Rocking curve width

One problem with methods that produce polycrystalline or nanocrystalline material is that it is not feasible to characterize electrically dopants in such materials by the traditional four-point-probe contacts needed for Hall measurements. Other characterization methods such as optical absorption, photoluminescence (PL), Raman, X-ray and electron diffraction, X-ray rocking-curve widths to assess crystalline quality, secondary ion mass spectrometry (SIMS), scanning or transmission electron microscopy (SEM and TEM), cathodolumi-nescence (CL), and wet-chemical etching provide valuable information, but do not directly yield carrier concentrations. 

Rocking curve width degree [Pg.7]

Reflection Bragg angle (degrees) Rocking curve width (arc Extinction distance (/im)... 

Formulae for rocking curve widths, profiles and intensities... 

The Laue case rocking curve width in the limit of a thick crystal and zero absorption is... 

Figure 6.1 Double-axis rocking curve of CdTe on GaAs showing the broadening due to the very high dislocation density in the layer. (Courtesy R.l.Port, Durham University.) The rocking curve width in such thick, high mismatched layers falls with increasing layer...

Figure 7.1 Double-axis rocking curves from a GaN epitaxial layer on (111) orientation GaAs. The measured rocking curve width is determined by the detector aperture...

Figure 7.6 Wafer maps of the triple-axis rocking curve width (specimen-only scan) for GaAs grown by different processes, (a) A LEG GaAs wafer and (b) a VGZ GaAs wafer...

The large rocking curve width associated with the extended source makes it easy to set up the Berg-Barrett topograph. This can be done with a counter but is most easily achieved with a phosphor screen and TV camera. The strength of the beams is such that only modest gain is needed and the equipment can therefore... 

An important featnre to note in double-axis topography experiments is that when the beam area is large, the measnred rocking curve widths are not necessarily intrinsic. For example, mismatched epitaxial layers curve substrate wafers by an amonnt which depends on the degree of mismatch and layer thickness. Topographs of snch curved wafers show bands of diffracted intensity. 

This instrument was much used in the early days of x-ray diffraction to compare the width and height of the rocking curve for a real crystal with the values predicted by theory for a perfect crystal [G.30]. This theory predicted a width of the order of 10 seconds (0.003°) for typical experimental conditions, and some crystals were found with rocking-curve widths approaching this value. However, most crystals exhibit widths 10 to 100 times greater. 

Figure 10. (A) The resolution of an arbitrary scattering condition, shown as a function of the detector slit size, (2 ). (B) and (C) A rocking scan is measured by scanning resolution function across a specular CTR (B) The surface rod is broader than the transverse resolution, AQt so that the rocking curve width is determined by the intrinsic width of the CTR. (C) The surface rod shape is more narrow than the transverse resolution, Qt, and the shape of the measured rocking curve is resolution limited (i.e., determined by the sht size instead of the intrinsic Une width).

A Lorentzian-like line shape indicates random defect distribution across the surface. The oscillation of the rocking curve width as a function of Lri is a direct result of constructive and destructive interference conditions that are alternately satisfied as the momentum transfer perpendicular to the surface, Qz, increases. The vertical extent of the defects, h, is revealed through the relation h = 27dbQz = Chid/5L where 8Q is the characteristic period of the oscillations. The periods of oscillations in Figures 26C and 26D are 80 = 2 / for both surfaces, implying that for each surface the predominant defects correspond to unit-cell-high steps, with h = 7.2 A and 3.4 A on the (001) and... 

To provide a more quantitative description of the surface defect structure and distribution, we use a model for randomly distributed surface defects (Lu and Lagally 1982). With this model, the rocking curve width and its variation with Q can be calculated from a few parameters that describe the probability of encountering a defect (i.e., a step) and the phase change in encountering that defect. (For specular reflectivity, this phase change reflects the height difference across the step.) Within this model, an approximately Lorentzian line shape is reproduced. 

These results show that X-ray reflectivity can be a powerful probe of the defect structure at the mineral-water interface, including the defect size and distribution. In this case, the result relied primarily on variation of the rocking curve width as a function of Qz. The rocking curve shape generally provides additional information concerning the correlations between steps (Robinson and Tweet 1992). 

The structural quality of the m-plane GaN LEO films was additionally characterized by X-ray diffraction. As can be seen in Figure 2.17a, m-plane GaN LEO films grown from 1120>-oriented stripes typically had narrower on-axis reflections compared with non-LEO films, on the order of 1200 arcsec at plane anisotropy of the crystalline mosaic. For comparison, the on-axis FWHM of the MBE GaN templates were typically 1100 arcsec at < = 0° and 7000 arcsec at < = 90°. No splitting of the 1100 reflections was observed when the scattering plane normal was parallel to the LEO stripe direction for either stripe orientation. Thus, no wing tilt was observed within the sensitivity of these X-ray measurements, which was limited by the mosaic... 

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