I'm learning about the band theory of solids. I learned that if the valence band is not full, as in a P-type semiconductor, it can conduct electricity because in the valence band there are unoccupied energy levels that electrons can move to. However, I don't understand why the movement between energy levels in an energy band is related to the movement of electrons in a solid.
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1$\begingroup$ Do you understand why a full band does not conduct? $\endgroup$– Jon CusterCommented Jul 23 at 1:20
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$\begingroup$ @JonCuster My understanding is that an electron can only move when it changes to a different energy level. In a fully occupied band, there are no empty energy levels for the electron to move into, so the electron can't move within the solid. $\endgroup$– cosmosCommented Jul 23 at 1:36
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$\begingroup$ Ok, now with some empty places (holes), an electron can take a step to the left, and another electron can take a step to the left into the just-vacated original spot of the first electron, and so forth. Now you can have net conduction. $\endgroup$– Jon CusterCommented Jul 23 at 1:51
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1$\begingroup$ How would it move if it remained in one state? $\endgroup$– Jon CusterCommented Jul 23 at 1:57
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1$\begingroup$ The main difficulty here is to learn to picture "an electron in a solid" as a wave phenomenon with a wave vector. The dispersion diagrams are showing you the energy of the electrons as a function of their k-vectors. If you want an electron to move faster, you have to increase its energy. It is not all that different from kinetic energy of classical objects, but one has to get used to the idea that electrons don't really move like particles. Only their average position shows similarities to classical motion (with come uncertainty). $\endgroup$– FlatterMannCommented Jul 23 at 2:22
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1 Answer
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In the ground state, there is no net current because the group velocities of electrons with opposite wavevectors exactly cancel each other.
When the valence band is full, you cannot make an infinitesimal change of the energy (this is the excitation gap). So the linear response to an electric voltage is zero, and the system is an insulator (or semiconductor).
When the valence band is not full, you can slightly deplete the occupied states near the Fermi surface on one side (say with negative k and negative velocity) and fill empty states near the Fermi energy on the other side (with positive k and positive velocity), resulting in a net current. One has a non-zero response to an inifinitesimal applied voltage, so the system is a conductor.
