Dielectric Relaxation of Lanthanide-Based Ternary Oxides: Physical and Mathematical Models

Cerium-doped hafnium oxides (CexHf1-xO2) and lanthanum-doped zirconium oxides (LaxZr1-xO2) 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 similar to 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 CexHf1-xO2 and LaxZr1-xO2 are simulated based on the Curie-von Schweidler (CS) or Havriliak-Negami (HN) relationships. Concerning the lightly doped CexHf1-xO2 and LaxZr1-xO2, the data extracted are best modeled by the HN law, while LaxZr1-xO2 with doping level from x = 0.22 to 0.63 are best modelled based on the CS law.