The density of states (DOS) is the number of different electron states whose occupation is allowed in a specific energy level, which is (N(states)∙E-1V-1). DOS is a very important concept to describe the properties of a macroscopic system quantum-mechanically. Moreover, it is one of the calculation data frequently used when obtaining the electronic structure of a substance. In terms of an experiment, it can be measured by the photoemission spectroscopy (PES), which is a photoelectron experiment. In addition, in terms of computer simulation, it is usually calculated by using the Kohn–Sham equation.
With a DOS graph, you can obtain the band gap, which is the energy difference between a conduction band and a valence band, as well as electric properties of metal, insulators, and semiconductors. In the case of semiconductors, g(E), and a DOS near band edges (Et), are induced by the following approximate expression. According to the formula, the higher the effective mass (m*) is, the larger the DOS.
Furthermore, you can get the information on the specific heat of a conducting solid, paramagnetic susceptibility, and transport phenomenon, which is contributed by electrons, by interpreting a DOS graph. 
DOS can be applied to the following cases: 👉 Checking the calculation results
The next one shows the DOS of silicon with a 2 × 2 × 2 Silicon bulk and oxygen doped. It is found that, as oxygen is attached to the silicon, the state, which is not seen in the silicon crystal, is created near the Fermi level. By adding Projected DOS (PDOS), it can be checked which atom/orbital induces the state. In this case, it is found that the electron state of the silicon is changed due to the doped oxygen, and, in particular, the state induced from the silicon p orbital is changed.
Figure 1. DOS of Substance having Trap State
The following shows the DOS of the structure that once Co is absorbed to a graphene sheet. When considering spin in DOS, the DOS of spin up/down is distinguished by using a symbol. Different up/down spin DOS shapes indicate there are magnetic properties. In addition, the existence of a different state when PDOS of Co is added means the difference between the up/down spin DOS is induced from Co.
Figure 2. DOS of Magnetic Substance
This weekly tip describes the definition of DOS and the DOS graph, and shows its application cases for easier understanding. The next article will cover how to calculate DOS using the Quantum Espresso module implemented in Materials Square.
 Sachs, M. (1963) Solid State Theory New York, McGraw-Hill Book Company
 Rössler, U. (2009). Solid state theory: an introduction. Springer Science & Business Media.
 Ali, M. O. (1993). Elementary Solid State Physics: Principles and Applications. Addison-Wesley Publishing Company.