Alloying amorphous GeO$\mathrm{<mrow\; data-mjx-texclass="ORD">2</mrow>}$ with Y$\mathrm{<mrow\; data-mjx-texclass="ORD">2</mrow>}$O$\mathrm{<mrow\; data-mjx-texclass="ORD">3</mrow>}$ has been found experimentally to improve its chemical stability and electrical reliability as a gate dielectric in Ge-based field effect transistors. The mechanism is explained here based on density functional calculations. The GeO$\mathrm{<mrow\; data-mjx-texclass="ORD">2</mrow>}$ reliability problem is correlated with oxygen deficiency defects, which generate gap states near the band-edges of the underlying Ge. These can be passivated through Y doping. This shifts the defect gap state out of the gap up into the GeO$\mathrm{<mrow\; data-mjx-texclass="ORD">2</mrow>}$ conduction band, thus effectively passivating gap states in the GeO$\mathrm{<mrow\; data-mjx-texclass="ORD">2</mrow>}$ layer.