The literature on experiments on a.c. conductivity in various disordered semiconductors is briefly summarized. A theory of the a.c. conductivity, suitable for hopping conduction in the pseudogap of amorphous semiconductors, is developed, and expressions applicable under various conditions are derived. Comparing some of the results with available experimental data, the concentration of localized states in the pseudogap of several materials is estimated.

On the frequency dependence of conductivity in amorphous 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

Dc conductivity measurements have been made between 90 and 520 K on three bulk samples of V 2 O 5 P 2 O 5 glass. Heat treatment is found to result in a reduction of the activation energy at a given temperature and this is most noticeable at low temperatures. The behaviour at low temperatures can be described using Mott's variable range hopping arguments, and at high temperatures by non-adiabatic small polaron hopping between nearest neighbours. At intermediate temperatures a simple model is used in which excitations by optical and acoustic phonons are considered to make independent contributions to the jump frequency. Mott's theory is extended to the polaron case for T> 1 4 ⊖ and is shown to be in good agreement with results. Values for r p (∼2.8 A ) the polaron radius and α(∼3.5 A −1 ) the electron decay constant are shown to be consistent with the model for small polarons. A method is suggested for obtaining α and N ( E F ) from the ac conductivity and the slope of 1nσ versus 1 T 1 4 at low temperatures. Values of N ( E ) are obtained which correlate with those obtained by the previous analysis. This implies that the disorder energy separating adjacent sites Δ 0 is large (∼0.4 eV) in these materials.

Small polaron conduction in V2O5P2O5 glasses

Hopping conductivity in ordered and disordered solids (II)

The dc conductivity of semiconducting vanadium tellurite glasses of compositions in the range 50 to 80 mol% V2O5 has been measured in the temperature region 77 to 400 K. Measurements have been made on annealed samples at different annealing temperatures. Annealing the samples at temperature of about 250°C causes the appearance of a complex crystalline phase resulting in an increase of conductivity. Results are reported for amorphous samples of different compositions. The conductivity of tellurite glasses is slightly higher than the corresponding composition of phosphate glasses, but the general trend of the increase of conductivity and decrease of high temperature activation energy with increasing V2O5 content is similar in the two systems. The data have been analysed in the light of existing models of polaronic hopping conduction. A definite conclusion about the mechanics of conduction (adiabatic or nonadiabatic) is difficult in the absence of a precise knowledge of the characteristic phonon frequency v0. Adiabatic hopping is indicated for v0∼1011 Hz, however this value leads to unreasonably low value for the Debye temperature θD, and higher values for v0∼1013 hz satifiies the conditions for nonadiabatic hopping which appears to be the likely mechanism of conduction in V2O5TeO2 glasses. The low temperature data (< 100 K) can be fitted to Mott's variable range hopping, which when combined with ac conductivity data gives reasonable values of α, but a high value for the disorder energy.

DC conduvtivity of V2O5TeO2 glasses

The dc and ac conductivity and thermoelectric power have been measured as a function of the ratio (V 4+ /V total ) in glasses in the system V 2 O 5 -P 2 O 5 . The conductivity goes through a maximum as the ratio (V 4+ /V total ) is varied but at a much lower value than that expected from a straightforward hopping model (i.e. 0.5) in which all sites contribute equally. The thermoelectric power tends to go through zero but at a different value of (V 4+ /V total ) than the maximum in conductivity. These discrepancies from simple behaviour may be connected with the structural complexity of the glass and at least two suggestions can be made to account for these deviations. The log conductivity versus (1/ T ) plots are not linear and their slopes decrease rapidly at low temperatures. Possible reasons for this behaviour are mentioned. The ac conductivity varies nearly linearly with frequency in the audio- to radio-frequency region and approximately as the square of frequency at higher frequencies. At the same time the high frequency conductivity tends to become independent of temperature. This is almost identical with similar observations in, for instance, chalcogenide glasses.

F.M. Hayatee

Papers

Electronic conduction in vanadium phosphate glasses