A review of dielectric data for a wide range of solids proves the existence of a remarkable ‘universality’ of frequency and time responses which is essentially incompatible with the multiplicity of currently accepted detailed interpretations. Certain unique features of the universal behaviour strongly suggest the dominant role of many-body interactions.

The ‘universal’ dielectric response

A brief description is given of the various manifestations of the universal fractional power law relaxation processes, which are contrasted with the classical or Debye law. It is shown that the universal law is indeed found in a remarkable variety of physical and chemical situations, and this is deemed to merit a special attempt at finding a suitably general theoretical model. Several such models are briefly described, and a novel very general approach based on the so-called energy criterion is introduced. It is concluded that it is not yet possible to establish with certainty the validity of any of the models. >

The universal dielectric response

A brief review of the history of ac ionic and electronic conduction in disordered solids is given, followed by a detailed discussion of the simplest possible realistic model: the random free‐energy barrier model. This model assumes conduction takes place by hopping, where the hopping charge carriers are subject to spatially randomly varying energy barriers. The model is solved in the continuous time random walk and in the effective medium approximation, and it is shown that the two solutions are almost indistinguishable. In the random free‐energy barrier model, the frequency‐dependent conductivity is completely determined by the dc conductivity and the dielectric loss strength. The model correctly predicts all qualitative features of ac conduction in disordered solids, and a comparison to experiment on a large number of solids shows that the model is also quantitatively satisfactory.

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The random free-energy barrier model for ac conduction in disordered solids

The frequency dependence of the dielectric response of solids shows an apparently bewildering variety of patterns, virtually none of which corresponds to the classical Debye behaviour. However, a wide ranging critical analysis of the existing wealth of data shows that the dielectric loss obeys power-law dependences on frequencies, both below and above any loss peaks that may be present. This corresponds to power-law dependences on time under step-function excitation and it applies completely generally regardless of the detailed physical and chemical nature of the materials in question and also applies equally to dipoles, ions and hopping electrons as the polarizing species. Moreover, the power-law responses persist down to the lowest temperatures in the milliKelvin range, thus proving the importance of non-thermal transitions. The power laws are characterized by exponents in the range ± 1 and they cover as special cases the complete range of the observed types of response, from virtually frequency-independent “flat” losses often seen in low-loss materials, through various forms of asymmetric loss peaks to strongly dispersive behaviour in which both the real and the imaginary components of the susceptibility vary almost inversely with frequency. The “universality” of the power law strongly suggests the dominance in all materials of a common mechanism of dielectric relaxation and this is found in many-body interactions which provide a model capable of explaining the totality of the observed responses of solids, including both the frequency- and the temperature-dependence. In this interpretation, the classical one-particle Debye law represents but a singularity in a more general behaviour and is usually overshadowed by the new many-body mechanisms.

A new understanding of the dielectric relaxation of solids

Studies of the electrical conductivity of semiconducting oxide glasses are reviewed in the framework of Mott's theory for such materials. An examination of the conduction processes in semiconducting oxide glasses confirms the applicability of the polaronic hopping model of electrical transport. Some deviation from Mott's theory are observed in phase-separated glasses. The thermal activation energy for conduction appears to be the dominating factor which controls conductivity, although in many cases the pre-exponential factor also has a great influence on conductivity. The diffusion-like conduction mechanism in a system of randomly distributed ions is probably not applicable to glasses that exhibit some kind of order in the structure, such as clustering.

Electrical properties of semiconducting oxide glasses

Conductivity and dielectric properties of semiconducting glass of composition 80% V2O5:20% P2O5 have been measured as a function of frequency from dc to 3.6 GHz over a temperature range from 77°K to 420°K. A fit of the dc results to a model of polaronic hopping conduction leads to an activation energy due to disorder ΔW=0.09 eV at 77°K and an optical phonon energy of 0.053 eV compared to a calculated Miller‐Abrahams energy of approximately 0.12 eV. The real and imaginary parts of the ac conductivity are shown to increase with frequency according to power law σ=Aωs, where s=0.85 to 0.95, and it is found that the dielectric behavior can be described by a Debye‐type relaxation behavior only if a broad distribution of relaxation times exists. The results are shown to be consistent with a model of ac conduction normally applied to impurity‐doped broad‐band semiconductors, and differences between the temperature dependence of the dc and ac conductivity are attributed to a distribution of site energies in the gl...

Polaronic Hopping Conduction in Vanadium Phosphate Glasses

The temperature dependence of the DC conductivity in the semiconducting phase of undoped and Al, Cr, and Ti-doped VO2 has been interpreted with the aid of AC conductivity and thermopower measuremen...

A. Mansingh

Papers

Polaronic Hopping Conduction in Vanadium Phosphate Glasses

Transport properties of impurity-doped VO2