The non-centrosymmetric phase of HfO2 with excellent Si compatibility has great importance in integrated photonic circuits, non-volatile memory, and ferroelectric field effect transistors. We report a theoretical study of pressure-induced phase transition from a centrosymmetric m-HfO2 to non-centrosymmetric o-HfO2 with Si doping. The reported phase transition pressures, i.e. 15, 14, 8, and 8 GPa for x = 0, 0.03, 0.06, and 0.09, respectively, for Hf1-xSixO2 are in excellent agreement with available experimental results. With increasing Si concentrations, the transition pressures reduce significantly, which is explained in terms of bond length and charge transfer. The thermal stability of the obtained o-HfO2 phase is examined via ab-initio molecular dynamics up to its synthesis temperature. The negative formation energy also confirms its thermodynamical stability. Density of states indicates the noticeable appearance of Si states in the lower conduction band and an increase in the extent of hybridization between Hf-5d, O-2p, and Si-2p atomic states. The doping changes the nature of band gap from indirect to direct, concurrently reducing the magnitude. The o-HfO2 shows a low value of static dielectric constant, which results in a smaller refractive index (1.82) and lower reflectivity in the infrared and visible regions.