Limitations in cooling electrons by normal metal - superconductor tunnel junctions

We demonstrate both theoretically and experimentally two limiting factors in cooling electrons using biased tunnel junctions to extract heat from a normal metal into a superconductor. Firstly, when the injection rate of electrons exceeds the internal relaxation rate in the metal to be cooled, the electrons do no more obey the Fermi-Dirac distribution, and the concept of temperature cannot be applied as such. Secondly, at low bath temperatures, states within the gap induce anomalous heating and yield a theoretical limit of the achievable minimum temperature.