1) A video describing how one creates and uses a model of a 1-dimensional metal. Starting with a 1D atom with a single electron (in the ground state), this model brings many atoms together to create the simplest approach to modeling a metal that I know of. In general, a metal must have a partially filled band; this one has a half-filled band. (A lot of cool physics is associated with systems with a half-filled band (or a very nearly half-filled band. High temperature superconductors, Mott insulators, Peierls instabilities...) But we will use the half-filled band to help us understand the basic nature of a metal, which is that it has a boundary where the states go from being occupied to being unoccupied -- rather abruptly! This is associated with Enrico Fermi and called the Fermi edge or Fermi surface and there is a specific k and energy where that occurs, $k_F$, $E_F$. Conductivity, current flow, in the presence of an electric arises from a shifting of the boundary. The electric field breaks the symmetry (of left and right being equivalent), shifts the boundary to one side, and then there is a net current associated with the uncompensated electrons.
The second video introduces a 1D model of a semiconductor. This is necessarily more complex because a semiconductor must have 2 bands: one that is fully occupied and one that is empty (to begin with). The occupied one is called the valence band; the empty one is called the conduction band. One of the goals of semiconductor physics is to find a way to get some electrons into the empty conduction band. This video presents the model and discusses how to do that (get electrons in the CB) by doping. That is, by substituting an atom with an extra electron at a few random points in the lattice with the hope that that extra electron will escape into the conduction band.
The second video introduces a 1D model of a semiconductor. This is necessarily more complex because a semiconductor must have 2 bands: one that is fully occupied and one that is empty (to begin with). The occupied one is called the valence band; the empty one is called the conduction band. One of the goals of semiconductor physics is to find a way to get some electrons into the empty conduction band. This video presents the model and discusses how to do that (get electrons in the CB) by doping. That is, by substituting an atom with an extra electron at a few random points in the lattice with the hope that that extra electron will escape into the conduction band.
I tried to make a 3rd video dealing with hole doping and the very interesting and subtle question of how a few empty states in the valence band behave as if they were mobile positively charged "electron-like" carriers. These are created by doping with "acceptor" atoms, atoms that need one more electron to meet their bonding-related obligations. Anyway, the sound didn't work, but here is the tiff from that.
Is E_0 equal to the atomic ground state energy? I feel like we never showed that in class.
ReplyDeletei don't think we ever showed that. Just discussed conceptually how a band might center around the energy of the atomic state it comes from. You would find a more rigorous treatment by searching "tight binding".
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