# [Physics] Band structure and Density of states (DOS)

density-functional-theorydensity-of-stateselectronic-band-theorysemiconductor-physics

Can someone explain how these two plots are related?

How are the peaks in the right are associated with the left figure?

The dos graph is on right. the band structure is on the left.

The DOS (right) is the density of the lines of the band structure for a specific energy. So there's no line that pass through -1 so there's no DOS there. At -0.5, there a almost flat line. On the dos, you can see a clear spike at that value.

That's how both graph are related.

Now let's further the explanation step by step.

1. There is 1 kpt for every 2*4π^3/V in the k-space. This is similar to a free electron enclosed in a volume (The most basic solution of Schrodinger equation).

2. For every energy, you can draw a fermi surface in k space. It is an isosurface of energy. For a free electron, the Fermi surface is a sphere. Every point on the surface of this sphere has an energy ε.

3. Take 2 energy : ε and ε + dε. You can find the volume between these 2 sphere. By that mean, you can also find the number of kpts between these 2 spheres. If dε is infinitesimal, you have the DOS.

I need to revise what the electronic band structure (left) exactly means. For now, I can say it is where the k point are located in the DOS. In other words, it is in which direction of k-space the surface ε+dε has expanded a lot compared to the surface ε.

Edit: You can only think of the electronic band structure with a sphere as a trivial case since a sphere can not grow more in a direction, it must grow equally in every direction. You will need to think of a Fermi Surface instead.