  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.
