# Properties that can be deduced from Band structure and DOS

Calculation of band structure and Density of States (DOS) is ubiquitous in matter modelling research publications.

What are some properties that can be deduced from a band structure plot and density of states diagram? Also if possible explain how to deduce them?

Some of the properties we can get from the band structure are:

• Band gap: energy between the bottom of the conduction band (CB) and the top of the valence band (VB). The gap will give you if the material is a metal (zero gap), a semiconductor (gap greater than zero and lower than $$\sim 3eV$$ or insulating (gap $$> 3eV$$). To identify the conduction/valence band, you need to identify the Fermi energy and look for the bands around it.
• The type of gap: direct or indirect gap. If the minimum of the CB is aligned with the maximum of the VB (they have the same value of $$\mathbf k$$) the system has a direct gap. If the are no alignment, the gap is indirect. This has direct implication in optical transitions.
• Electron and hole effective masses. In semiconductor physics, the effective mass is a very useful concept. Assuming that the bottom of the CB (an the top of the VB) are parabolic, the effective mass can be obtained from fitting the expression $$E(\mathbf k) = E_0 + \frac{\hbar^2\mathbf k^2}{2m^*}$$.
• Spin polarization. Normally, the calculations are done considering both spins. In case the system present spin polarization, there would be split of the bands: one set for spin up and one set for spin down.
• Very nice answer overall. However, why do you say in "band gap" that it is restricted to the energy difference between CV and VB "at the Gamma point"? The band gap can be found at any point in the Brillouin zone, not only Gamma. And indeed, as you explain in the next part, the VBM and CBM need not be at the same k-point. – ProfM Jul 30 '20 at 6:38
• @ProfM you are absolute right. Should I add something like "in general" before "at the Gamma point"? – Camps Jul 30 '20 at 15:00
• I would simply remove "in the Gamma point" and then it would be perfect I think. – ProfM Jul 30 '20 at 15:29

I would like to add some information to Camps's answer. In essence, the band structure should consider the information about each quantum state obtained by solving the Kohn-Sham equation for the periodic solids. The quantum state for solids can be formally expressed as:

$$|atom, k, orbital,spin\rangle$$

The band-gap can be considered as global information extracted from the whole band structure while the effective mass can be considered as the deduced information from the local part of the whole band structure.

As the state indicated, you can obtain more information from the projected band structure. [If you use VASP, all related information is printed in the PROCAR file.] Therefore, you can know that each state in the band structure is contributed by atom, orbital, and spin. I will give you some examples:

• Project to the atom (PtSe$$_2$$/MoSe$$_2$$):
• Projected to the orbital (PtSe$$_2$$/MoSe$$_2$$):

• Projected to the spin (MoS$$_2$$):

As for the density of states, the $$k$$ information in each quantum state is integrated.

$$|atom,orbital,spin\rangle$$

What information can be obtained is like the band structure.