Numerical modelling of the diffusion cooling response in superconducting hot-electron mixers

Superconducting bolometric mixers that exploit hot-electron diffusion over electron-phonon inelastic scattering as the quasiparticle cooling mechanism are rapidly becoming a dominant technology for low-noise terahertz spectroscopy. We report on the results of modelling a microbolometer treated as a distributed element, as a refinement of the simple discrete-element model commonly used so far. The diffusion equation governing the hot-electron subsystem is solved numerically for a submicron niobium bridge, in the limit of local thermal equilibrium. There is reasonable agreement between the present mixer performance calculations and experimental data reported in literature. However, this model seems to overestimate conversion gain, perhaps indicating that the finite time required for energy sharing among hot-electrons inside the bridge should not be disregarded. It is also found, in the frame of this work, that terahertz radiation is dissipated more effectively than dc electrical power, which has implications on how mixer sensitivity is calculated.