Collective Excitation Spectroscopy in Superconductor-Semiconductor Tunnel Junctions

The transfer-Hamiltonian description of the influence of electron-boson interactions on the electrical characteristics of metal-semiconductor tunnel junctions is extended by considering the combined effects of electrode self-energy phenomena and boson-assisted tunneling. The current associated with these processes is evaluated for superconducting metal electrodes described by the pairing model as well as for normal metal electrodes. Numerical evaluations of the conductance are made using models and parameters appropriate for the description of the influence of electron (hole) interactions with optical phonons ($\mathrm{energy}\cong \hslash {\omega }_0$) on the tunneling characteristics of metal contacts on boron-doped silicon.