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Right, so it turns out this is quite simple. See the figure below. (a) shows the 1st BZ resulting from the hexagonal and rectangular unit cells of the honeycomb lattice. Note that the hexagon has twi …

I'd say that your interpretation is basically right. Just keep in mind that a hole is simply an absence of an electron, so you can view any problem from the electron or hole point of view. So, in the …

I would answer "no", but it depends what you mean. An electron going from the conduction to the valence band eliminates both a conduction band electron and a valence band hole. Both helped with conduc …

I don't think we should be so quick to say that there's no way to know without doing a calculation. In some cases, there are rules of thumb: https://journals.aps.org/prb/abstract/10.1103/PhysRevB.98.2 …

Fundamentally, you need to somehow fit a parabola to the conduction band minimum and find the second derivative of the parabola. How you do this depends on the tools at your disposal. If it's truly pe …

The heat of a solid is related to the energy contained in the solid. Hotter solids have more energy in them. Where is the energy in the solid? It's in the atoms and charge carriers moving/bouncing ar …

Can the "well-known properties" be developed using free particles? (I think that the answer should be "yes".) Because the two equations are the same for free particles. For free particles: $$\epsilon\ …

I believe that you are correct; there would be Bloch oscillations and the dc conductivity would arguably be zero (or undefined). However, I don't think that the AC conductivity would be zero. That sai …

You asked two separate questions: Is it possible to draw an EK diagram for the infinite square well? No. Such a diagram only makes sense if the potential is periodic, and that's not the case for an …

First, as you note, in the context of semiconductors, the Fermi level is synonymous with the chemical potential, which is a meaningful quantity at all temperatures. (In contrast, the Fermi energy is s …

As other have noted, it's discrete but with fine enough spacing to treat as continuous. However I disagree that quantum mechanics is the reason. You see the exact same thing in a classical 1-D chain o …

You're right that this can be a tricky point if there is a gap, and I think that a number of common definitions fail in this case. It gets even trickier at zero temperature. Let me give an alternativ …

As Pieter noted, in some metals, arguably, all the carriers are holes. This can be seen by measuring a material's Hall coefficient, which tells you the effective carrier charge, and for a number of me …

Both confusing diagrams show heterostructures (i.e. one device containing different materials), and the different materials can have very different properties. In the first figure: At the left is a m …

Depending on what is shown in the band diagram, you can see if it's a topological insulator. Most band diagrams just show what's going on in the bulk material -- what you'd get with an infinitely larg …