Time-dependent shot noise in multi-level quantum dot-based single-electron devices

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.