One suggestion was "stacking fault"? That shouldn't reduce the relative intensity of GaN (1st peak from the left of RCP) peak to below that of the AlN (1st peak from right of RCP) buffer layer. There is no observed "shift" or perceivable "broadening" from a cursory glance. Only the peak intensity and hence the integrated intensity only for the GaN peak.

Image shown includes normalized data w.r.t. the AlN peak and data from 2 different literature sources.

you observe a relative reduction of intensity. From the classical point of view this is possible if the "effective" structure changes. One simple idea could be stacking faults but I have to agree: the common effect of stacking faults is a peak broadening...except the stacking faults are that systematic over a longer range that one can discuss them as other phase... However, I do not see a real reason why a systematic change should vary the intensity of 111 compared to 0002 that much (and the distance possibly also changes so that the peak would shift as well). Is there any (strange) interference with the substrate or the buffer layer thinkable? What would happen with 0002 if you would replace Ga by Al? The difference between Al and N is smaller...like for GaAs, where the 200 de-facto also disappears...

It may be related to the thickness variation and consequently the modification on the strain. Thermal gradient may affect the structure. Check the thickness by XRR across the radius.

XRR, especially with the conventional 0D methodology, is generally a "gross" thickness measurement technique along the equatorial plane. The examination depth is limited to only the top 250-350nm in the case of XRR (so I learn). At those shallow incidence angles most incident beams would flood the entire specimen surface and the orientation of the specimen will not matter. I do have some 2D XRR data for this sample and will re-examine it. Never-the-less, each 2D pixel (placed perpendicular to the diffracted beam) is distorted (on the sample surface) along the equatorial plane due to the shallow angle measurement. I'd still need two orthogonal measurements to verify, which I don't yet. https://www.youtube.com/watch?v=yB5FXYAW_L8&list=PLmpho52CoOEhPCGeTMxn2S05foGIE3clL

You may get an estimate of the distortion of the sampling voxel on the specimen surface by examining the above displayed relationship between incidence angle and the magnification factor. Watch this video example to get a clearer visualization as to exactly how the specimen surface "sees" the "line source" incident beam in 2D at various angles of incidences in the vicinity of the XRR measurement range.

https://www.youtube.com/watch?v=GV-EYO-IeJI&list=PL7032E2DAF1F3941F&index=3

"the common effect of stacking faults is a peak broadening"

Is it possible to tell from these Bragg profiles (RCPs, rocking curve profiles) for a LiF specimen as to which part of the distortion to the RCP is due to "stacking fault"?

https://www.researchgate.net/post/What_is_the_likely_Nanostructural_origin_for_observations_of_the_LiF_113-XRD_reflection_rocking_curve_integrated_breadth_squared_b2_map?

GaN (0002)s data at selected topographic locations, normalized w.r.t AlN peak intensity then contrasted with literature data for similar specimen:

Thanks to Dirk Luetzenkirchen-Hecht for this link!

X-Ray Attenuation Length: http://henke.lbl.gov/optical_constants/atten2.html

GaN - 9.58481um

AlN - 17.4403um

AlGaN - 27.6432um

Si -21.2367um

Well above the typical combined layer thickness (1-2um) of all layers @ 8 keV.

I was able to use Origin Pro in order to do some curve fitting to extract peak parameters including peak positions, peak heights, peak widths and peak integrated intensities from the diffraction profiles (RCPs) at each spatial pixel.

If I was to translate (raster) various topographic locations to the same detector pixel, while maintaining all other experimental conditions the same, then I should be able to directly compare the Bragg profiles to estimate contributing diffracting volumes and hence thicknesses of individual layers. This was not done for the current data set. Will do so February 2018.

This method is very different from XRR "gross" measurements for estimating individual layer thickness and other parameters locally at each spatial voxel on the "flat" sample surface. I would think that with a sensitive detector and/or large data integration times, it would be possible to even quantify "mono layers" of Graphene perhaps. Yes?

Here is the latest compendium of analyses! Getting closer!

COD - Coefficient of Determination! Learning a lot now with statistics :-)

Image above shows the parameters derived using Origin with a 5 Gaussian model yielding:

The ordinate axis in above images is in "mm" displacement on the specimen surface.

Preferred COD value is as close to 1 as possible. The maximum value for this parameter is 1. Our values range from 0.3 to 0.99. Due to an abundance of data, 750x200 pixels (150,000 RCPs, rocking curve profiles), we restricted "meaningful" data to those with COD values above 0.8. However, the signal level in areas with lower than 0.8 COD is worth examining further as well to harness Nano structural parameters.

Once we are able to record the incident beam foot-print for the entire rocking curve (incident angles), we will then be able to potentially deconvolute the effect of the incident beam spatial charecteristics from the diffracted images. Thus, allowing us to image individual layer Nano structural characteristics without the need to translate (raster) the specimen surface through a fixed pixel or ROI, region of interest (contiguous pixels).

A problem for analysis via rocking curves is that all layer are slightly differently relaxed. This is reflected in their 2Theta values, but does not affect their omega position.

The best way is to analysis such a sample is probably to get the AlN content from a quick asymmetric (20.5) rsm (open detector in less than an hour is fine), which gives the Al content almost independent from strain from the 2Theta positions in the rsm, see: Article Measuring the composition of AlGaN layers in GaN based struc...

For (0002) you measure an omega-2Theta scan (best with an analyser crystal), and then fit this with the Al content from the 20.5 space map. Typically the AlN is not fully relaxed and even the GaN has about 5% strain (of course these number depend on your structure and device). Also the peaks are often assymetrical, which may origin from varying strain along the thickness.

Since strain and ist relaxation is the biggest problem for the growth of GaN on Si, I would rather chose another than 0002 for that analysis from a single space map.

The essential question is still, whether we can use the integrated intensity of individual peaks (0002) or (205) to quantify the diffracting volume contributing to that reflection? Thickness estimation? By using other reflections these thickness measurements may be confirmed as well.

M. Pristovsek! Thanx for opening this doorway for us. I'll study this in great detail. Nice article. I see this publication even uses pseudo color to show 3rd dimension. "Semicond. Sci. Technol." Rocks!

Measuring the composition of AlGaN layers in GaN based structures grownon 150 mm Si substrates using (2 0 5) reciprocal space maps, D J Wallis, D Zhu, F Oehler, S P Westwater, A Pujoland, C J Humphreys.

"Typical collection times for the reciprocal space maps shown were about 10 h compared to more than 40 h with a conventional triple crystal geometry. If lower quality data can be tolerated, collection times as low as 2 h have been demonstrated for the (2 0 5) reciprocalspace maps reported, making the technique compatible with a production environment." Really?

Some day soon we will be able to display RSM for individual pixel on the 2D topographic data in real time. Any thoughts to share?

Happy Holidays & Happy New Year!

For my analysis I used w-2T/w rsms or so (I have to look in the lab) so that exactly the mostly relaxed AlN and the mostly strained GaN peak are seen. The shortest optimised setting used 0.2 degree steps or so, with 50-100 ms integration time, which took 20 min plus 5 minutes for finding peaks etc. That is enough to see the 2T maximum position, omega was ignored mostly and had 0.5/1 degree steps. The degree of relaxation is easier fitted with the symmetric 002 peak positions. The symmetric w-2T scan took longer, since it is done with an anlyser (otherwise the peak positions are slightly off, depending on bow).

In situ is theoretical possible, although the challenge is the large range of ca. 20° in 2Theta (since the 205 are really far out). That would either require very big detectors or one must be very close, which is a thermal challenge.

There is an in-situ XRD MOVPE reactor in my lab, but even this has only 7° range (and of course is rather optimised for symmetric 002). The problem is that the more Al the less Xrays are scattered, and 205 is not the brightest peak to begin with, less than 1/30 is so of 002 (the table with the relative intensities is at the lab, too).

Good luck and happy holidays!

Please post as much helpful info as possible without breaching confidentiality or propriety like "the table with the relative intensities".

What about the use of integrated intensity to estimate relative layer thickness spatially on the sample surface? Should the (0002) or other reflection yield identical results provided the same sampling area is used?

BTW how uniform (thickness) are films that you grow, using CVD, spatially on the sample surface? How have you verified this in the past?

I mainly wrote the script and did some initial XRD measurements on 8" samples. The script also estimated the bow and some other stuff.

But the thicknesses are almost impossible to estimate without big error margins using conventional analysis (apart from the top base layer of the transistor), since the different relaxation would cause only weak fringes at each interface. I am not sure about your approach of adsorption, but given my experience with ellipsometry I am a little sceptical of its chances to have unique solutions (since each top layer affects the layer below; especially the thickness of the top GaN cannot be estimated by this but needs to be put in). I have almost never had the expected peak height and shape of the GaN peak fit its absolute value, and the numbers from fitting the entire w-2T 002 scan are more guideslines which are not more precise than 20% at best.

Especially peak shape rarley fitted the calculated shapes, often the valley between the peaks was higher (even when using the results from cross section measurements) or the peaks were asymmetric.

I admit I'm a bit puzzled. "approach of adsorption" ? Please help me out.

"(since each top layer affects the layer below; especially the thickness of the top GaN cannot be estimated by this but needs to be put in)" - please clarify. We need to make no asumptions. The diffracted intensity is directly proportional to the relative thickness within the voxel. No film, no peak, no integrated intensity!

"I have almost never had the expected peak height and shape of the GaN peak fit its absolute value" - Why would you or should you? Since you are using the conventional 0D approach (even with the 1D detector) for rocking curve ananlysis you never could. Unless, you are magically able to go back to the exact same voxel on your sample surface each time maintaining identical optics and power conditions.

Just curious, how is your LynxEye mounted? Parallel to the equatorial plane or perpendicular? Probably parallel as you mentioned a 7o coverage or so. Are you using a "line source" or "point source"?

You need the integrated peak volume, which is challenging to get from asymmetric peaks, or from highly overlapping ones, not to mention instrument scattering. This is very challenging, my respect if you can pull this. Furthermore, the incoming X-ray light is attenuated, and cannot contribute to scattering. The latter is mostly important for low incidence though, with adsorption of GaN at 8048 keV is rather low at 0.4/cm. If adsorption is an issue, any error in thickness will accumulate the deeper the layers are. (In-situ, of course, everything is fine, since the first layer is a single material.)

And you are right, from a w-2T 1dimensional 00.2 scan I cannot guess the shape of the peak in 3D reciprocal space and hence cannot do things like stacking faults etc.

The X-ray spectrometer I used was a PanAnalytic Expert, with a 4 Ge monochromator and either an open detector (with 0.5° slit) or 3 Ge analyser. So all my reciprocal space maps were taken point by point.

The insitu reactor here at Nagoya was described here Article In situ X-ray diffraction monitoring of GaInN/GaN superlatti...

Just to re-cap. There is no argument about using the relative Bragg peak position (composition) or the profile FWHM (integrated breadth, defect density) to quantify Nano structural parameters. The only question is whether "peak intensity" or "integrated intensity" may be used to estimate relative diffracting volume. In this regard, here are some details I've understood better thus far:

My gut feeling is, that if the instrument broadening is bigger than the layer broadening, you can use peak intensities. Otherwise you have to use integrated intensities. So the better the sample the more accurate you estimation based on peak heights may be. Also, I wonder if with a Ni filter only and open detector there would not be many intrument contributions to the peak who makes them no gaussian ( because of a linear combinations of two gaussions).

No doubt the instrumental profile is huge with these optics. We've done other work with HRXRD as well with other samples. However, relative values may still be effectively quantified. Correct modelling would be key, I'd think. Peak values make me a bit nervous but integrated intensity values and integrated breadth values may be more reliable.

Actually with those conditions, "only Ni filter", the Bragg profile tends to be "Gaussian" experimentally. On the other hand, the HRXRD instrumental profile seems skew symmetric pseudo Voigt.

"Also, I wonder if with a Ni filter only and open detector there would not be many intrument contributions to the peak who makes them no gaussian ( because of a linear combinations of two gaussions)." Valid point! I'll double check the profile shapes again and post.

"Open detector" in the case of 2D detectors is by default a "receiving slit" defined by the pixel dimension, detector surface inclination to diffracted beam and diffractometer radius (detector to diffractometer axis distance).

Happy New Year! An example of the incident beam "foot-print" on the sample at 90o & 17o angles of incidence are shown above. The full dynamic range image without "image saturation" may be used to normalize the relative intensities in the diffracted image. The 90o image is the incident beam as it exits the source slit. This would be the dimension of the diffracted beam for all symmetric reflections. The same image may then allow the spatial thickness determination without the need to "raster" the sample by placing the 2D detector parallel to the specimen surface. I'm not there yet, but am excited about the prospect of being able to determine thickness values in a "snap shot" without the cumbersome rastering method.

Happy New Year.

Is this a parallel beam setup? Then indeed you could indeed get a 2D profile with resolution of 0.25 degree (depending on your beam parallising optics).

Still, you channels would have different intensities due to the illumination profile, and due to bow. (The latter would shift also the angles, so the maximum may be at a different value.) If you only work with relative peak heights, I wonder on your normalisation.

Thanks for engaging and sharing your expertise.

Attached is the peak center positions (degree) for various topographic positions. The ordinate axis is displacement in mm along sample surface. COD is coefficient of determination as computed using Origin to fit 5 Gaussians. We have restricted "usable data" to those with COD values above 0.9 in purple rectangle. I use only the relative values normalize w.r.t. any one layer. Substrate would have been better to normalize w.r.t. The peak angles appear to be fairly "well behaved". I would think any "bow" (long range) would manifest itself on all the peak positions uniformly. But I wonder??

SNR to COD relationship for data set at location "800" on topograph.

I'm fully convinced that the individual layer relative thickness may be detected using the integrated intensity under the individual layer XRD reflection. The key is to correctly deconvolute each layer reflection and calibration. This is especially critical when the incident beam is not fully monochromated as in our case. It is obvious by inspecting literature data for similar structures that the use of HRXRD or higher angle reflections may help resolve (deconvolute) these peaks experimentally as well.

I intend to unequivocally confirm this in February 2018. Any such confirmation would have to include complimentary techniques like AFM, SEM, TEM, etc.. Stand by for updates :-)

"channels would have different intensities due to the illumination profile, and due to bow. (The latter would shift also the angles, so the maximum may be at a different value.) If you only work with relative peak heights, I wonder on your normalisation."

Right! I've not yet stopped wondering myself regarding peak shift and surface modulations along with normalization. I think I'm close to an experimental breakthrough though. That is why I wonder aloud. Thanks for any suggestions and critique any time!

Got a bit closer by including the Si substrate (111)s along with the (0002)s for the layers in the diffractograms for a different sample with similar layer composition. The Si (111)s should provide an excellent internal standard. A conventional diffractogram (STANDARD) using the 0D point counter is used as the "measuring stick". All our diffractograms for each pixel is compared with this STANDARD 0D diffractogram.

Just working on the YouTube videos, WIP:

XRD Background for Bragg XRD Microscopy: https://www.youtube.com/edit?o=U&video_id=08g44fmdu6g

Data analyses for GaN-AlGaN-AlN on Si: https://www.youtube.com/edit?o=U&video_id=ezcJUt9GSE4

Your critique will be immensely appreciated!

https://www.flickr.com/photos/85210325@N04/albums/72157697325433441

https://www.flickr.com/photos/85210325@N04/albums/72157698987361455

https://www.flickr.com/photos/85210325@N04/albums/72157695811158822

https://www.flickr.com/photos/85210325@N04/albums/72157693182784000

https://www.flickr.com/photos/85210325@N04/albums/72157695922010022

I'm closer! Using Origin and XRD data integration over a ROI (region of integration) of 3x10 Pixels (30 rocking curve profiles over a 270x270um sampling area), we were able to produce the relative integrated intensity profile across both "equatorial" and "axial" cursor lines on the topograph as shown in the attached image.

Once this data is normalized w.r.t. individual layer structure factor, the appropraite individual layer thickness may be determined. The only assumption is that the atennuation depth is significantly larger than the combined layer thicknesses above the substrate.

Note: The statistics are a near certitude above COD (coefficient of determination in Origin) values of 0.9.

As of now, I'm unaware of any other technique to precisely image the spatial profile of individual epitaxial layer thickness in a "sandwich" structure without destroying (cross-sectioning) the specimen in the process. Do you know otherwise?