Abstract
We study the thermopower of a disordered nanowire in the field effect transistor configuration. After a first paper devoted to the elastic coherent regime (Bosisio, Fleury and Pichard 2014 New J. Phys. 16 035004), we consider here the inelastic activated regime taking place at higher temperatures. In the case where the charge transport is thermally assisted by phonons (Mott Variable Range Hopping regime), we use the Miller–Abrahams random resistor network model as recently adapted by Jiang et al for thermoelectric transport. This approach, previously used to study the bulk of the nanowire impurity band, is extended for studying its edges. In this limit, we show that the typical thermopower is largely enhanced, attaining values larger than and exhibiting a non-trivial behaviour as a function of the temperature. A percolation theory by Zvyagin extended to disordered nanowires allows us to account for the main observed edge behaviours of the thermopower.
Highlights
The conversion of temperature to voltage differences or its inverse, enabling respectively waste heat recovery or cooling, is the purpose of a thermoelectric device
The proper way to tackle this issue is to map the hopping model to an equivalent random resistor network [27] and to reduce it to a percolation problem [26]. Such microscopic approaches are needed for giving precise quantitative predictions, but Motts original argument [28, 29] gives the main ideas: assuming the localisation lengths and the density of states to be constant within a certain window of energies Δ to be explored (ξi ≈ ξ, ν (E) ≈ ν), the electron transfer from one localised state to another separated by a distance x and an energy δE ∝ 1 (D = 1 for us) results from the competition between the elastic tunneling probability ∝ exp − (2x ξ) to do a hop of length x in space and the Boltzmann probability (∝ exp −) to do a hop of δE in energy
We have studied thermoelectric transport in a disordered nanowire in the field effect transistor configuration, focusing on intermediate to high temperatures
Summary
The conversion of temperature to voltage differences or its inverse, enabling respectively waste heat recovery or cooling, is the purpose of a thermoelectric device. An ideal thermoelectric device should exploit to the maximum such asymmetry, while at the same time ensuring a poor thermal and a good electrical conductance [2] Whereas the former requirement is necessary to increase efficiency, the latter is needed for enough electric (cooling) power to be extracted from a heat engine (Peltier refrigerator). From this perspective, semiconductor nanowires appear as very promising central building blocks of flexible, efficient and environmentally friendly thermoelectric converters [3,4,5,6,7,8,9]. Various technical details, skimmed over in the main body for ease of reading, are gathered in the appendices
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