Locality of information obtained from proximity-electron-tunneling spectroscopy

The locality of the information obtained by the technique of proximity-electron tunneling (PETS) is analyzed, with particular attention to the effects on the measured effective-phonon spectrum $a^{2}F\left(\omega \right)$ of disorder or impurities near the surface of the superconductor electrode. As in conventional tunnel junctions it is determined that the (energy-dependent) electron mean free path determines the maximum depth of the superconductor of which the measured phonon spectrum is characteristic. An averaging length $L\left(E\right)\mathrm{}$ is defined and found to be typically larger in proximity junctions than in conventional junctions. This can make PETS results inherently less susceptible than conventional results to surface disorder of the superconductor.