Structural stability and polarization analysis of rhombohedral phases of HfO2

Since the experimental observation of a rhombohedral phase of hafnium oxide, there remains controversy over whether this phase belongs to the R3 or R3m space group. Moreover, the origin of polarization in these two rhombohedral phases has not been comparatively elucidated. Here, we present a theoretical study comparing the relative stability and ferroelectricity of the R3 and R3m phases of HfO2, representing two potential forms of heavily Zr-doped ferroelectric thin films of hafnia found recently. We comprehensively investigate their structural stability and polarization response under in-plane compressive strain. A phase transition from R3 to R3m is discovered under biaxial compressive strain. The direction and magnitude of polarization in both phases can be tuned by strain. Through symmetry mode analysis, we elucidate the improper nature of ferroelectricity. These findings may advance understanding of ferroelectricity in hafnia thin films.