Two-Electron Photon Emission from Metallic Quantum Wells

Unusual emission of visible light is observed in scanning tunneling microscopy of the quantum well system Na on Cu(111). Photons are emitted at energies exceeding the energy of the tunneling electrons. Model calculations of two-electron processes which lead to quantum well transitions reproduce the experimental fluorescence spectra, the quantum yield, and the power-law variation of the intensity with the excitation current.

Figure 1

Fluorescence spectra from Na monolayers on Cu(111). (a) 2 ML Na, $U=1.42\mathrm{V}$, $I=100\mathrm{n}\mathrm{A}$. (b) 0.6 ML Na, $U=1.80\mathrm{V}$, $I=357\mathrm{n}\mathrm{A}$. Solid lines serve to guide the eye. The data have been corrected for detector response. However, due to uncertainties of the rapidly decreasing detector sensitivity at photon energies below $\sim 1.25\mathrm{e}\mathrm{V}$ the correction is reliable only at higher photon energies. The insets show the uncorrected data as measured (in counts vs wavelength in nm).

Figure 2

Intensity of quantum well emission (dots, $1.45\mathrm{e}\mathrm{V}<h\nu <2\mathrm{e}\mathrm{V}$, corrected for detection efficiency) and emission due to inelastic tunneling (circles, $1.1\mathrm{e}\mathrm{V}<h\nu <1.45\mathrm{e}\mathrm{V}$) vs current $I$ evaluated from 830 fluorescence spectra of a 0.6 ML coverage at $U=1.8\mathrm{V}$. As a guide to the eye a slope of $I^{1.5}$ is indicated (line).

Figure 3

“Allowed” and “forbidden” light emission calculated for a model system with QWS at $E_1=0.2\mathrm{e}\mathrm{V}$ and $E_2=2.5\mathrm{e}\mathrm{V}$. Results are shown for the various currents indicated and a voltage $U=2\mathrm{V}$. The thickness of the Na overlayer was set to 0.613 nm, corresponding to 2 monolayers.