To improve the crystallinity and phase composition of the Hf0.5Zr0.5O2 films, the effects of annealing temperature on metal-ferroelectric-metal devices are studied by electrical measurements, nanobeam electron diffraction (NBD), and TEM. Forming gas annealing (FGA) at 400 o C partially crystallizes the films, and more crystallization can be achieved by FGA at the increasing temperature of 500 o C and 800 o C. After FGA at 400 o C and 500 o C, metastable ferroelectric orthorhombic phase can be obtained as shown by electrical measurements and NBD. By the density functional theory (DFT) simulation, we propose that o-phase formation happens during both the annealing step as well as the cooling step. During the FGA at 800 o C, the metastable orthorhombic phase overcomes the activation barrier and transforms into stable monoclinic phase. In this work, the systematic experimental study of phase transformation, free energy simulation for different phases, and schematic diagrams of free energy for phase transition at different temperatures are reported.