensity enhancement depends on the waveguide parameters, particularly on the thickness of layers. Our purpose was to find out the thicknesses of the layers which would provide the high degree of XSW field intensity enhancement in the core layer. In this case one might expect the high intensity of the guided beam at the waveguide exit. To describe X-ray propagation through matter it is common to use a complex refractive index n = 1 -δiβ. Since both δ and β are of the order of 10 -6 , the XSW field intensity distribution calculated for s-polarized (electric field parallel to the interface) and for p-polarized (magnetic field parallel to the interface) incident beams is the same if the glancing angle is small (see, for example, de Boer). 6 Consequently, all calculations were performed for s-polarized incident beam only. A genetic algorithm (GA)-based procedure was used to find out the suitable thicknesses of the carbon layers. In principle, since the structure, which should be optimized, is known, the optimum waveguide parameters can be found in manual trialand-error search. The search can be rather fast since layer materials are fixed. In our case a computational program, which allows one to find out the thicknesses of waveguide layers within several minutes, was already developed. 7 This is the only reason why GA was applied for the particular problem. It 811 ANALYTICAL SCIENCES JULY 2005, VOL. 21 2005 A numerical simulation was done to check the possibility of using planar C/C/C multilayers with density contrast 0.2 and 0.7 g/cm 3 as an X-ray waveguide. After an optimization procedure, suitable waveguide layer thicknesses were found which provide a high degree of resonant standing wave field intensity enhancement in the core layer at incident beam energy of 13 keV. The obtained results were compared with those of the Mo/Be/Mo waveguide, whose high waveguiding capability at the same energy value was reported in the 1990s. The comparison shows that standing wave field intensity resonant enhancement provided by C/C/C planar multilayers is very high and, consequently, a guided beam can be well detected.