Quantum Oscillations of Surface Electronic Structure: Inter-relation Between Quantum Well States, Work Functions and Surface Energies

Quantum size effects (QSE) in ultra-thin metallic film has been a topic of intense investigations. Of particular interests are the inter-relationship between the quantum well states (QWS), work function (W) and surface energy (E{\_}s). In ultrathin Pb films on semiconductors, quantum oscillations of E{\_}s as a function of layer thickness (L) have been investigated by various experimental methods which have all yielded identical results. Experimental studies of work function, however, took a longer journey. Photoemission can probe the work function for an uniform film but in this case uniform film only exists for certain thicknesses. Scanning tunneling microscopy, can probe ``local'' properties for all thicknesses, but the very existence of QWS in these films profoundly affects the measured tunneling decay constant $\kappa $. Consequently, L-dependence of $\kappa $ also depends on the bias voltage. It was then discovered that at a very low sample bias ($\vert $Vs$\vert <$ 0.03 V) the measured $\kappa $ vs. L accurately reflects the quantum size effect on the work function [1]. With this last obstacle removed, we are able to simultaneously measure the W vs. L, E{\_}s vs. L and to correlate these quantities with the measured QWS locations, yielding the quantitative phase relationship between the quantum oscillations of work function and surface energy. To our surprise, instead of a predicted $\raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/ \kern-.15em\lower.25ex\hbox{$\scriptstyle 4$} $ wavelength phase shift, we find that the quantum oscillations of these two quantities are exactly in-phase. A new model is proposed.