Arrhenius Plot

In figure 4.1 the dc conductivity of 0.5 µm thick layers of SiOx, measured in the co-planar configuration, is plotted as a function of temperature (30 K≤ T ≤ 300 K) in an Arrhenius plot. Whereas a band conduction model predicts an Arrhenius temperature dependence of the conductivity, the deviating temperature dependence observed in our samples clearly reveals a different conduction mechanism, at least at low temperatures up to room temperature.
Taking the slopes in the Arrhenius plots of figure 4.1 as activation energies results in values at room temperature increasing from 0.12 ± 0.01 eV to 0.35 ±0.02 eV with x increasing from 0 to 1.3. Although these values indeed rise with increasing x, they do not resemble 0.7 eV, as expected according to the hypothesis of a pinned chemical potential around the Si:DB states, as discussed in the last part of the previous section.

The measured values are much smaller and suggest that the electronic processes that are dominant in the conduction, at least up to room temperature, occur in a much narrower energy band around the level of the chemical potential. Because the electronic states in semiconductors around this level within the gap are localized, the transport of charge requires a conduction mechanism through localized states. This mechanism, which is known as hopping conduction, is observed in two well-known varieties, i.e. nearest neighbor hopping and variable range hopping. The latter conduction mechanism is distinguishable from other conduction mechanisms by its different temperature dependence: log σ ∼ T^−1/4 (see section 4.3.1, equation 4.23).

In figure 4.2 the data of figure 4.1 is represented in a log σ versus T^−1/4 plot, clearly showing this temperature dependence over the entire temperature range.