Polaronic Hopping Conduction in Vanadium Phosphate Glasses

Abstract

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 glass. The estimated static dielectric constant is found to change from about 30 at room temperature to about 14 at 77°K and it is suggested that this temperature dependence affects calculations of both the disorder energy and the polaron binding energy. The coupling constant for the small polaron in the glass is about 14, indicating that it is a valid assumption to apply polaron theory to the material.

Electrical Conductivity in Mixed Calcium and Barium Iron Phosphate Glasses

“…It is very interesting to note that the values of S decrease with increasing temperature. For instance, S decreases from 0.03 to 0.68 as the temperature decreases from 333 to 493 K. This characteristic feature is well known for the amorphous system and has been attributed to the distribution of relaxation times arising from local disorder [18,19]. This behaviour demands that the loss mechanism should have a very wide range of possible relaxation times t. The values of S are found to be less than unity and dependent on both frequency and temperature (values of S decrease with increasing temperature which agrees with the overlapping large polaron tunnelling (OLPT) model [8,20]; this will be discussed in a future paper).…”

d 1 Electrons in amorphous semiconducting V2O5 and MoO3 compounds. (ESR measurements)

“…Measurements of the ac-and de conductivity, published by Sayer etal. [6], yielded a value of Wo,~0.09 eV for amorphous V2Os-P205.…”

“…The charge carriers (vanadium 3d 1-or molybdenum 4d 1 electrons) are assumed to be small polarons [5,6]. An important result of the small polaron theory is that at a critical temperature T c a transition takes place from polaron band conduction (bandwidth Ip) to a phonon-assisted hopping process.…”

Electrical Conductivity of Semiconducting Tungsten Oxide Glasses

“…It should be mentioned that a number of models have been put forward to explain the frequency dependent conductivity, but they all have limitations. The model of Pollak and Geballe [21] assumes single hops between pair of sites with wide distribution of jump distances, and has been widely used to explain the frequency dependent conductivity [22,23]. This model when applied to V 2 O 5 -P 2 O 5 glass systems yielded highly reasonable values of a and N(E F ) [24].…”