Dielectric relaxation of lanthanide-based ternary oxides: Physical and mathematical models

Cerium-doped hafnium oxides (Ce _x Hf _1-x O ₂) and lanthanum-doped zirconium oxides (La _xZr _1-x O ₂) were investigated. The highest dielectric constants, k, were obtained from lightly doped oxides with an La content of x = 0.09 and a Ce content of x = 0.1, for which k-values of 33 ∼ 40 were obtained. The dielectric relaxation appears to be related to the size of crystal grains formed during annealing, which was dependent on the doping level. The physical and mathematical models were used to analyze the relationship between k-values and frequencies. The variations in the k-values up to megahertz frequencies for both Ce _x Hf _1-x O ₂ and La _xZr _1-x O ₂ are simulated based on the Curie-von Schweidler (CS) or Havriliak-Negami (HN) relationships. Concerning the lightly doped Ce _x Hf _1-x O ₂ and La _xZr _1-x O ₂, the data extracted are best modeled by the HN law, while La x Zr 1-x O2 with doping level from x = 0.22 to 0.63 are best modelled based on the CS law.