Fig. 3: Ferroelectric phase fraction in the doped HfO2 system obtained through Boltzmann distribution theory.

The ferroelectric phase fraction distributions are presented for cases where the doping elements are Ba, Ca, Sr, Al, Y, La, Gd, Si, Sn, Zr, Ti, Pb, V, Nb, and Ta, corresponding to a–o respectively. The horizontal axis represents the doping concentration, while the vertical axis represents the normalized polarization. The color gradient from purple to red indicates an increasing ferroelectric phase fraction.