This study presents the fabrication of amorphous hafnium oxide (HfO_x) films with a remarkably high dielectric constant of up to 41.57 at room temperature. This accomplishment is synergistically paired with both low leakage current and a smooth interface, thereby striking an optimal balance between insulating properties and capacitive coupling. Specifically, we concurrently achieve a low leak-age current ranging from 5.89 to 50.1 nA cm^-2 and a high dielectric constant ranging from 30.99 to 41.57 by varying the oxygen flow rate. The high κ-value is attributed to the cubic-like short-range order in the HfO_x structure. X-ray diffraction reveals a direct crystallization path to cubic HfO₂ at an unusually low annealing temperature of 500 ^oC, while also noting the concurrent formation of mono-clinic HfO₂, which reduces the κ-value to 19. This finding is of considerable significance as the cubic phase of HfO₂ is typically realized at markedly higher temperatures, often exceeding 1000 ^oC.