Germanium material holds great potential applications in low-power, high-mobility field-effect transistors because of their advantages of high electron and hole mobility, narrow bandgap, and compatibility with silicon CMOS technologies. The development of high-quality gate oxide processes is crucial in fabricating high-mobility Ge-based transistors, especially those with high dielectric constant for superior gate control and preferable gate stability. Rare-earth oxides represented by LaLuO₃ have high dielectric constants and high crystallization temperatures, making them potential candidates for Ge-based metal-oxide-semiconductor field-effect transistor (MOSFET) gate technology. In this work, a germanium (Ge)-based oxide dielectric LaLuO₃ is fabricated utilizing a p-type Ge substrate with a (111) crystal orientation and a doping concentration of 1×10¹⁶ cm^–3, and radio-frequency (RF) co-sputtering 2-inch 99.9% La₂O₃ and Lu₂O₃ targets. Systematical investigations are conducted to evaluate the effects of annealing process conditions on the characteristics of the LaLuO₃/Ge MOS gate structure under three specifically designed annealing atmospheres, i.e. nitrogen, oxygen, and a nitrogen-oxygen mixed gas with an N₂:O₂ ratio of 0.999∶0.001. Meanwhile, the influence of annealing pressure is also explored. The results show that annealing in pure oxygen at atmospheric pressure can reduce the hysteresis of gate capacitance, but it can lead to the formation of interface layers. Correspondingly, annealing technique based on high-pressure and low-oxygen-content (0.1% O₂) atmosphere is developed, which not only improves the LaLuO₃/Ge interface quality and suppresses the oxygen vacancy generation, but also achieves an extremely low equivalent oxide thickness (EOT) of 1.8 nm and a hysteresis voltage of only 40 mV, resulting in an ideal LaLuO₃/Ge MOS structure. This work thus provides a high-performance LaLuO₃/Ge gate process solution for Ge MOSFETs.