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Bachelor's in engineering physics (condensed matter experimental)/EE specializing in semiconductors here. The explanation starting at 4:00 is very accurate. Wh

Bachelor's in engineering physics (condensed matter experimental)/EE specializing in semiconductors here. The explanation starting at 4:00 is very accurate. When he talks about the electrons "feeling" the neighboring atoms, he's talking specifically about a result that follows from the materials being crystalline, that is, having regular ordered structure. The regular structure gives rise to a periodic potential. You plug that periodic potential into the Schrodinger equation and apply continuity conditions and translational symmetry to the wavefunction. Computing the solutions to the Schrodinger equation with those conditions reveals that there are allowed and disallowed energy levels, and also reveals the relationship between energy and momentum in the crystal lattice. You can step through this by reading the wikipedia page on the Kronig-Penney Model. This depends on the periodicity, which obviously can change depending on direction in a crystal. His explanation, and the result that "the" band gap is a single number, isn't dishonest because when we grow semiconductor devices, we grow them such that the crystal is oriented such that current flows in the desired direction, so that simple result holds true. Even his portrayal of the bands leaning down as potential/voltage is applied mirrors how potential change is shown in diagrams of semiconductor devices, see Streetman and Banerjee - Solid State Electronic Devices.

cypherpunks01 3y ago
That's great! Much appreciated, thanks :)
- archontes 3y ago
  Do be careful, though. Some other folks here are saying, correctly, that this glosses over the "direct" or "indirect" nature of a semiconductor. I only very slightly alluded to this when mentioning the relationship between energy and momentum. Trying to make a long story short, it can be the case that in order to transition to another energy level, an electron also has to exchange momentum with something, usually the lattice in the form of quantized vibrations. Photons carry energy but almost no momentum, so an indirect semiconductor (one that requires both energy and momentum exchange for a transition to the conduction band) is usually an abysmal choice for optoelectronics.

cypherpunks01 3y ago

That's great! Much appreciated, thanks :)

archontes 3y ago
Do be careful, though. Some other folks here are saying, correctly, that this glosses over the "direct" or "indirect" nature of a semiconductor. I only very slightly alluded to this when mentioning the relationship between energy and momentum. Trying to make a long story short, it can be the case that in order to transition to another energy level, an electron also has to exchange momentum with something, usually the lattice in the form of quantized vibrations. Photons carry energy but almost no momentum, so an indirect semiconductor (one that requires both energy and momentum exchange for a transition to the conduction band) is usually an abysmal choice for optoelectronics.