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Dims is almost correct, in that you would only see resonant tunnelling effects at very low temperatures. In other words, at very low temperatures the electrons will sit at very well defined energy levels within the transistors. Under certain biases (voltages), the energy levels on either side of the thin barriers between devices will line up, and electrons ...

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Crystal lattices are classified in a way that is not necessarily the most natural one. A first classification is by their lattice class, which is determined by its associated unit cell, which is not necessarily the same as a fundamental domain for the lattice. There can be different Bravais lattices in each lattice class, determined by possible additional ...

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Just to be clear, the two or more atoms do not have to be of different type. Optical phonons are related to the relative vibrations of atoms within the unit cell, while acoustic phonons describe the relative vibration of different unit cells. Optical phonons arise whenever the unit cell has at least one such degree of freedom, meaning at least two atoms in ...

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You might find the wiki article on this topic helpful. Summarizing: When you have a 1-D box, the energy states of an electron can be given by $$E_n = E_0 + \frac{\hbar^2 \pi ^2}{2 m L^2} n^2$$ Now the things to note are this: Two electrons (with opposite spin) can occupy the same level The Fermi level is the energy of the last electron After each pair ...

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Single particle energy eigenstates for a system of particles in a box are given by $$E_n=\frac{\hbar^2 \pi^2}{2mL^2}\,n^2 + E_0.$$ The Fermi energy for a single particle is, by definition, the value of its energy that exhausts all the possible states given by $N$ indistinguishable particles; in the case at hand, for fermions (electrons), this is given by ...

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The lack of the $e^{-i \omega t}$ term is just because we're using complex wave notation. If you've ever taken an electrical engineering course, it's the same sort of thing that is used there: We're using $A e^{i \omega t}$ to stand for $A \cos (\omega t - \delta)$, with the implicit assumption that we're only interested in the real part of the quantities ...

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