Gate-modulated thermopower of disordered nanowires: II. Variable-range hopping regime

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 ∼ − k e 10 1 mV K B 1 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. efficiency is controlled by its dimensionless figure of merit, with T the temperature, S the Seebeck coefficient or thermopower and Ξ G, respectively the electrical and thermal conductances. As ZT increases, the efficiency moves closer to the Carnot limit. The stronger the particle-hole asymmetry in a system is, the higher S will be. An ideal thermoelectric device should then 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]. Whereas their thermoelectric properties can be easily tuned by gates [6,9], the phononic contribution to thermal transport Ξ ph is suppressed due to the reduced dimensionality [4,5], and a good power output could be achieved by stacking them in parallel [4,7,10]. Furthermore Si-based devices, already under intense investigation [4,5,7,[10][11][12][13][14][15][16], exploit an abundant and non-polluting resource.Most existing works concentrate either on highly doped samples [4,7,8,10,11,13] or on the thermal conductivity of undoped wires [5,12,[15][16][17]. On the other hand, recent studies by Jiang et al [18,19] have rekindled the interest for systems in which electronic transport takes place via phonon-assisted hopping between localised states, of which disordered nanowires with low carrier density are a paradigmatic realization. Whereas in our first paper [1] we focused on the low-temperature coherent regime, in this work we extend the approach reviewed in [18,19] in order to investigate band-edge transport in the (activated) hopping regime. Two simple physical mechanisms have in this regime a synergy which is ideal for thermoelectric conversion [20,21]: (i) a strongly broken...

From Thermal Rectifiers to Thermoelectric Devices

“…The advantage of such ap-proach lies in its simplicity and independence from microscopic details of inelastic processes. Probe terminals have been widely used in the literature and proved to be useful to unveil nontrivial aspects of phase-breaking processes [49], heat transport and rectification [22,23,118,52,24,112,13,120], and thermoelectric transport [73,57,56,75,76,124,126,135,136,122,67,15,11,27,25]. The approach can be generalized to any number n p of probe reservoirs.…”

Nanowire-based thermoelectric ratchet in the hopping regime

“…Note that in Refs. [33][34][35] the contacts were symmetric, and both ν and ξ were chosen energy dependent to infer band-edge properties [56].…”

“…Propagation through the NW takes place via (inelastic) phonon-assisted hops [31,33,34,37]. The transition rate between states i and j , at energies E i and E j , is…”

“…[33,37]). The method yields the nonequilibrium steady-state occupation probabilities f i , and thus the transition rates (3) and (4).…”

“…For completeness, temperature effects are discussed in Appendix A. For this set of parameters, the Mott hopping energy, i.e., the range of energy states effectively contributing to transport, is [33] √ 2k B T /(ξν) = . Having fixed a specific size is no limitation: As we discussed in a recent work [34] the transport coefficients are basically independent of the NW size in the activated regime.…”