Quantum computing is expected to break the computing power bottleneck with the help of quantum superposition and quantum entanglement. In order to fabricate the fault-tolerant quantum computer for encoding quantum information, it is important to improve the cryogenic mobility of silicon-based metal oxide semiconductor field effect transistor (MOSFET) with thin gate dielectric layer as much as possible. Based on a thin SiO2/HfO2 stacked dielectric, we investigate the effect of post-deposition annealing (PDA) temperature on the MOSFET cryogenic transport properties. The results show that silicon atoms will diffuse into the HfO2 to form silicate during PDA, leading to the HfO2 dielectric constant decreases. As the PDA temperature increases, the proportion of monoclinic hafnium oxide decreases and tetragonal phase increases gradually. The oxygen vacancy content increases gradually, resulting in the fixed charge density increases and the mobility decreases. The contribution of the forming gas annealing (FGA) to the mobility enhancement is clarified and the HfO2 recrystallisation process is revealed from the perspective of long-time annealing. Finally, the mobility peak of silicon MOSFET with thin SiO2/HfO2 dielectric is enhanced to 1387 cm2/(V·s) at 1.6 K, which provides a technical pathway for the development of silicon-based quantum computation.