FIRST-PRINCIPLES STUDY OF ELECTRONIC PROPERTIES OF SnS THIN FILMS
Nowadays solar energy conversion becomes one of the most dynamically growing branches of the high-technological industry. Modern solar cells are promising in terms of cost-effectiveness as well as ease of fabrication. However, most of materials used for fabrication of thin-films solar cells are toxic and rare. In contrary to that, tin sulfide (SnS) does not have these disadvantages. It consists of elements which are abundant in nature and possesses attractive optical properties. Tin sulfide can be experimentally formed in several phases and stoichiometries. It was reported as being a semiconductor both theoretically and experimentally. Unfortunately, the SnS low-dimensional structures are less investigated. Futherwe present the results of theoretical simulation of electronic properties of two-dimensional SnS thin films as well as the band gap modification depending on the film thickness or surface orientation.
The energy spectra of bulk SnSalong the high-symmetry directions are presented in Fig. 1. Both phases of tin sulfide appeared to be indirect-gap semiconductors, that correlates well with experimental data. The theoretical band gap values are 0.90 and 0.32 eV for α-SnS andβ‑SnS, respectively, while the experiment gives ~1.0-1.5 eV. The distinctive feature of electronic structures is that the valence band minimum (VBM) is not located at the Γ point as it usually happens in semiconductors (like Si or GaAs). The conduction band minimum (CBM) for β‑SnS is located at the Γ point while for α-SnS it lies in the Γ–Y direction. That can be explained by rather complex crystal structures with non-ideal atomic positions.
Figure 1. The band structures of bulk orthorhombic α-SnS (a) andβ‑SnS (b). Zero at the energy scale corresponds to the Fermi energy.
The band structures of SnS 6-layer films for three surface orientations are plotted in Fig. 2. It is evident that materials in both phases remain semiconductors. Moreover, the β‑SnS films with (100) and (001) surfaces are characterized by the direct-gap in the Γ point. The behavior of the highest valence and lowest conduction bands for α-SnS (100) and β‑SnS (010) surfaces are similar to that for bulk compounds.
Figure 2. The band structures of orthorhombic α-SnS (a) and β-SnS (b) 6-layer films. Thick dot‑dashed line corresponds to the highest valence/lowest conduction bands of the bulk material. Zero at the energy scale corresponds to the Fermi energy.
The detailed analysis of the projected density of states (DOS) has shown that independently on the phase and, the valence band near the Fermi level (‑2...0 eV) is characterized mainly by hybridization of 3p‑electrons of S with 5s‑ and 5p-electrons of Sn. The conduction bands near the Fermi level are defined mainly by 5p-electrons of Sn with small admixture of S 3p‑electrons. The similar behavior has been observed previously for bulk SnS. Moreover, it was found that the states near the Fermi level both for valence and conduction bands are mainly defined by the electrons of Sn and S atoms lying far from the film surface. The only exception is α-SnS (010) in which the surface atoms play the main role. The analysis of the interatomic distances has shown that the Sn-S bond length at the surface is smaller than that for the deep‑lying atoms and for bulk compound, except for α-SnS (100) and β‑SnS (010) surfaces where these values are equal.
The dependence of the band gaps on the film thickness is presented in Fig. 3. It is obvious that with the increase of the film thickness the band gap values decrease for all compounds and surfaces considered. The values approach to the band gaps in the bulk and in the case of (001) surface of α‑SnS they go even smaller.
Figure 3. The band gap values of orthorhombic α-SnS (a) and β-SnS (b) films depending on the film thickness (d). The horizontal dashed line corresponds to the band gap in bulk compounds.
The electronic properties of thin films of two orthorhombic phases of SnS with three surfaces (100), (010) and (001) have been studied by first-principles calculations. All structures were shown to be semiconductors. The band gaps of thin films, which are larger, than in bulk materials due to the quantum‑confinement effect, decrease with the increase of the film thickness approaching to the values of bulk SnS. For most cases the electronic states near the gap region are defined by the bulk rather than by the film surface.