  The oxidation-related issues in controlling Si doping from the Si source material in oxide molecular beam epitaxy (MBE) is addressed by using solid SiO as an alternative source material in a conventional effusion cell. Line-of-sight quadrupole mass spectrometry of the direct SiO-flux ($\Phi_{SiO}$) from the source at different temperatures ($T_{SiO}$) confirmed SiO molecules to sublime with an activation energy of 3.3eV. The $T_{SiO}$-dependent $\Phi_{SiO}$ was measured in vacuum before and after subjecting the source material to an O$_{2}$-background of $10^{-5}$ mbar (typical oxide MBE regime). The absence of a significant $\Phi_{SiO}$ difference indicates negligible source oxidation in molecular O$_{2}$. Mounted in an oxygen plasma-assisted MBE, Si-doped $\beta$-Ga2O3 layers were grown using this source. The $\Phi_{SiO}$ at the substrate was evaluated [from 2.9x10$^{9}$ cm$^{-2}$s$^{-1}$ ($T_{SiO}$=700{\deg}C) to 5.5x10$^{13}$ cm$^{-2}$s$^{-1}$ (T$_{SiO}$=1000{\deg}C)] and Si-concentration in the $\beta$-Ga2O3 layers measured by secondary ion mass spectrometry highlighting unprecedented control of continuous Si-doping for oxide MBE, i.e., $N_{Si}$ from 4x10$^{17}$ cm$^{-3}$ ($T_{SiO}$=700{\deg}C) up to 1.7x10$^{20}$ cm$^{-3}$ ($T_{SiO}$=900{\deg}C). For a homoepitaxial $\beta$-Ga2O3 layer an Hall charge carrier concentration of 3x10$^{19}$ cm$^{-3}$ in line with the provided $\Phi_{SiO}$ ($T_{SiO}$=800{\deg}C) is demonstrated. No SiO-incorporation difference was found between $\beta$-Ga2O3(010) layers homoepitaxially grown at 750{\deg}C and $\beta$-Ga2O3(-201) layers heteroepitaxially grown at 550{\deg}C. The presence of activated oxygen (plasma) resulted in partial source oxidation and related decrease of doping concentration (particularly at $T_{SiO}$<800{\deg}C) which has been tentatively explained with a simple model. Degassing the source at 1100{\deg}C reverted the oxidation. 
Towards controllable Si-doping in oxide molecular beam epitaxy using a   solid SiO source: Application to $\beta$-Ga2O3