Antiferroelectricity in ZrO2 and Ferroelectricity in Zr, Al, La Doped HfO2 Nanoparticles
Advances in Materials Physics and Chemistry
The dependence of the polarization P in Hf 1-x Zr x O 2 nanoparticles on electric field, dopant concentration x, size and temperature are studied using the transverse Ising model and the Green's function method. Pure ZrO 2 shows at high electric fields an antiferroelectric behavior. Pure HfO 2 is a linear dielectric in the monoclinic phase. With increasing ZrO 2 content the ( ) P E of HZO shows a ferroelectric behavior. The composition dependence x of the remanent polarization ( ) r P x has a
... n ( ) r P x has a maximum for x = 0.5. For x = 0, pure HfO 2 , and x = 1, pure ZrO 2 , 0 r P = . P increases with decreasing HZO nanoparticle size. The influence of Al and La doping on r P in HfO 2 nanoparticles is also studied. The exhibiting of the ferroelectricity in ion doped HfO 2 is due to a phase transformation and to an internal strain effect. The observed results are in good qualitative agreement with the experimental data. − − − ( ) ij i j J J r r = − in the defect sizes (denoted as d J ) compared to the undoped samples. The radius of the tetravalent Zr ion (86 pm) is a little larger than that of the Hf ion (85 pm), i.e. there is a small tensile strain ( d b J J < ), in agreement with the experimental data A. T. Apostolov et al. d J = ); (2) La ( 451 K d J = ) ions. A similar behavior for the Al concentration dependence of the dielectric constant in HfO 2 thin films is reported by Yoo et al. . The electric properties of La doped HfO 2 NPs are also studied. The radius of the La ion (117.2 pm) is larger compared to the ionic radius of Hf (85 pm) (this means d b J J < ). Batra et al.  have shown that La doping stabilizes the or-A. T. Apostolov et al.