Tinker with quantum transport models! Download the MATLAB scripts used to demonstrate the physics described in Supriyo Datta's book Quantum Transport: Atom to Transistor. These simple models are less than a page of code, and yet they reproduce much of the fundamental physics observed in experiments.
After downloading, you may want to watch the lectures from Prof. Datta's two courses Quantum Transport: Atom to Transistor (graduate level) or Fundamentals of Nanoelectronics (undergraduate level), which are keyed to specific sections of the book.
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