Electronic properties and stabilities of bulk and low-index surfaces of SnO in comparison withSnO2: A first-principles density functional approach with an empirical correction of van der Waals interactions

Abstract

The electronic properties and stabilities of SnO and $\mathrm{Sn}{\mathrm{O}}_{2}$ bulk materials and their low-index surfaces are investigated by density functional theory. An empirical method has been adopted in this study to account for the van der Waals interactions among the Sn-O layers in the bulk and low-index surfaces of SnO. Compared with $\mathrm{Sn}{\mathrm{O}}_{2}$, the structural and electronic properties of SnO bulk and its low-index surfaces present some unique features due to the dual valency of Sn. In SnO, the $s$ orbital of Sn has larger contributions than its $p$ and $d$ orbitals in the first valence band (VB) and the $p$ orbital of Sn has a larger contribution than its $s$ and $d$ orbitals in its conduction band (CB). In $\mathrm{Sn}{\mathrm{O}}_{2}$, the $p$ and $d$ orbitals of Sn play an important role to form the upper part of the VB and its $s$ orbital dominates in forming the lower parts of the VB and the CB. In both oxides, the $s$ orbital of O forms the second VB with lower energy and its $p$ orbitals are involved in forming the first VB and the CB. The calculated bulk modulus and cohesive energy agree well with the experimental measurements. By constructing all possible symmetrical low-index surfaces of SnO and the (111) surface of $\mathrm{Sn}{\mathrm{O}}_{2}$, our results reveal that the calculated surface energies of SnO stoichiometric surfaces are lower than that of the corresponding surfaces of $\mathrm{Sn}{\mathrm{O}}_{2}$ due to different bonding between Sn and O in these two oxides. The calculated stabilities of the low-index stoichiometric surfaces of SnO are in the order $(001)g(101)∕(011)\ensuremath{\ge}(010)∕(100)g(110)g(111)$ while the order in the case of $\mathrm{Sn}{\mathrm{O}}_{2}$ is $(110)g(010)∕(100)g(101)∕(011)g(001)g(111)$. The calculated relationships between surface free energies $[\ensuremath{\gamma}(p,T)]$ and oxygen chemical potentials $[{\ensuremath{\mu}}_{\mathrm{O}}(p,T)]$ indicate that the nonstoichiometric O-terminated (110) and (111) surfaces of SnO could be more stable than their corresponding stoichiometric ones when the ${\ensuremath{\mu}}_{\mathrm{O}}(p,T)$ reaches its higher O-rich bound, and one Sn-terminated nonstoichiometric (111) surface of $\mathrm{Sn}{\mathrm{O}}_{2}$ could be more stable than its stoichiometric ones when the ${\ensuremath{\mu}}_{\mathrm{O}}(p,T)$ falls into its lower O-poor region. During surface formation from the bulk, the stable surface usually has small atom displacements. For both SnO and $\mathrm{Sn}{\mathrm{O}}_{2}$ the atoms on the (111) surface have larger relaxations than on their other low-index surfaces.