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

The measurements of the crystals were done in several

Info icon This preview shows pages 182–185. Sign up to view the full content.

The measurements of the crystals were done in several laboratories [156– 158]. According to Vegard’s law ((3.93) and Fig. 3.47) the lattice parameter
Image of page 182

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

162 A. Erko increases linearly with Ge concentration. At a rough estimate, this is a suitable approach. However, measurements on the lattice parameter revealed devia- tions from Vegard’s law. For the measurements of the absolute lattice parame- ter variation was used, the Bond method in combination with two-dimensional scanning X-ray diffractometry [159]. Measurements of the lattice parameter done on the test samples with the known Ge concentration are shown in Fig. 3.50a. A similar result was published in [160]. One can see very clearly a difference between the linear dependence (Vegard’s law) and experimental value. The dependence of the coefficient J (3.93) from the Ge concentration can be derived by the empirical formula J 3 . 67 · 10 4 + 1 · 10 6 C (3.103) and is shown in Fig. 3.50b. Here C is the Ge concentration in at.%. A scanning double-crystal X-ray diffractometer was used at BESSY for two-dimensional local lattice parameter measurements. The beam size in diffraction plane was about 100 µ m. The sample holder can be translated automatically parallel and perpendicular to the incident beam in the range of ± 50 mm in horizontal and ± 10 mm in vertical-direction with a linear repro- ducibility of 10 µ m. Using this diffractometer it was possible to measure the Bragg angle variation at different points on the sample. The Ge-concentration was derived from the experimental diffraction data for the Si 1 x Ge x -samples with (111) and (220) reflecting planes orientations. Furthermore, the width of 0.5430 0.5435 0.5440 0.5445 0.5450 0.5455 (a) (b) Measured Vegard's Lattice parameter (nm) Ge (at.%) 0 3.5 3.6 3.7 3.8 3.9 4.0 4.1 4.2 4.3 Measured Vegard's J (1/at.%) x 10 - 4 Ge (at.%) 2 4 6 8 10 0 2 4 6 8 10 Fig. 3.50. The measured SiGe lattice parameter variation vs. Ge concentration ( a ) and measured value of the J coefficient in comparison with Vegard’s linear dependence ( b )
Image of page 183
X-Ray Optics 163 the peak permits some conclusions about the quality of the sample-crystal in comparison to Si-reference crystals. In addition, the absolute reflectance of the specimen can be measured, providing further information about the quality and the homogeneity of the crystal. In Fig. 3.51a a two-dimension scan of the Si 1 x Ge x sample is shown. The grey scale variation in this figure corresponds to a different value of the lattice parameter in the sample. From only one experiment we obtained information simultaneously about the Ge distribution and the sample curvature. The same procedure was used for the calculations of Si (111) and Si (333) reflections. Figure 3.51b shows a comparison of an infrared spectroscopy method [161] and diffraction measure- ments of a sample with < 111 > surface orientation for the horizontal dash line shown in Fig. 3.51a.
Image of page 184

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

Image of page 185
This is the end of the preview. Sign up to access the rest of the document.
  • Spring '14
  • MichaelDudley

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern