How Small Can You Go?
Daniel j -
Despite the vastness of our universe, many of us find ourselves wondering not about the glistening stars in the sky but instead about a single atom and the paradoxically vast quantum world inside it. And among these philosophers are semiconductor nanotechnology experts and researchers, who focus on creating smaller and more efficient pieces of technology by exploring the miniature universe within our own.
So, in a world where smaller pieces of technologies and miniaturization are increasingly favored, we must investigate and refine the designing process of these nanotechnologies, especially those that utilize semiconductors. Because these semiconductor devices can perform anything from controlling electricity flow to storing memory, their development is essential to modern technology.
Fascinated by the idea of working on these fundamental electrical components, I decided to do my senior research project on testing the effectiveness and accuracy of a newly developing transmission simulation method for semiconductor nanodevices named the “Usuki method.” Simply put, this “Usuki method” could potentially be a new way that researchers can visualize electron behavior through these devices.
This past week, I specifically focused on trying to understand the calculations behind the Usuki method.
I started off by diving into the beginning chapters of Quantum Mechanics: An Introduction for Device Physicists and Electrical Engineers by Dr. David Ferry. As I learned these basics, I was amazed by the drastic difference between the behavior of particles and that of classical mechanics objects, especially when it came to the mathematics. This reading in particular was also very interesting because I could see how many of the subjects I learned at school, whether it be calculus, physics, or even history, converged into one topic.
I then made my way through different conventional transmission calculation methods. This was very much a mathematics-intensive process, but in the end, I learned how these traditional methods find transmission values through different potential barriers and wells—that is, how electrons behave and flow in environments with differing energy levels.
After all this preparation and background knowledge, I finally got to the Usuki method itself and how it calculates the transmissions. Without diving too deep into the details of the mathematics, I found that this Usuki method offers a more efficient way than the other methods in outputting electron density transmission graphs. This is because while some traditional methods are unstable due to certain exponential components, the Usuki method uses a discretized potential space to perform its calculations, which, in short, allows calculations to be more controlled and more efficient in longer systems via a numerically stable recursion pattern.
Given my research into these very technical topics, I began to realize just how much work goes into the electrical devices and machines that we all use today. The constant movement toward better, more efficient technologies seems to be primarily driven from the bottom, where the smallest discoveries influence the greatest groundbreaking innovations.
Moving forward, I am excited not only to learn more about how to visualize and manipulate the behavior of fundamental particles but also to test a developing calculation method in order to contribute to semiconductor research.
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