The ac conductivity of disordered and dielectric solids. II. Distributions of relaxation times for clusters

V. Halpern

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

For the calculation of the contribution to the ac conductivity σ(ω), or to the dielectric loss ε{lunate}″(ω), from transitions of charge carriers between states in a small cluster, the rate equations provide the most convenient formalism. These equations are derived for carriers obeying either classical or Fermi-Dirac statistics, and their formal solution is presented in terms of a distribution of relaxation times. The application of our results to amorphous semiconductors reveals, inter alia, an error in previous applications of the pair approximation in the case of uncorrelated charge carriers obeying Fermi-Dirac statistics. Our method also has considerable advantages over previous methods for the numerical calculation of σ(ω) for any given real or model system. For dielectrics, our analysis permits some general predictions as to the number of relaxation times that will be observed, and their dependence on temperature in some cases.

Original languageEnglish
Pages (from-to)336-349
Number of pages14
JournalPhysica B: Physics of Condensed Matter & C: Atomic, Molecular and Plasma Physics, Optics
Volume79
Issue number4
DOIs
StatePublished - 1975

Bibliographical note

Funding Information:
The Author thanks the Israel Academy of Sciences and Humanities and the Royal Society for a travel grant to enable him to spend the academic year 1973/4 at Chelsea College, where part of this work was performed, and Professor A. K. Jonscher for his hospitality there.

Fingerprint

Dive into the research topics of 'The ac conductivity of disordered and dielectric solids. II. Distributions of relaxation times for clusters'. Together they form a unique fingerprint.

Cite this