We present measurements of the time-dependent fluctuations of electrical current in a voltage-biased tunnel junction. We were able to simultaneously extract the first three moments of the current counting statistics. Detailed comparison of the second and the third moments reveals that the statistics is accurately described as Poissonian, expected for spontaneous current fluctuations due to electron charge discreteness, realized in tunneling transport at negligible coupling to environment.

The control and measurement of local non-equilibrium configurations is of utmost importance in applications on energy harvesting, thermoelectrics and heat management in nano-electronics. This challenging task can be achieved with the help of various local probes, prominent examples including superconducting or quantum dot based tunnel junctions, classical and quantum resistors, and Raman thermography. Beyond time-averaged properties, valuable information can also be gained from spontaneous fluctuations of current (noise). From these perspective, however, a fundamental constraint is set by current conservation, which makes noise a characteristic of the whole conductor, rather than some part of it. Here we demonstrate how to remove this obstacle and pick up a local noise temperature of a current biased diffusive conductor with the help of a miniature noise probe. This approach is virtually noninvasive for the electronic energy distributions and extends primary local measurements towards strongly non-equilibrium regimes.

We investigate the current noise in HgTe-based quantum wells with an inverted band structure in the regime of disordered edge transport. Consistent with previous experiments, the edge resistance strongly exceeds $h/e^2$ and weakly depends on the temperature. The shot noise is well below the Poissonian value and characterized by the Fano factor with gate voltage and sample to sample variations in the range $0.1