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.

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By means of three-dimensional self-consistent simulation, we investigate the time-and frequency-dependent shot noise in multi-level quantum dot (QD)-based double-tunnel junction by analyzing auto-correlation functions and distribution of waiting times between consecutive tunnel events through a given barrier. We derive analytic expressions for correlation and waiting time distributions (WTDs) in the case of a maximum of two electrons in the QD. We separate the contributions of the different evolution paths of the number of electrons in the dot between two consecutive current pulses, called 'basic paths'. The close relation revealed between probabilities, WTDs and correlation functions associated to basic paths allows a good understanding of the specific dynamics in spectral densities. The analytic results show a perfect agreement with those obtained from numerical Monte-Carlo simulation.

Communicated by Kamal BardhanThe 3D Monte Carlo simulation of an Si dot-based double-tunnel junction shows not only the possibility of shot noise suppression down to the Fano factor of 0.5, but also of super-Poissonian noise. The counting statistics of the tunneling events provides a clear interpretation of the different noise regimes according to the balance between the different tunneling rates involved.the Fano factor is also known as the dispersion index in probability theory and in statistics.Many works have been devoted to the SN in resonant tunneling diodes (RTDs), operating either in coherent or sequential regime. Noise suppression is commonly observed in resonant bias while the super-Poissonian noise has been evidenced in the negative differential conductance (NDC) regime, both experimentally [7-9] and theoretically [10][11][12][13][14]. The effects of Pauli exclusion, Coulomb correlations, charge accumulation in the quantum well and the interplay of these effects have been shown to generate both sub-Poissonian noise in the linear regime and super-Poissonian noise in the NDC regime.Coulomb blockade systems, where the granularity of charge is an essential ingredient, are also of strong interest regarding SN. In the case of quantum dots (QDs) coupled to external leads via tunnel junctions, it has been predicted [15] and experimentally observed [6,16] that if the I-V characteristics exhibits well-defined Coulomb staircase, the SN may be suppressed down to the limit F min = 1/2 when the symmetry between in-and out-tunneling rates is achieved. Super-Poissonian SN has been also predicted theoretically in metallic systems with multiple dots capacitively coupled [17][18][19]. It has been also experimentally observed in semiconducting QDs in high bias regime by probing excited states in the dot of long relaxation time [20] and formulated for the general case of nano-objects asymmetrically coupled to the leads giving rise to an NDC regime [5].Theoretical studies of SN in Coulomb blockade systems are commonly based on one of the two following methods. In the Korotkov formalism [21] derived in the framework of the "orthodox" approach to single electron transport, a Fourier transform is performed on the master equation to derive a general expression for the spectral density of current fluctuations [18,22,23]. Alternatively, the method developed by Levitov and Lesovik, known as the full counting statistics (FCS) [24], consists in the evaluation of the probability distribution functions of the number of electrons transferred to the contacts during a given period of time. These probability distributions contain all the information on the terminal currents, their fluctuations and their correlations. Bagrets and Nazarov have extended the theory to propose a general approach to FCS in the Coulomb blockade regime [25]. The framework of FCS has been used successfully to model the experimental data of time-resolved measurements of electron transport through a quantum dot [20]. However, though these methods may be powerful to ...