Reciprocal space mapping

We surreptitiously introduced reciprocal space in Figure 4.1, in an attempt to show its usefulness before giving the formal definitions. It is so very helpful in the interpretation of many diffraction experiments that we need to understand it more fully. We shall use it extensively in the discnssion of triple-axis experiments, in which reciprocal space mapping is an essential technique. 

The angular precision required is substantial. The most important factor is for the detector axis to track the specimen axis accurately and continnonsly, to better than an arc second for most semiconductor work, corresponding to a reciprocal space resolution of 5><10 A. Random errors in the tracking result in noise in reciprocal space, while systematic errors give rise to systematic distortions of the reciprocal space map. Artefacts due to backlash and eccentricity of gear trains are noticeable, and direct axis encoders are mnch preferred. Absolute... 

Figure 7.11(b) shows the reciprocal space map after a high temperature anneal of the film. The effect of this has been to precipitate ont the arsenic, resnlting in the lattice parameter of the now stochiometric matrix reverting to that of the substrate. The scattering around the layer peak, which arises from the precipitates, is circnlarly symmetric and mnch more extensive than in the substrate. 

The method used by the group was first to determine the direction of substrate tilt by means of reciprocal space maps in each of the <110> directions contained in the plane of the wafer. These are shown in Figure 7.14. A narrow slit was used instead of an analyser ciystal, so some analyser streaks are seen near the substrate peaks (on the right of each map— the origin in this case is on the left-hand sides). It is seen that in (a) and (b) the beam is oriented perpendicular to the substrate tilt axis, as these maps show only strain. In (c) and (d) the effect of the grading can be seen, since both the tilt and the strain are changing, but these views are insufficient to make a complete analysis. For this we need an... 

Figure 7.10 (a) Double-axis rocking curve of a microgravity-grown GaAs crystal after heater failure, (b) Equivalent triple-axis reciprocal space map CuK 004... 

Figure 7.11 Reciprocal space map around 004 for a low temperature grown GaAs epilayer on GaAs. (a) As grown, (b) After high temperature anneal...

In this chapter we have seen the new dimension that triple-axis diffractometry and reciprocal space mapping bring to the characterisation of complex materials. 

Figure 7.12 Reciprocal space map of the GaN sample shown in Figure 7.7...

Figure 7.13 Reciprocal space map of a HEMT structure which contains an approximately 10 nm thick InGaAs quantum well and is capped by a thick GaAs layer. The substrate is (OOl)GaAs...

Figure 7.14 Reciprocal space maps of GaAs with graded InGaAs buffer layer around the 004 point with different directions of the incident beam, (a) Along [110], (b) along [ 0] (c) along [ 10],(d) along [1 0] In this and the next figure the orientation is such that the origin is on the left (not the bottom) of the maps, hence the horizontal direction represents strain and the vertical direction, tilt...

The picture shows an X-ray diffraction reciprocal space mapping (XRD-RSM) measurement at the 204 diffraction of a PZT 52/48 thin film on a SRO-STO substrate. A tetragonal phase with 90° domains as well as a pseudocubic phase induced by the strain of the substrate are observed. 

Structural characterization of processed Si N was performed by cross-sectional transmission and high resolution electron microscopy techniques (XTEM and HRTEM, respectively). The structure of Si N samples was also investigated by X-ray diffractometry (XRD). The X-ray rocking curves, 20/co scans as well as X-ray reciprocal space maps (RSM) were registrated. 

More recently, measurements have been developed based on the complete evaluation of the intensity distribution over the entire diffraction spot. This reciprocal space mapping [FEW 97] can be used to give an account of all the microstractural effects that have an influence on the diffraction signal. Thus, it is possible to obtain the distribution functions of orientation, size, morphology and the size distribution of the diffracting domains, as well as the microstrains. 

We will first describe the methods for accurately determining the orientation of the crystals and then, in a second step, we will ejq)lain in detail how reciprocal space mapping can be used to quantitatively analyze the microstracture of epitaxial films. 

This shows that decomposition of the diffracted intensity s two-dimensional distribution should enable us to determine the microstractural characteristics of the film. It is initially necessary to measure these intensity distributions, which is something referred to as reciprocal space mapping. 

BOU 03] BOULLE A., CANALE L., GUINEBRETIERE R GIRAULT-DIBIN C., DAUGER A., Defect structure of pulsed laser deposited LiNbOj/ALOs layers determined by XRD reciprocal space mapping Thin Sol. Films, vol. 429, p. 55-62,2003. 

BOU 06] BOULLE A., CONCHON F., GUINEBRETIERE R., Reciprocal space mapping of epitaxic thin films with crystallite size and shape polydispersity , Aeta. Cryst A., vol. 62, p. 11-20,2006. 

GOL 04] GOLSHAN M. LAUNDY D, FEWSTER, P.F., MOORE M, Three dimensional reciprocal space mapping application to polycrystalline CVD diamond , in MITTEMEIJER E.J., SCARDI P. (eds.). Diffraction analysis of the microstructure of materials, Springer Series in Materials Science, vol. 68, p 527-539,2004. 

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