Statistics of rare events in single-electron devices

Developments in fabrication and control of nanoscale devices have made precise single-electron counting possible. Due to the improved stability of these devices, increasing amounts of data can be collected leading to unprecedented statistics. These features have enabled the experimental verification of various statistical physics concepts, such as fluctuation relations and Maxwell's demon, with high precision. The recent theory results on extreme fluctuations in the entropy produced by a system, and first passage times, have not yet been verified experimentally. The experimental studies of these theoretical concepts using single-electron devices are the focus of this thesis. The thesis starts with a brief introduction to the physics of single-electronic devices used in the experiments along with the experimental setup used to study them. Next, the experimental methods used to fabricate the samples and the basic sample characterization techniques are presented. Later, the theoretical concepts are discussed and compared to the experimental results. This part starts with the probability distribution of the filtered telegraph signal from a bistable system, here a single-electron transistor. The filtering is done in two different ways: low pass filtering and finite time-averaging of the signal. The former allows us to propose a new method to obtain the transition rates between two states of the bistable system using the cumulants of its distribution. The latter allows us to see the rare fluctuations of current and observe theoretically predicted elliptic tail of the logarithm of the averaged current distribution. Next, the stochastic entropy produced by a system is discussed. This part also includes the properties of its distribution and its minimum value. The theory is presented along with the experimental observations. Finally, an introduction to the theory of first-passage-time distributions is provided.