  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.
