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

Abstract

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 ofx=0.09and a Ce content ofx=0.1, for whichk-values of33~40were 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 betweenk-values and frequencies. The variations in thek-values up to megahertz frequencies for bothCexHf1−xO2andLaxZr1−xO2are simulated based on the Curie-von Schweidler (CS) or Havriliak-Negami (HN) relationships. Concerning the lightly dopedCexHf1−xO2andLaxZr1−xO2, the data extracted are best modeled by the HN law, whileLaxZr1−xO2with doping level fromx=0.22to 0.63 are best modelled based on the CS law.