Incident angle diffraction

Fig.3 Diffracted signal amplitude at various incident angles for different EMAT distances...

Illuminating the sample at grazing angles. The penetration depth of photons depends on the cosine of the incidence angle and, therefore, can be reduced by this procedure. Although such an approach has limited use, it has been successfully employed in a few instances, such as for x-ray diffraction experiments. 

This section briefly discusses the fundamental principles of XRD the reader is referred to the works by Warren, Cullity, and Schwartz and Cohen for more detail. " Figure 1 shows the basic features of an XRD experiment, where the diffraction angle 20 is the angle between the incident and diffracted X rays. In a typical... 

For ultrathin epitaxial films (less than "100 A), Grazingincidence X-ray Diffraction (GrXD) is the preferred method and has been used to characterize monolayer films. Here the incidence angle is small ("0.5°) and the X rays penetrate only "100-200 A into the specimen (see below). The exit angle of the diffracted X rays is also small and structural information is obtained about (hkl) planes perpendicular to the specimen sur e. Thus, GIXD complements those methods where structural information is obtained about planes parallel to the surface (e.g., Bra -Brentano and DCD). 

Grazing incidence angle X-ray diffraction pattern for InSe... 

Fig. 39. Grazing incidence angle x-ray diffraction (XRD) pattern of an InAslO/InSblO-41x superlattice.

XRD Characterization The powder x-ray diffraction of the mechano-chemically milled complex borohydride has been carried out by the Philips X pert diffractometer with Cu-Koi radiation of X= 5.4060 A. The incident and diffraction slit width used for the measurements are 1° and 2° respectively. The sample holder was covered with Polyethylene tape (foil) with an O-ring seal in an N2 filled glove box in order to avoid or at least minimize the 02/moisture pickup during the XRD measurements. The diffraction from the tape was calibrated without the actual sample and found to be occurring at 29 angles of 22° and 24°, respectively. The XRD phase identification and particle size calculation has been carried out using PANalytical X pert Highscore software, version l.Of. 

The llrst experimental evidence for a uniaxial soliton reconstruction of the Au(l 11) surface was obtained in 1977 by Miller and Home unfortunately, they missed the significance of the data. They scattered He beams with energies of 11-63 meV from Au(l 11) surfaces. Figure 35 shows a polar He diffraction scan with a beam energy of 11 meV, at a hxed incident angle dj = 80° obtained... 

Figure 1.1 Diffraction of a plane wave off successive crystal planes. Strong diffraction results when the angles of incidence and diffraction,, are equal and the path difference AOB between the two beams is equal to , an integral number of wavelengths. Hence the Bragg law, n =2rfsin...

Figure 1.3 The addition of waves scattered by an angle 2 from an atom at the origin and one at a vector r from the origin. The wavevectors k q and k jj are in the directions of the incident and diffracted beams, respectively, and k o = k h =l/...

In reflection, the intensity of the X-ray wavefield inside the crystal falls off very rapidly away from the surface, due to transfer of energy to the diffracted beam. Absorption also becomes important at low incident angles to the surface. By choosing the radiation and the reflection (inclnding its symmetry), the penetration may be varied between about 0.05 and 10 micrometres. This is ideally matched to device stmctures. This is quantified by the extinction distance g, defined as the depth at which the incident intensity has decreased to 1/e of its value at the surface. This may be calculated from diffraction theory, and some examples, for GaAs with CuK radiation, are shown in Table 3.2. It is assumed that the wafer surface is (001), hence the 004 reflection is symmetric and the others asymmetric. 

However, at grazing incidence angles near the critical angle the reflected beam becomes important, and eventually becomes dominant. This is an important effect and the two-beam case is seriously in error for angles of incidence close to the critical angle. Fortunately, the reflected beam decreases in intensity as the fourth power of the scattering angle, and is weak compared with the diffracted... 

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