Some commercial, laboratory XRD systems include attachments to perform small-angle (or glancing angle) analysis of thin films.
As others have noted, XRD is not just a "bulk-analysis only" method. Indeed, thin film analysis with XRD methods is a healthy research topic in its own right.
Yes if the thickness of thin film is of the order of wavelength used in X RAY diffractometer so you can get a peaks of X-ray intensity for your material...
thin film should be uniform and and calibrate your x ray data with substrates on which you have fabricated thin film
Due to limited amount of material in thin film a certain deviation in distance between the atoms may take place. Strains existing due to the lattice mismatch between a substrate and the deposited film is a one of reasons. A broadening of the XRD peaks is described by the Scherrer equation.
Additionally to XRD, you can carry out X-ray reflectivity measurements. From the obtained curve it is possible do determine a total thickness of the film (Kiessig fringes), roughness of the surface (interfaces) and a modulation period (Bragg peaks) when a multilayer structure is investigated.
Some commercial, laboratory XRD systems include attachments to perform small-angle (or glancing angle) analysis of thin films.
As others have noted, XRD is not just a "bulk-analysis only" method. Indeed, thin film analysis with XRD methods is a healthy research topic in its own right.
The overall intensity of diffraction peaks depends on the volume sampled to first order. You can calculate from geometric considerations what this means for a fall-off in overall intensity as incident angle changes.
This is not a true / false question as to observing or not observing. Here is a calculation that you can do as a homework assignment. Assume that you require at least a 3:1 ratio in S/N to obtain a valid "peak" assignment. Suppose you have a thin film of thickness z. Assume that you start with a S/N ratio of 100 at a grazing angle of 5 degrees with a given XRD instrument. Calculate the incidence angle at which the S/N will drop below a value of 3 to make the peak assignment unreliable.
Now go research about what thicknesses values for z are possible to measure with thin-film XRD systems. Apply that answer to your own system.
I spent several years analyzing organic thin films for a collaborator (as administrator for a multi-user facility). I have to (gently and without condescension) state that your assumption that pXRD is a bulk technique is entirely false. There are several systems available that allow very finite analysis of specific structures. Such as the Rigaku "superbright" systems used for analyzing protein crystals and grazing incidence SAX systems used to analyze thin films.
The thickness of a thin film can be obtained through reflectance experiments. In this case the X-ray absorbance of the material is going to be the limiting factor for measuring thickness. We were successfully able to measure films from 50 to 300 nm. Do you remember diagrams for Snell's Law in regards to ATR-FTIR experiments? (e.g. http://sites.temple.edu/strongingroup/laboratories/atr/) Light would bounce (refract) off the bottom surface of a medium then some would escape through the top but some would bounce off the top layer. In reflectance measurements, there should be specific angles ( 0.05 to 10 degree 2*theta) in which X-rays bounce and escape through the surface of your film. Based on where these reflectance peaks occur, the thickness can then be calculated. There are deviations to the straight-forward application of the calculations though. It is with these deviations that you can find parameters like lattice mismatch and strain of the interface, deviations in film density, and surface roughness.
I used a multi-purpose Eulerian cradle to perform these measurements, although with the right set of absorbers/attenuation. This device helped me to orient the film/substrate/beam correctly to achieve the best measurement. If you have a system with either this attachment or an "in-plane" arm, you can very easily accomplish such measurements and there is much published on the subject. It is generally the calculation of parameters that gives people troubles.
soft X-rays tend to be about 10 KeV and lower (depending on your information source), hard X-rays are of course anything higher. An X-ray wavelength of 0.154 nm is approximately 8 KeV (E=hc/lambda, give or take a few tens of eV). You should be okay with anything that has a wavelength below 0.2 nm. In other words, just about anything that is commonly available except chromium targets.
As to your earlier question about procedure
My system was a 40 kV 44mA, line shape Cu anode. When I aligned the beam to the sample I used about 0.4 mm of copper sheeting in between the sample and the detector in order to keep the count rate low. We were also not set up for grazing incidence SAX experiments.
1. Set goniometer at 0 degree 2*theta (you can see why the absorber was in place)
2. Move Z-axis of Euler cradle until the position of the top of the film was known. This was discovered when the X-ray intensity was at it's highest. This step helps to prevent X-rays from penetrating too deeply into the sample.
3. Set Z-axis position to provide approx. 80 - 90% of full beam intensity.
The following steps are where material dependence really comes into play. Since my samples were organic films with thickness between 50 - 150 nm, the procedure may seem strange to researchers who work with thin films composed of higher Z elements. I actually adapted this from an X-ray study of thin layer dissolution on sustained-release pharmaceuticals. If I find the exact reference I'll post it.
4. Determine the critical angle for analysis. This was done by scanning from 0.01 degree to 0.1 degree 2*theta. The angle which produced the highest amount of signal as was the critical angle for me.
5. Set the source arm to 75-90% of the critical angle. This had to varied in order to achieve the most uniform results through scan range of the experiment.
6. Scan the detector arm only through the desired range of theta (0.1 to 0.25 degree/s for data acquisition). I could usually get about 5 degrees of good data on an average film. If they were really good films, closer to 9 degrees. Once again, remember these were low Z materials with low reflectivity.
Now you are at the simulation step. We had a nice, proprietary, software from Rigaku for doing the calculations. However, the theory and mathematics necessary for determining things like film thickness and surface roughness are nicely outlined in a book by Mario Birkholz: Thin Film Analysis by X-ray Scattering.
Dear Abbas, the penetration depth of soft X-rays is smaller compared to hard X-rays. You may check the different attenuation length in given materials under
there you will see that hard X-rays are usually penetrating deeper.
In the context of your original question: Take care that the Bragg equation (n*lambda = 2*d*sin (theta) still needs to be satisfied when you are using soft X-rays, i.e. X-rays with a larger wavelength. So all Bragg peaks will shift to larger Bragg angles if the wavelength is increased (i.e. X-rays of smaller energy are used). Finally, for a given lattice spacing d, there is a distinct critical wavelength for which the Bragg equation cannot be satisfied any more (since the sine only provides values smaller or equal than "1" !
So I guess that soft X-rays are not an universal recipe for thin film analysis!
I want to know the actual penetration depth of X-rays (in um).
In my case, I have applied a 60 um carbon coating on to a cellulosic substarte. I have obtained the spectrum. I wonder if the spectrum does contain the peak of substrate or not. because as per my understanding the peak for cellulose and carbon are observed between 21 degree to 25 degree.
I am using Rigaku Denki X-ray generator (Rigaku, D/Max-2500) equipped with CuKα radiation (λ=1.54181 Å) at 40 kV.
Ok! I see some of the best minds in XRD exhibited here. In the interest of advancement & progress, I'm hoping to leverage :-)
I need some help! I am on the verge of a solution. Check out this data set and analyses for a GaN-AlxGa(1-x)N-AlN-Si sample wafer. I have the 3D XRD rocking curve data collected using a commonly available lab based XRD instrument below 2kW. I have the relative intensities for five distinct Bragg peaks around the GaN (0002)s reflection. How do I figure out the spatial thickness of the individual layers from these well resolved diffractograms? Am I missing the Si substrate peak for "reference"? Should I be using the integrated intensity? Should I track FWHM as well?
I'll post a separate question as well and include the link here soon. Meanwhile, I've atfor tached the original data in Microsoft Moviemaker format to download directly and examine for yourselves. I've also attached a PDF file that is, work in progress. I'll post updates routinely with changes and advances. This would be a wonderful project to synergize.
Peace be up on you, your question's readers and all RG members.
Please check the pamphlet of your Rigaku Denki X-ray generator,, sure you will fined the penetration depth, such this parameter in an important one sure it is mentioned.
I know I'm getting signal from each of the layers well within the penetration depth. Now how do I apportion each peak and derive the integrated intensity? Thus be able to detect the diffracting volume corresponding to that Bragg peak.
Naveed Mengal! C - 663um; Cellulose Acetate - 395um
"Assume that you require at least a 3:1 ratio in S/N to obtain a valid "peak" assignment." Jeffrey J Weimer, that appears to be a statement seeped in copious experience with well-defined principles in statistical analysis techniques :-)
How would I compute S/N?
Do I use the max intensity on profile for "S"?
Do I use a standard deviation on the "base line" (Bragg profile "tail") for "N"?
I'm trying to estimate this (SNR) for various Bragg profiles at several topographic locations on a "flat" wafer.
@R Avanth: Assume noise is normally distributed. Measure a histogram of noise and compute the standard uncertainty of the histogram plot. To be 99.7% confidence that what you see is a peak and not just noise, the height of the peak must be at least 3 standard deviations greater than the standard uncertainty of the noise. So S/N ~ 3 is a confidence bounds for 99.7% (three sigma). Copious experience yes, but based on well-defined principles in statistical analysis of data.
Thanks Jeff! You helped me tremendously already. I'm close but not there yet. Help!
I'm trying to detect the onset of signal from the sample in these rocking curve profiles, (RCP, diffractograms) for a GaN Epi film on Si. I'm starting far away from the sample edge. My SNR computations are a lot higher than 3 even at the "base-line". I'm making some sort of a computational error.
Any clue where I'm straying? Some of the data I'm using is shown below.
SD - Standard Deviation computed for the last 50 data points of 3600.
MAX - Maximum value on the RCP
SNR - MAX/SD
I've attached a Word file and PDF of the data I'm referring to. The Word document will even allow you to view the data values on the charts. 15 point smoothed trendline is shown in "red".
The ordinate axis is in mm displacement on sample surface in the "SNR 300" chart and inordinate axis is SNR at topographic location 300:-)
Are you measuring signal after you subtract a baseline? If not, you are essentially obtaining a rough metric of maximum baseline to noise (B/N) on those scans that have no peak.
* Baseline (B) - Fit a straight line with slope zero through the average over about 10 points on the left and right ends. Use the height of that baseline as B. Subtract B from the spectrum.
* Signal (S) - Measure the average over about 5 points in the region where your peak is always to appear.
* Noise (N)
- Method I (easiest): Take the standard deviation over 50 - 100 points at the high end of the spectrum.
- Method II (clever): Curve fit the peaks. Subtract the envelope. Take the standard deviation of the difference.
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.
If I was to translate (raster) various topographic locations to the same detector pixel, while maintaining all other experimental conditions, 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.
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?
I'm just learning about COD, "coefficient of determination", or "R2". Cool stuff, statistics! Never liked it in school without computers in the old days :-)
I have an abundance of data. Nearly, 200x800 =160,000 diffractograms. My objective is to select the data that is "meaningful". There are two main reasons for diminishing relative intensity.
No sample (past sample edge).
No beam (past beam edge).
We were using a sampling size of roughly 0.275x.27 mm (10x3 pixels on detector) on the sample surface for the (0002)s data. The first image I uploaded was the FWHM computed by Origin along with the COD. It seems like 0.8 COD is reasonable "cut off" based on the SD for FWHM at the extremities below 0.8 value for COD in this analysis. Several example are also show for COD values down to 0.3.
The thickness of thin film play a role in determining its structure. The first mono-layers or less than a monolayer in different studies need to investigate structures carefully. The other thing is the effect of the reflected XRD by the underlying surface or the substrate. Glancing angle of the incident XRD on thin films can assist in studying the structural properties.
"The other thing is the effect of the reflected XRD by the underlying surface or the substrate."
The substrate reflection may actually be taken advantage of as a "standard" to compare with. It may be used to normalize the data spatially as well. Remember in epitaxial films you cannot use the GIXRD like with poly crystalline films. You'd have to find an appropriate reflection at the desired shallow angle range. In our case for GaN sample, we used a 17o reflection with a guarantee to produce signal from all the epitaxial layers. I missed the Si substrate reflection in hind sight. Next time!