The density of electronic states (DOS) quantifies the number of electronic states having a given energy in the material considered. In other words, it represents the number of states available to electrons. It is a function that only depends on energy.
The density of states is an important parameter for the calculation of the electronic, optical, chemical and magnetic properties of materials.
The densities of partial states for the Bi and S atoms are shown in the following figures:
From Figure V.8, we note that the region of -10 to 7 eV in the valence band is dominated by the states s of Bi and the region of -5 at the Fermi level and that of the conduction band is dominated by the states p of Bi. We also note that the contribution of the 5d states of Bi is nonexistent in the region of the valence band and even in the region of the conduction band, it presents only a small contribution of the same order as that of the states 6s and 6p. of the same atom from energy 5.3 eV.
From the figure in V.9, we see that the region of -10 to 7 eV in the valence band is dominated by the states s of S and the region of -5 at the Fermi level and that of the band of conduction is dominated by the states p of S.
From the partial densities of Bi2S3 (Fig. V.10), we see that the 6s states of Bi and the 3s states of S form the mean group of bands with an energy interval of - 10.48 to -7.13 eV. The highest group of bands in the region of the valence band which lies between -5.06 eV and the energy of Fermi EF is due to the hybridization of the 6p states of Bi and the 3p states of S. The bands of energy in the interval 1.24-5.3 eV in the region of the conduction band are composed of the 3p states of S and the 6p states of Bi. In the region of 5.3 to 15 eV, the energy bands are due to an equitable contribution from the 3p states of S and 6p of Bi.
The total densities of the Bi1 atom, the S1 atom and the crystal are presented in the following figure:
As seen in the figure (V.11), there is a narrow peak centered at around -11 eV. It is dominated by the states of the Sulfur atom. Note that the contribution of the atom S is equal to that of B except for the region of -5 eV at the Fermi level.
The total densities of the atoms Bi1 and Bi2 and those of the atoms S1, S2 and S3 are shown in the following figures:
We also see in the figure (V.12) that the states of the atoms Bi1 and Bi2 have almost equal contributions. The small difference in contribution is due to the non-equivalent coordination of the Bi atoms. We also see that the structural imbalance of the atoms S1, S2 and S3 has left an impact on the contribution of their p states in the high valence group bands (Fig. V.13)
We can tuy the nature of the chemica bonding from the DOS
We take the following picture
The chemical bonding character of Bi2S3 can also be studied from the density of the states. From the partial densities of the figure above, it is clear that the main mechanism of the chemical bond is the hybridization between the 6p states of Bi and the 3p states of S. The chemical bond has a covalent character and ionic at the same time, covalent because the 6p states of Bi and the 3p states of S are strongly hybridized and degenerate over a large part of their extension, and ionic since the relative quantity of the 6p states of Bi and the 3p states of S is different below and above Fermi level. Below the Fermi level, the 3p states of S dominate and above Fermi level, the 6p states of Bi dominate.
My name is Dr Abderrahmane Reggad. I'm a 54 year old and I am a researcher in materials' sciences. 
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