[B._Beckhoff,_et_al.]_Handbook_of_Practical_X-Ray_(b-ok.org).pdf

All results obtained with graded samples were

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All results obtained with graded samples were compared with reference sil- icon single-crystal diffraction curves at the same experimental conditions. For the rocking curve measurements Si 1 x Ge x samples with uniform Ge surface concentrations of 1.5–7 at.% were examined. The surface orientation of those crystals was < 110 > . The rocking curve width of a Si 1 x Ge x crystal with a different Ge concentration is identical to a pure Si crystal. Both crystals show full width of half maximum (FWHM) of 4.5 arcsec, which is only slightly above the theoretical predicted width of 4.2 arcsec for this configuration for a perfect crystal. The intensity of the beam reflected by the sample was normalized to the flux from the crystal monochromator. The measurements were performed at a fixed Bragg angle and with variable beam energies [162]. Energy scans were made by the double-crystal monochro- mator with two perfect Si (111) crystals. The energy spectra with a small beam divergence ( 1 arcsec in both directions) and large divergence ( > 50 arcsec in horizontal and 1 arcsec vertical directions) were compared. We also compared the energy resolution from a reference Si (220) crystal. The experimental results are shown in Fig. 3.52a,b. One can see the sim- ilar energy resolution of the Si 1 x Ge x and Si crystals for a beam with the divergence less than intrinsic rocking curve width. In case of high-beam diver- gence the energy resolution is very different. For the graded crystal angular 0 5 10 15 20 25 0 5 10 15 20 Rocking Curve Shift (arcsec) Ge gradient X (mm) Y (mm) - 19.0 -- 0 - 38.0 -- - 19.0 - 57.0 -- - 38.0 - 76.0 -- - 57.0 - 95.0 -- - 76.0 0 5 10 15 20 25 30 2,5 3,0 3,5 4,0 4,5 Si Ge (111) Diffraction measurements IR measurements Ge concentration (at. %) Position on crystal (mm) (a) (b) Fig. 3.51. The two-dimensional scanning diffractogram of the SiGe crystal ( a ) and the Ge concentration along the X -axis ( b ) measured with two different methods
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164 A. Erko 8260 8265 8270 0 1 2 3 4 5 6 7 8 Data: Si 220, 1" FWHM 1.1eV Data: SiGe1" FWHM 1.2eV Si SiGe (a) Flux (Rel. units) Energy (eV) 8260 8265 8270 0 2 4 6 8 10 12 14 16 18 Data: Si 220, 40" FWHM 4.1eV Data: SiGe 40" FWHM 1.2eV Data: SiGe 59" FWHM 1.2eV Si, div. 40" SiGe, div. 40" SiGe, div. 59" (b) Flux (Rel. units) Energy (eV) Fig. 3.52. Energy spectrum from the SiGe and Si (220) crystals, reflected in hori- zontal plane. ( a ) Beam divergence 1 arcsec, ( b ) beam divergence 40–59 arcsec divergence is compensated by the lattice parameter variation along the crystal surface. Energy resolution of the graded crystal is the same, as for Si reference crystal in a parallel beam. Beam Collimation and Focusing by a Graded Crystal It was found experimentally that the Ge concentration gradient is always followed by the lattice plane bending. Depending on the cut orientation, the average Ge concentration and the value of the Ge gradient one can choose optimal crystal parameters: gradient and crystal plane curvature for a partic- ular beamline geometry.
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