In order to use XRD to measure the epi film thickness precisely, several conditions must be met including and not limited to:
1. The sample must be assumed optically flat which is invariably the case for the samples used in electronic applications.
2. The incident beam wave length dispersion is independent of the location on the 2D incident beam and invariant during the experiment. A reasonable expectation.
3. The incident beam is "reasonably well monochromated, collimated and invariant", reasonable source stability. "Perfection" is unnecessary. http://www.flickr.com/photos/85210325@N04/9531061382/in/set-72157635534175171
4. An Omega-2Theta coupled scan is required with the substrate and epi reflection included in the rocking curve profile acquired for analyses. This allows the ability to normalize the XRD relative intensities across the 2D pixels laterally on the topograph. http://www.flickr.com/photos/85210325@N04/10653618416/
5. Sufficient data to precisely identify the BG (back-ground) signal must be acquired. This is the key for precise "Integrated Intensity" measurements for quantification of epitaxial film thickness (related to the diffracting volume) laterally across the "XRD Topograph".
Our sample was a SL (super lattice) epitaxial film 0.5um thick with 25nm layer 10 periods of InAsSb/InAs on (001) GaSb substrate (http://www.flickr.com/photos/85210325@N04/10647827636/). A Panalytical MRD [Ge (220) Bartel Hybrid + Soller Slits] type diffractometer was used with a Bragg XRD Microscope made by Onsight Technology USA. The data was acquired at the Air Force Research Lab @ WPAFB, OH.
Well you would make a GIXRR (grazing Incident X-Ray Reflectivity) measurement in order to measure your superlattice periods. It is substantially a diffraction, but in particular due to the interfaces. Moreover if your materials have too similar cross sections (X-Rays absorbance) than the best would be to use synchrotron source in order to use a resonant condition, in which you 'tune' to one of the materials used in your superlattice (for example I think it would be a line of Sb) so to enhance the contrast at interface. After that you fit your measurements with the parratt model (which is, in the end, bragg diffraction by the interfaces).
Hope to be of any help
REMINDER! Panalytical Seminar TODAY Dec 10th 10AM EST on "XRR".
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Topic: X-Ray Reflectivity and Thin film Research
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We determined the thickness of a triglyceride nanoplatelet (in the 001 plane direction) by merely using a Scherrer analysis of the 001 reflection. From the FWHM, we determined a crystalline domain size in the appropriate direction, corresponding to the epitaxial growth of our system. We confirmed the dimensions using cryo-TEM and the were spot on. Maybe we were lucky that our nanoplatelet thicknesses were in the range 30nm, but this gave us the exact extent of epitaxial growth of our nanocrystals.
Alejandro! Please feel free to post some of your data or publication relevant to the subject and discussion when convenient.
Luck follows those that strive and leverage information properly. Scherrer analysis involves considerable amount of modeling and assumptions about the sample Nano structure in order to match that well with TEM or STEM analyses. In general, the match is at best dubious since the parameters measureable are not necessarily identical. However, it is perhaps your accurate assumptions that have lead you in the right direction. My understanding of the details of the Scherrer methodology is sparse. Please feel free to expound & embellish.
The data displayed is that from a mono-crystalline materials system with tilts less than fractions of Arc Sec Pixel-to-Pixel. We've used the XRD Rocking Curve Technique which essentially deconvolutes most instrumental aberrations while isolating (deconvoluting) the strain effect (both components, "plastic"-Bragg Peak FWHM & "elastic"-Bragg Peak Shift) for individual 76um Pixel in a 25mm diameter field of view. The Incident beam was monochromated and collimated with a Hybrid Bartel Ge (220) + Soller Slit. Incident beam size was roughly 2mm(H) X 20mm(V).
interesting post, Ravi... we did ourselves some work on XRD characterization of very thin layers of InAs in QD structures, but we had to rely to simulation of diffraction patterns to determine composition and thickness. See these papers:
1 L. Seravalli, G. Trevisi, P. Frigeri, F. Rossi, E. Buffagni, and C. FERRARI, J. Phys. D Appl. Phys. 46, 315101 (2013).
1 L. Seravalli, C. Bocchi, G. Trevisi, and P. Frigeri, J. Appl. Phys. 108, 114313 (2010).
I recommend reading the explanation given by F. D. Bloss [Crystallography and Crystal Chemistry, pages 335-338 (1971) Holt, Rinchart & Winston] on "oriented growth between unlike crystals".
In summary it is stated these explanations:
"In solid-state reactions in which a substance remains solid while undergoing a chemical or structural change, Bernal and McKay (1965, p. 331) distinguish 3 types of reactions in which the crystallographic orientation of the reactions products may be inherited or controlled by that of a pre-existing crystal reactant. These are (1) polymorphic transformations, which involve no compositional changes; (2) solid-state reactions, which involve compositional changes and where reagents or products may enter or leave the system; and (3) epitaxial growths...
Epitaxy signifies the oriented overgrowth of a crystal A upon the surface of a second phase upon which growth occurs being sometimes called the substrate. Crystals A and B are not necessarily related chemically (for example, the epitaxy of vitamin B12 on quartz), but their lattice dimensions along their common plane must be fairly close....
As originally defined by Ungemach, syntaxy signifies an oriented intergrowth of two polymorphs of a given substance...................Gabrielle and J.D.H. Donnay recommend that this definition be extended to include intergrowths between chemically unlike crystals.
The term topotaxy is used to indicate that the product crystals of a reaction have inherited their orientations from the reagent crystals. Structural features of the reagent crystals, frequently the packing of the bulkiest atoms or ions, survive relatively unchanged in the product crystals and control their crystallographic orientation........Occasionally the geometrical and symmetry conditions of topotactic reactions are sufficiently powerful to permit formation of phases not normally stable.
The distinction of epitaxy from topotaxy is clear-cut if the substract remains inert as the epitaxial overgrowths crystalline on it. However, if the overgrowth crystals form by decomposition or reaction of a substrate that imparts the initial orientation to these overgrowths but subsequently disappears (completely or in part), it may be difficult to decide whether the reaction was epitaxial or topotactic. According Bernal & Nackay (1965), it should designated as an epitaxial reaction if the initial and final products do not resemble each other in structure and only fit each other in 2-D (although fully oriented). Whereas, if the reagent substrate and the overgrowth crystals show a 3-D accord, then the reaction can be called topotractic or surface topotactic"
https://www.researchgate.net/post/How_do_I_figure_out_the_spatial_thickness_of_the_individual_layers_from_these_not_so_well_resolved_diffractograms
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