Here are some important experimental factors:

http://www.flickr.com/photos/85210325@N04/8613308001/in/photostream

Estimated Beam Size = 0.5mm x 1mm

0.5mm at 100mm radius subtends an angle of

I think I got some of it. The Caltech work. Still figuring out how to relate parameters to thickness, periodicity, etc.

Please review and share your suggestions:

http://www.flickr.com/photos/85210325@N04/8628027356/in/photostream

http://www.flickr.com/photos/85210325@N04/8628389243/in/photostream

My analysis shows that the convoluting experimental "delta function" in their (Caltech 1984) case was 0.29 degree assuming (no receiving slit) 1mm beam size at 100mm SDD (sample to detector distance).

Sampling VOXEL size = 0.5mm*1.0mm*10µm =5*10^(-3)mm^3

In contrast, our experimental convoluting "delta function" was 0.043 degree (0.076 mm pixel size). An order of magnitude better than in the Caltech example (as in most current data in literature). See bottom left of image above to grasp the scale of the convoluting windows in the two cases.

Sampling VOXEL size = 76µm* 76µm*10µm=5.78*10^(-5)mm^3

Two orders of magnitude improvement over the Caltech type data.

Now I’m beginning to understand the conventional 0D Detector based Rocking Curve data a lot better. The power of measuring in the reciprocal space is becoming vividly clear!

Someone help please! I'm unable to understand the possible origin of the asymmetry in relative intensity of the epi reflections (harmonics).

Why is Harmonic Peak # 2+ more intense than all else?

Why is there any shift in relative intensity at all?

What nano-structural parameter may be inferred by this data?

What do harmonics positions, peak shapes etc. imply?

Why does the lattice missmatch change radially? (Curvature?)

http://www.flickr.com/photos/85210325@N04/8628389243/in/photostream

Am I the only one out here on this frontier? Is anybody there? Help!

Real Time Bragg XRD Microscopy!

Dear Ananth,

I did my perfection in electronic materials in CALTEC with Prof. T. Vreeland, Jr. group. I Still am not understand yours problems with X-Ray diffration there. However, they published with me work on the epitaxial layers with X-ray diffraction. It will be attachet to the letter. In the case you will explain me exactly the poblems you have in yours study I will try to sent you the answers.

Dear Ananth,

Please find my publication in CALTECH.

Thanks Paul!

Thanks for your comments & the paper. I'll read through the details and then respond more intelligently.

Would you have any experience with super-lattice MBE epi XRD?

In Figure 1.:

1. How do I determine nano-structural parameters from the multiple harmonics?

2. What advantage is the exact peak position and FWHM of the Epi harmonic?

3. Is it possible to determine super-lattice layer dimensions from peak positions and FWHM?

Portable Real Time 2D Bragg XRD Microscope:

Figure 1. http://www.flickr.com/photos/85210325@N04/8628389243/in/photostream

3D X-ray Rocking Curve Data. Up to 400x400=160,000 rocking curve profiles (similar to the one in your paper) are available instantly and portions of this data are displayed in Figure 1. This method is about a Billion times faster than the method you used for your rocking curve profile in 1991. In addition, at least 2 orders of magnitude better in spatial resolution.

1.Why is Harmonic Peak # 2+ more intense than all else? Related to the structure factor of the "sandwich" layers in the super-lattice?

2. Why is there any shift in relative intensity at all?

3. What nano-structural parameter may be inferred by this data?

4. What do harmonics positions, peak shapes etc. imply?

5. Why does the lattice miss-match change radially? (Curvature?)

If I need to, I'll explain the details of Figure 1 better.

[email protected]

The 0th order SL peak of the epi is buried in the "shoulder"/"tail" of the most intense Bragg peak of the GaSb substrate. Deconvoluting and determining the peak details (position, FWHM, integrated intensity), would need a lot of computing. 0th order peak position alone may be determined precisely and unequivocally by using the center point of the +nth and -nth order reflections. This is relatively less complicated to accomplish numerically. This operation would be key in deconvolutiong the XRD signal contribution from the epitaxial film and the substrate.

Would it be reasonable to assume nearly the same penetration depth (epi+sample) of incident X-rays irrespective of the film thickness locally? I'm sure there are ways to actually compute based on atomic structure factors for the compounds. I'd appreciate some guidance/suggestions in terms of links and publications to expand my knowledge base.

"problems with X-Ray", I have none. Challenges, maybe? I need to understand how to read diffractograms from super-lattice epitaxial films. If you have knowledge & wouldn't mind sharing some suggestions, I'd appreciate it much. Thanks Paul!

Dear Ravi Ananth,

We know exectly to calculate the layer thickness that from him diffraction reflections peaks is comimng. You can write examples in my last papers published in Metalurgical Transaction A. Please send me the multilayer structure (schematically) you was built by MBE (maybe you was prepared TEM cross section picture) and rocking curve from superllatice epitexial films ( needs all parameters you are working) and I will prepare for you the equations for calculation of the superlattice of epitaxial films thickness on the base of diffraction reflection peaks. Paul

That is awesome! Thanks Paul!

The SL was 10 periods of 25nm each layer of alternating InAs & InAsSb on GaSb (001) substrate grown by MBE. Total epi thickness of 0.5um. Cu K Alpha 1, Hybrid Monochromator, 1.8kW, 100mm SDD (sample to detector distance), 76um detector pixel size, 25mm detector diameter, detector plane normal to the diffracted beam, Omega resolution of 1.972 Arc Sec (0.0344179 Radians). Any other parameters?

The rocking curve profiles are for the (004) symmetric reflection in the coupled Omega-2Theta mode. Each image may contain up to 160,000+ (8 Bit) rocking curve profiles (RCP's) displayed topographically. I've displayed only one of the RCP's with the multiple harmonics (up to +-4).

What else would you need to know? Most of the experimental details are on the images:

Figure 1. http://www.flickr.com/photos/85210325@N04/8628389243/in/photostream

Figure 2: http://www.flickr.com/photos/85210325@N04/8543228208/

Figure 3: http://www.flickr.com/photos/85210325@N04/8561945111/

Video 1: YouTube video of the 2D real time rocking curve data for this sample -

http://www.youtube.com/watch?v=De_Nh7iN6y4&list=PL7032E2DAF1F3941F

Appreciate any help you may provide. Thanks Paul!

[email protected]

Dear Ravi Ananth,

Thank you very much for yours results. First, let me to check carfully yours results. I will be in touch with you in the near future.Paul

Dear Ravi Ananth,

Please find attached molecular beam epitaxy conference files. Is there more X-ray diffraction results from epitaxial superlattice. For yours interesting. Paul.

Great! I hope other experts in this field also get involved and expand this thought process. Thanks Paul!

Certainly post such questions and others like it on the following LinkedIn Group post if possible:

1. X-ray Diffraction Imaging for Materials Microstructural QC:

http://www.linkedin.com/groupAnswers?viewQuestionAndAnswers=&discussionID=189258615&gid=2683600&commentID=140532636&goback=%2Eanp_2683600_1369907189536_1%2Eamf_2683600_12045948%2Egmr_2683600&trk=NUS_DISC_Q-subject#commentID_140532636

2. X-Ray Diffraction and Scattering Techniques

http://www.linkedin.com/groupItem?view=&gid=3614857&type=member&item=241973911&qid=ae9fa84f-1f22-47b8-9f9b-c529426e3119&trk=group_most_recent_rich-0-b-ttl&goback=%2Egde_3614857_member_244782133%2Egmr_3614857

[email protected]

Parallel discussion on LinkedIn:

http://www.linkedin.com/groupItem?view=&gid=2683600&type=member&item=238135655&commentID=141338448&goback=%2Egmr_2683600%2Egde_2683600_member_245989945%2Egmr_2683600&report%2Esuccess=8ULbKyXO6NDvmoK7o030UNOYGZKrvdhBhypZ_w8EpQrrQI-BBjkmxwkEOwBjLE28YyDIxcyEO7_TA_giuRN#commentID_141338448

Dr. Rozenak! Thanks for your help with the computations. I'm still trying to wrap my mind around it.

Thanks for going the "extra mile"!

If any of you are involved with materials or X-ray Diffraction, then here are some tools to help improve both the quality and quantity of your publications:

Come join us and share in the wealth of knowledge. Free Webinar, July 12 at 11am EST on X-ray Diffraction Techniques in Transmission Geometry

http://www.linkedin.com/groupItem?view=&gid=2683600&type=member&item=252069645&commentID=149420591&goback=%2Egmr_2683600&report%2Esuccess=8ULbKyXO6NDvmoK7o030UNOYGZKrvdhBhypZ_w8EpQrrQI-BBjkmxwkEOwBjLE28YyDIxcyEO7_TA_giuRN#commentID_149420591

BTW come join us and learn: Friday August 30th, 2013 10AM EST! TAKE ADVANTAGE! "The 3rd Dimension & Beyond in XRD 2013" by Weiguang Guan of McMaster University! http://www.chemistry.mcmaster.ca/facilities/xray/221-max3d

http://www.linkedin.com/groupItem?view=&gid=2683600&item=268765048&type=member&commentID=159428290&trk=hb_ntf_COMMENTED_ON_GROUP_DISCUSSION_YOU_CREATED#commentID_159428290

NDE Imaging of Crystallographic strain fields & Epitaxial film thickness in real time:

a. We normalized the relative intensity (RI) w.r.t. the max peak intensity of the GaSb substrate reflection for each pixel. 98%+ of the total XRD signal originates from the substrate even with 0.5um Epi. So we are at least 98% precise if not more. To be closer to 100% precision, we must record the Nano structure (RCP – Rocking Curve Profile or RSP-Reciprocal Space Profile) of the substrate prior to MBE deposition. In such case, it would be possible to deconvolute the precise shape of the substrate alone from the convolution thus leaving only the signal from the epi including the “0th order reflection”. Exciting! Atomic Numbers: Sb-51, In-49, As-33, Ga-31.

b. We’ve assumed that the penetration depth, epi plus substrate, is invariant throughout the irradiated surface (up to 25mm and higher diameter). The incident beam profile is nearly FIXED throughout the rocking curve profile.

http://www.flickr.com/photos/85210325@N04/10126843246/

The integrated intensity for each VOXEL would be proportional to the thickness of the epi at each VOXEL. This may be precisely calibrated for each instrument using some “known” standards.

http://www.flickr.com/photos/85210325@N04/10126843246/

Wow! This is cool, esoteric, real-time and mundane! This is a break-through! I challenge anyone out there to cite higher resolution (both real space and reciprocal space) data anywhere else in the literature using a laboratory based X-ray source.

We can truly map the variations in epi film thickness by precisely monitoring the NORMALIZED INTEGRATED INTENSITY beneath individual Bragg Peaks on each RCP (Rocking Curve Profile) or RSP (Reciprocal Space Profile) for each Pixel (VOXEL). As you can see the quality of both the substrate and the 0.5um MBE super lattice epi are superb in this sample. Yet, the sensitivity of the Real Time Bragg XRD Microscope allows us to image Nano structural INHOMOGENEITIES with exceptional contrast and dynamic range. The use of pseudo-color substantially enhances the ability of the human eye to perceive the contrast.

These are the most recently updated images:

a. Shape Fitting 1:

http://www.flickr.com/photos/85210325@N04/10225966185/in/photostream/lightbox/

b. Shape Fitting Super Lattice Epi: http://www.flickr.com/photos/85210325@N04/10225984176/in/photostream/lightbox/

Your feed-back would be deeply appreciated!

http://www.flickr.com/photos/85210325@N04/10225966185/in/photostream/lightbox/#!

More cool stuff! Quantitatively mapping precise MBE Super Lattice Epi film thickness:

http://www.flickr.com/photos/85210325@N04/10254196143/

The individual RCP's were normalized by assuming that the GaSb Peak Intensity should be constant within 1-2%. 99%+ Relative Intensity contribution may be attributed to the GaSb substrate. To reiterate, it would be more appropriate to use the Integrated Intensity below the deconvoluted substrate peak alone when normalizing the data rather than the Bragg peak intensity value.

http://www.flickr.com/photos/85210325@N04/10254196143/

Updated with scale and wafer orientation w.r.t. the rocking axis and image plane:

http://www.flickr.com/photos/85210325@N04/10255348743/

It would also be best if the integrated intensity were to be computed through parameters of the Lorentzian fitted. The II (Integrated Intensity) computed thus far is directly from the data after back-ground deconvlution and relative intensity normalization only.

http://www.flickr.com/photos/85210325@N04/10254797923/in/photostream/

Dr. Sigmund Weissmann of Rutgers: https://www.google.com/search?site=&source=hp&q=SIGMUND+WEISSMANN+CRYSTALLOGRAPHER&oq=SIGMUND+WEISSMANN+CRYSTALLOGRAPHER&gs_l=hp.3...2113.16362.0.16916.34.29.0.0.0.0.280.2064.16j2j2.29.0.eshsj%2Cj%3Dbottom%2Cjnum%3D2%2Cjlen%3D3%2Cjprob%3D-08...0...1c.1.25.hp..25.9.725.KbU3y5IMM-s

Here is the original Model "T":

http://www.google.com.hk/patents/US2926258

Back to the FUTURE!

Here's a summary of the data thus far (images updated 11-3-13):

1. GaAs (004) RCP, Theory=Experiment (+-)Small Asymmetric Deviation (one sided of Bragg Peak below FWHM):

http://www.flickr.com/photos/85210325@N04/9430820747/in/photostream/

2. GaSb (004) RCP Shape=GaAs Theoretical (+-)Small Deviations (on both sides of the Bragg Peak below FWHM):

http://www.flickr.com/photos/85210325@N04/10647827636/

3. CVD grown 3 inch production wafer of SiC 6H (0006) micrographs indicate large variability in RCP shape based on location on the topograph:

http://www.flickr.com/photos/85210325@N04/10019182954/

4. LSAO (LaSrAlO4) (004) RCP shape is nearly identical with GaAs theoretical RCP with small deviations:

http://www.flickr.com/photos/85210325@N04/10502185905/

5. Super Lattice Sample W20110221 with 0.5um MBE Super Lattice Epi 25nm period InAs/InAsSb on (001) GaSb Substrate:

A. Entire RCP Substrate & Epi (004) Symmetric XRD Reflection Mode Coupled Omega-2Theta Scan: http://www.flickr.com/photos/85210325@N04/10653618416/

B. Just the Epi peak isolated nearly Lorentzian profile shape: http://www.flickr.com/photos/85210325@N04/10653888653/

The YouTube video "Play List" below contains all the raw Bragg XRD Microscopy data for all these samples listed above. You may download and analyze for yourself if and when you have the capability. Please turn off Google Ads and the Music (listen to this instead if you like: http://www.shoutcast.com/Internet-Radio/grateful%20dead) to minimize distractions.

Suggestions for improving are always welcome!

[email protected]

https://www.youtube.com/watch?v=dFCQS8oUyT0&list=PL7032E2DAF1F3941F

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