Scanning tunneling microscope light emission: Effect of the strong dc field on junction plasmons

The observed energies of the localized surface plasmons (LSPs) excited at the tip-sample junction of a scanning tunneling microscope, as identified by spectral peaks in the light output, are very significantly redshifted with respect to calculations that use standard optical data for the tip and sample material, gold in this case. We argue that this anomaly depends on the extreme field in the sub-nm tunneling proximity of the tip and the sample, across which a dc bias (1--2 V) is applied. Finite element modeling analysis is presented of a gold nanosphere-plane (NS-P) combination in tunneling proximity and, crucially, in the presence of a high static electric field ($\ensuremath{\sim}{10}⁹\phantom{\rule{0.16em}{0ex}}\mathrm{V}/\mathrm{m}$). It is argued that the strong dc field induces nonlinear corrections to the dielectric function of the gold via the effect of a large background polarizability through the nonlinear, ${\ensuremath{\chi}}⁽³⁾$ susceptibility contribution. When fed into the model system the modified optical data alters the LSP cavity modes of the NS-P system to indeed reveal a large redshift in energy compared to those of the virgin gold NS-P system. The net outcome may be regarded as equivalent to lowering the bulk plasmon energy, the physical interpretation being that the intense field of the tunneling environment leads to surface charge screening, effectively reducing the density of free electrons available to participate in the plasmon oscillations.