Nonequilibrium electron cooling by NIS tunnel junctions
  We discuss the theoretical framework to describe quasiparticle electric and heat currents in NIS tunnel junctions in the dirty limit. The approach is based on quasiclassical Keldysh-Usadel equations. We apply this theory to diffusive NIS'S tunnel junctions. Here N and S are respectively normal metal and superconductor reservoirs, I is an insulator layer and S' is a nonequilibrium superconducting lead. We calculate the quasiparticle electric and heat currents in such structures and consider the effect of inelastic relaxation in the S' lead. We find that in the absence of strong relaxation the electric current and the cooling power for voltages $eV < \Delta$ are suppressed. The value of this suppression scales with the diffusive transparency parameter. We ascribe this suppression to the effect of backtunneling of nonequilibrium quasiparticles into the normal metal. 
A. S. Vasenko, F. W. J. Hekking