Abstract
By means of advanced numerical simulation, the thermoelectric properties of a Si-quantum dot-based single-electron transistor operating in sequential tunneling regime are investigated in terms of figure of merit, efficiency and power. By taking into account the phonon-induced collisional broadening of energy levels in the quantum dot, both heat and electrical currents are computed in a voltage range beyond the linear response. Using our homemade code consisting in a 3D Poisson-Schrödinger solver and the resolution of the Master equation, the Seebeck coefficient at low bias voltage appears to be material independent and nearly independent on the level broadening, which makes this device promising for metrology applications as a nanoscale standard of Seebeck coefficient. Besides, at higher voltage bias, the non-linear characteristics of the heat current are shown to be related to the multi-level effects. Finally, when considering only the electronic contribution to the thermal conductance, the single-electron transistor operating in generator regime is shown to exhibit very good efficiency at maximum power.
Highlights
Thermoelectric effects refer to the ability of a material to directly convert internal heat fluxes into electrical power and vice-versa, via the so-called Seebeck and Peltier effects, respectively[1]
According to the rigorous calculations by Valentin et al.[47], the most likely phonon modes activated in such structure at this temperature correspond to spectral functions with full width at half maximum (FWHM) ranging from H = 0.001kBT to 0.05kBT
The case of discrete energy levels is considered as a reference to be compared with the results obtained in the case of Lorentzian broadening of energy levels with aforementioned realistic FWHMs
Summary
DwohmeraeinS5b5a,r5r6,isψda,ns(u→rrf)aacnedinψsLid(→er t)haeretuthneneellebcatrrorineirc which separates arbitrarily the dot domain from the electrode wave functions in the QD and the lead, respectively, and mbarr is the electron effective mass in the tunnel barrier. Since tunneling between dot and electrodes is considered as sequential, electrons are assumed to rapidly lose their quantum coherence in the QD due to interactions in the dot, and in particular to electron-phonon coupling. The consequence of these interactions is a broadening of energy levels, called collisional broadening[57], which is not negligible in Si-QDs57–61. With the introduction of level broadening, the expressions for tunnel transfer rates (3) become From these tunnel rates, we determine the probabilities Pε(n) to find n electrons in the dot with a deviation ε from equilibrium, and the expressions for currents (5–7) are given by.
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