Isolated oxygen impurities and fully oxidized structures of four stable two-dimensional (2D) SiS structures are investigated by {em ab initio} density functional calculations. Binding energies of oxygen impurities for all the four 2D SiS structures are found larger than those for phosphorene, due to the lower electronegativity of Si atoms. The most stable configurations of isolated oxygen impurities for different 2D SiS structures are decided and the corresponding 2D structures with saturated oxidation (SiSO) are predicted. Among all the four fully oxidized structures, $alpha$-SiSO is demonstrated to be stable by phonon spectra calculations and molecular dynamics (MD) simulations. Electronic structure calculations indicate that $alpha$-SiSO monolayer is semiconducting with a direct band gap of ${approx}2.28$~eV, which can be effectively tuned by in-layer strain. The value of band gap and thermodynamic stability are found depending sensitively on the saturation level of oxygen.
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