As an undergraduate at the University of Missouri – St. Louis I had a joint project with the NASA Missouri Space Grant Consortium and my current company, SunEdison Semiconductors. The aim was to better understand helium and hydrogen ion implantation into silicon before a thermal treatment. This was an active area of research to help optimize the SmartCut technology for transferring thin films to create Silicon on Insulator (SOI) materials.
Our data set would be gathered via the preparation of cross-sections of implanted silicon for analysis via Transmission Electron Microscopy. Interestingly, there were highly regular dark bands parallel to the surface and at depths expected for the implantation species and damage. The bands remained dark regardless of imaging conditions–bright field or darkfield. This suggested the contrast was the disruption of electron channeling due to displaced atoms in the crystal. In other words, the darker it was, the more displaced silicon atoms, the more damage. See the image and intensity profile plot below. The take-away was: TEM is a reasonable way to at least see the damage.
Goal and Method
Aside from measuring standard things under different conditions, we also wanted to be able to say something quantitative about the structure in the damage layer and that’s what we’ll focus on here. For sufficiently thin samples we could see a sort of mottled contrast. In the image below you can see the thinner part of the sample highlighted as Region 1 shows significantly more structure than the thicker Region 2.
How can we be quantitative about this structure? One way is to look at the makeup of the spatial frequencies needed to construct the two image regions. This map can be obtained by taking the magnitude of the Fourier Transform of the image, called the Power Spectrum (PS). This can be done so that the center of the PS is an intensity called the DC Peak which is the zero frequency and gives a measure of average image intensity. Further away from this center point corresponds to increasing frequency. So low-frequency (read: long range) contrast correlations are near the center and quickly changing intensities at short-range require high frequencies. If you take the average intensity of a band at a given radius in the PS, this tells you something about the amount of those spatial frequencies required to construct the image.
Power Spectrum/Fourier Transform Intuition
To build intuition, lets think more about this relationship. Imagine you have an image of a zebra-stripe vertical pattern where there’s 10,000 lines counted from the left to the right of the image. If you were to make a profile plot of intensity similar to Fig. 1 above, you would see a very fast-changing signal that would look like a high frequency square wave. If the number of lines were reduced to 10, you would see a similar plot but with a much lower frequency. Similarly, the PS of the first case would show a bright peak far away from the center (indicating high frequency) and the second image would have a peak much nearer. The angle of this point gives us information on the orientation of the corresponding spacings in the image. More specifically, drawing a line in the PS from the center to the bright dot of interest is a line that is perpendicular to the spacing in the image. So vertical lines would have points to the left and right of the center at angles 0 and 180 degrees.
How do we apply this to our problem? We simply take a PS in the damaged region and another PS nearby as a baseline and compare the spatial frequencies. If some particular band of frequencies is strong (indicated by a radial intensity average in a band of the PS) in the damaged area, that tells us something about the size scale of the texture.
To show we were actually getting spatial frequencies as a result of the damaged texture, we compared PS from the regions marked above since the average intensity profiles are similar but in the case of region 2 the texture information is washed out due to the sample thickness. (Note: ion milling was used to thin the sample and the presence of the oxide near region 2 indicates it is less thinned than region 1, where the oxide has been milled away). We normalized the PS intensities to match at the DC peak.
Observe that in the thinner region there’s a significant bump in intensity in the 40 – 80 pixel range. This says something about our characteristic damage size. 2g measures in pixels can be converted to spatial frequencies if you know the camera constant, magnificantion…etc of your image. In this case the 40-80 pixel 2g range corresponds to 90-180 Angstrom spacings.
To complete the analysis of this damage layer we wanted to confirm that the regions of the image that were using these frequencies were indeed the regions we were interpreting as implantation damage. This was achieved by applying a filter to the fourier transform to only select the frequency range of interest, and then inverse-transforming to see our filtered image that only allowed spatial frequencies we let pass.
Specifically, we made a doughnut shape where inside the doughnut we multiplied the FT of the image by 1 and outside (and in the middle) of the doughnut we multiplied by zero. The width of the doughnut was defined by our 2g measures in the image above and was the 40-80 pixel distance from the center of the PS.
After this multiplication, only the frequencies within the doughnut remained and we then took the inverse transform. There are so-called “ringing” effects due to this abrupt cut off in frequency, but the image below shows that the damaged region in the thin part of the sample lights up much more brightly than other regions. It also shows that this texture is washed out as the thickness increases, as our intuition might suggest.
It’s important to note that this result is completely independent of the damaged area being dark compared to the rest of the sample. This shows that the frequencies required to create the “damaged region” in the original image lie in a particular range and therefore give us information on its characteristic size scale. The fact that this region lights up when we filter out all other spatial frequencies confirms this.
Phil Fraundorf at UMSL for teaching me how to do all of this stuff as well as providing the ideas/tools.
Jeff Libbert, Lu Fei, and MEMC/SunEdison Semiconductors for providing guidance, funding, and materials.
The NASA Space Grant Consortium and UMSL for providing funding and the opportunity to do undergraduate research!