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Journal of Nanomaterials
Volume 2012, Article ID 241470, 6 pages
Research Article

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

1Department of Electrical and Electronic Engineering, Xi'an Jiaotong-Liverpool University, Suzhou 215123, China
2Department of Electrical Engineering and Electronics, University of Liverpool, Liverpool L69 3GJ, UK
3Department of Microelectronics, Xi'an Jiaotong University, Xi'an 710049, China
4Department of Materials Science and Engineering, University of Liverpool, Liverpool L69 3GH, UK

Received 18 July 2011; Accepted 4 October 2011

Academic Editor: Shafiul Chowdhury

Copyright © 2012 Chun Zhao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Cerium-doped hafnium oxides (CexHf1xO2) and lanthanum-doped zirconium oxides (LaxZr1xO2) 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 CexHf1xO2 and LaxZr1xO2 are simulated based on the Curie-von Schweidler (CS) or Havriliak-Negami (HN) relationships. Concerning the lightly doped CexHf1xO2 and LaxZr1xO2, the data extracted are best modeled by the HN law, while LaxZr1xO2 with doping level from x=0.22 to 0.63 are best modelled based on the CS law.