Asymmetric reflections

When reflection geometries are set up in modern scattering applications to study the structure of thin layers, the simplifying assumption of infinite sample thickness is not allowed, and the absorption correction becomes more difficult. Moreover, symmetrical-reflection geometry is utilized less frequently than asymmetrical-reflection geometry with fixed incident angle. Thus both cases are of practical interest. 

For very thin sample thickness t and a scattering angle 29 that is well above the critical angle of total reflection, the exponential factor is approximately unity and a simple background subtraction without consideration of absorption is allowed. Symmetrical-reflection geometry is only a special case of asymmetrical-reflection geometry. 

For asymmetrical-reflection geometry the absorption factor is changed as well, as the primary beam is illuminating the complete sample surface. In this case... 

For asymmetrical-reflection geometry the relation is more complicated. Considering the geometry sketched in Fig. 7.5, the true tilt angle is... 

For symmetric reflections the peak search may now begin. For asymmetric reflections, the specimen must be rotated about its normal until the desired diffraction vector lies in the incidence plane of the beam conditioner. This is normally the diffractometer surface. An accurate knowledge of the orientation of the specimen in two axes is required to set asymmetric reflections this is usually taken from the position of the orientation flat or groove. 

Different effect on symmetrical and asymmetrical reflections Integrated intensity increases with layer thickness, up to a limit... 

Interface dislocations give a specified relaxation of strain between the substrate and the epilayer, which gives quantifiable shifts in the positions of peaks in asymmetric reflections as discussed later in this chapter. As stractures become more complex it is difficult to know which effects may be ascribed to interface relaxation and which to the layer stracture itself It is therefore often... 

Figure 4.20 The dependence of the range of strong diffraction on the diameter of the dispersion surface, (a) Symmetric reflection, (b) Asymmetric reflection...

Subject to the caveat that there can be a significant shift in peak position when the total layer thickness is sub-micrometre we can determine the average composition of the MQW using the zeroth order, or average mismatch, peak. Asymmetric reflections are often used, both to determine any relaxation and to enhance the diffraction from thin layers. Let the period of the superlattice in real space be A, and the thickness of layers of A B i of composition x i and x 2 be D 1 and D 2 respectively. Then... 

Figure 9.2 (a) Simple (+n, -n) double-crystal topography arrangement in the parallel setting, (b) Use of asymmetric reflection to expand illuminated area and eliminate image doubling, (c) Double-crystal topography with a standard duMond-Hart monochromator system... 

In general, unlike for the perfect epitaxial structures of fully strained materials, for nitride heteroepitaxial layers it is essential to perform not a single scan for a symmetrical reflection, but a set of two- or even three-dimensional maps of symmetrical and asymmetrical reflections. Additionally, for some applications, an intense beam is needed and therefore low-resolution X-ray diffractometry can be sometimes a preferable technique to the commonly used high-resolution XRD. For example, if we examine a heterostructural nitride superlattice, low resolution diffractometry will give us a broader zeroth-order peak (information on the whole layer) but more satellite peaks (information on the sublayers). Therefore, multipurpose diffractometers with variable configurations are the most desirable in nitride research. 

More comprehensive studies should include other reflections and rotations around psi- (for symmetrical reflections) and phi- (for asymmetrical reflections) axes. The psi rotation is around the in-plane axis which is in the diffraction plane. The phi rotation is around the normal to the sample surface. Both psi and phi scans supply important information on the sample mosaicity, but should be corrected with respect to the instrumental function, as most diffractometers possess X-ray beams which are highly divergent in the direction perpendicular to the diffraction plane. 

The lattice mismatch of the nitrides to 6H-SiC is about 13.5%, 3.5% and 1% for InN, GaN and AIN, respectively. This mismatch is a main factor influencing the FWHM of the X-ray RC. Reference [12] reports on the change of FWHM for MOCVD AlxGai xN layers on SiC versus Al-content. For 0.2 - 2 pm thick layers (all almost fully relaxed), the 00.2 FWHM changed from about 300 arc sec for GaN down to about 30 arc sec for AIN simultaneously, for the 10.5 asymmetrical reflection, the FWHM decreased from about 220 arc sec down to about 50 arc sec. 

According to [18,19] and our experience, it is usual that the smaller FWHM for symmetrical reflections (measuring mostly tilt mosaicity) corresponds to a larger FWHM for asymmetrical reflections (measuring together twist and tilt mosaicity). For example, for the MOCVD GaN layer which possessed a 00.2 RC of only 40 arc sec, the 10.2 reflection exhibited an FWHM of 740 arc sec [18], Similarly, for a 0.76 pm MBE layer, Amano et al [19] reported 48 arc sec for the 00.2 reflection and 5226 arc sec for the 10.0 reflection (grazing incidence geometry). The other sample (1.7 pm) possessed 365 arc sec and 1581 arc sec, respectively, for those two reflections. 

In summary, rocking curve analysis is a rapid, non-destructive X-ray technique for evaluating the mosaicity of the samples. For GaN technology makers, the following goal FWHMs can be proposed. 10 - 20 arc sec for bulk crystals, 30 - 50 arc sec for layers on SiC and 150 - 200 arc sec for layers on sapphire, for both symmetrical and asymmetrical reflections. 

Error in the determination of the position of a simulated, asymmetrical reflection (without noise) at 29 = 20° and with 0.17° half width (W). Top With minimum of 2nd derivative calculated with a polynomial of 2nd/3rd order. Middle With zero of the 1st derivative calculated with a polynomial of 3rd/4th. order (best result as long as the filter width does not appreciably surpass the half width) Bottom With zero of 1st derivative with a polynomial of lst/2nd order. (After Huang, 1988, or Huang and Parrish, 1984. )... 

Figure 4.13 For asymmetrical reflections the peak position depends on its definition.

For not too asymmetrical reflections this one-parameter correction is sufficient and as good as the two-parameter correction of SP7. The amount added and the wide slope is subtracted on the narrow side, i.e. the integral intensity itself remains unchanged. The corrected curve remains positive, as long as Pkl < 1- Up to Pkl = 2, however, a slight sag of the narrow flank into negative values is tolerable. 

As shown in Fig. 1, the combination of good AR coating and small microcavity effect apparently lead to a contradiction of the anode s role it must have simultaneously a low external reflectance when seen from the substrate and a relatively large internal reflectance when seen from the cavity layers. It has been observed for a long time in thin-fUm optics that a thin layer of a material with a large extinction coefficient k can lead to the kind of asymmetric reflectance (Goos, 1937). In our design, such a layer has thus to be introduced on the anode side of the OLED structure. 

Optical consideration, electrode with asymmetric reflection... 

Clearly, the exponential term differentiates r and /. It can be shown from Eq. 5 that a large k value is essential to increase the asymmetry in reflectance, with a sufficiently large thickness d a large n value will also increase the asymmetry, but is not essential. In the case of the anode (as in many other cases involving asymmetric reflectance), a reduction of the hght absorption in the layer is important. The irradiance absorbed by a layer is given by the following relation (Macleod, 2001) ... 

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