Abstract
Using a one-dimensional tight-binding Anderson model, we study a disordered nanowire in the presence of an external gate which can be used for depleting its carrier density (field effect transistor device configuration). In this first paper, we consider the low temperature coherent regime where the electron transmission through the nanowire remains elastic. In the limit where the nanowire length exceeds the electron localization length, we derive three analytical expressions for the typical value of the thermopower as a function of the gate potential, in the cases where the electron transport takes place (i) inside the impurity band of the nanowire, (ii) around its band edges and eventually (iii) outside its band. We obtain a very large enhancement of the typical thermopower at the band edges, while the sample to sample fluctuations around the typical value exhibit a sharp crossover from a Lorentzian distribution inside the impurity band towards a Gaussian distribution as the band edges are approached.
Highlights
Semiconductor nanowires emerged a few years ago as promising thermoelectric devices1
Since thermoelectric conversion strongly varies from one sample to another in the coherent regime, we have carefully investigated the mesoscopic fluctuations of the thermopower around its typical value
We have shown that the thermopower is Lorentzian-distributed inside the impurity band of the nanowire and that its fluctuations follow the behavior of the density of states at the Fermi energy when the gate voltage is varied
Summary
Semiconductor nanowires emerged a few years ago as promising thermoelectric devices1 In comparison to their bulk counterparts, they provide opportunities to enhance the dimensionless figure of merit ZT = S2σT /κ, which governs the efficiency of thermoelectric conversion at a given temperature T. We will mainly consider nanowires of size N larger than their localization length ξ, characterized by exponentially small values of the electrical conductance This drastically reduces the output power associated with the thermoelectric conversion. To study thermoelectric conversion in this crossover regime would require to use the scaling theory discussed in Ref.20,21 Another reason to consider N ≫ ξ is that the delay time distribution (which probes how the scattering matrix depends on energy) has been shown to have a universal form in this limit.
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