Decay channels of gap plasmons in STM tunnel junctions

We study the decay of gap plasmons localized between a scanning tunneling microscope tip and metal substrate, excited by inelastic tunneling electrons. The overall excited energy from the tunneling electrons is divided into two categories in the form of resistive dissipation and electromagnetic radiation, which together can further be separated into four diffierent channels, including SPP channel on the tip, SPP channel on the substrate, air mode channel and direct quenching channel. In this work, we study the enhancement factor, i.e. Purcell factor, of the STM tunnel junctions, which are mediated by the nearby metallic structures. We find that the gap plasmon mode is most likely to couple to the SPP channel on the tip, rather than the SPP channel on the substrate or the air mode. The direct quenching in the apex of tip also takes a considerable portion especially in high frequency region, the enhancement factor of direct quenching in the tip is much higher than the direct quenching in the substrate. We adopt four tips with diffierent apex radii, i.e., 1 nm, 5 nm, 10 nm, 20 nm. When the apex size is small, the frequency dependent enhancement factor from the SPPs contribution has a pronounced peak at 1.55 eV, however, as the radius increases, the peak of enhancement factor in the high frequency region appears, the 1.55 eV peak becomes less dominated. This phenomenon can be attributed to the change of tip shape, in the form of mode coupling. Our results also show a relationship between the direct quenching in the substrate and in the tip. With the larger radius of apex, the ratio of these two part of energy approaches 1, which indicate that the energy distribution of direct quenching is sensitive to the shape of the tip-substrate gap.