I was reading about diffusion coefficients for common dopants when the diffusivity of Boron in crystalline Si was compared to that in amorphous Si. Decided to dig into the differences between the crystalline and amorphous materials. These are the resources I used.
Fertig’s video piqued my curiosity about how we determine these structures, hence his other crystallography video on x-ray diffraction. It introduces Bragg’s law.
Diffusion is a key step in wafer processing for microprocessor manufacturing. Fick’s laws are therefore an important component in understanding diffusion. Fortunately, there are great resources online for an overview of Fick’s law. I started with the Khan Academy video on Fick’s law of diffusion (embedded below). It was informative but did not go into the level of detail I had hoped for.
Some digging around led to a series of lectures from the Mechanical Engineering’s Fertig Research Group at the University of Wyoming. This video on the mathematics of diffusion (Fick’s 1st law) was the level of detail I was hoping for and was therefore a good supplement to the Khan Academy diffusion overview.
And here’s the video on Fick’s 2nd law (again showing how to derive it and some brief comments about PDEs). I wonder if there is some accessible visualization that could be done of various solutions to the diffusion PDE.
After learning about Czoralski crystal growth last month, I saw a mention of simulating this growth process and realized that this simulation would be a great candidate for a high performance computing project. A search for such code on GitHub.com revealed arvedes’ simple example for transient Czochralski growth simulation with Elmer. I’d never heard of this program before but it is open source and on GitHub as the elmerfem repo! Since I am a total newbie to finite element analysis, I found a video to introduce me to the field.
As for Elmer, there is a decent (as far as I can tell) set of webinars on YouTube ranging from an Introduction to Elmer to how to use Elmer in various scientific applications. Looks like a promising place to begin exploring this tool to see what it can do and how it has been used.
Here is a very helpful video I found on Czochralski Growth. Some concepts that come up include nucleation, meniscus, segregation coefficients, and Lorentz force.
Dislocation loops can form if the pull rate is too low. Here is a discussion about dislocation loops.
Czochralski growth also turns out to be an interesting area for numerical modeling. I stumbled into some interesting papers when searching for more information about pulling rates. The paper that exposed me to this area is Numerical modeling of Czochralski silicon crystal growth and has various interesting citations as well.
Crystal defects play an important role in semiconductor fabrication. One type of defect is a Frenkel defect. Understanding such defects involves determining the vacancy concentration as given by Arrhenius function. I reviewed several videos to help me understand this equation:
I took a detour to remind myself about activation energy, electron volts, and Boltzmann’s constant (all of which feature when studying Arrhenius function).
Another type of crystal defect is a line defect, e.g. edge dislocation. These videos contain additional information about edge dislocations.
A stacking fault is an extra plane of atoms. Some resources about stack faults:
Gettering is a process by which impurities and defects diffuse through the crystal (controlling where defects occur). This can be used to improve yield in semiconductor manufacturing as explained in this video:
The previous post outlined my introduction to materials science with interest stemming from applications in microfabrication. Reading section 2.2 of Fabrication Engineering at the Micro- and Nanoscale left me curious for more information about crystal structures. A YouTube search for “face centered cubic structure” led me to the videos below, which proved sufficient for gaining a basic understanding of crystal structures.
These are also discussed in section 2.2 of the text and are explained in these videos. Interestingly, neither of the videos mentioned the fact that the plane notation also denotes a vector (from the origin) that is perpendicular to that plane!
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