Photoemission Studies of the Alkali Metals. I. Sodium and Potassium

Abstract

Measurements have been made of the photoelectric yield and the photoelectron energy distribution curves (EDC's) on Na and K in the photon energy range 2.3-11.6 eV. The samples were thick films prepared by evaporation onto various substrates in a specially constructed ultrahigh vacuum chamber. The results are interpreted in terms of a model which assumes that each of the three stages of the photoemission process-optical excitation of electrons, transport to the surface and escape across the surface---may be treated independently. The most noteworthy feature of the frequency dependence of the photoelectric yield, expressed in electrons per incident photon, is a sharp drop on passing through the plasma frequency. It is shown that this may be understood in terms of the rapid variations of the optical constants in this region. The EDC's are characterized by a pronounced peak at the high-energy edge which is identified as arising from primary or unscattered electrons. Its width is found to increase with increasing photon energy, an effect which can be understood in terms of the direct (or k-conserving) nature of the optical transitions. The simple theory of direct transitions in a nearly free-electron metal is expounded, and the form of the EDC is derived. It is predicted that the optically excited electrons should originate from initial states which are distributed uniformly between a maximum energy equal to the Fermi energy ${E}_{F}$ and a minimum energy ${E}_{min}$ which varies quadratically with photon energy. In the experimental range, the width ${E}_{F}\ensuremath{-}{E}_{min}$ is predicted to increase with photon energy, in agreement with the observed behavior. However, the predicted shape of the EDC's is rectangular, whereas the observed shape is more triangular. The other main feature of the EDC's is an abudance of electrons at energies below the leading peak. These are identified as electrons which have undergone an inelastic scattering due to electron-electron interactions before emerging from the metal. This region of the EDC may be regarded as a kind of characteristic energy-loss spectrum. Na shows a single, rather wide low-energy peak in this region. K shows a narrower low-energy peak and a broad intermediate bump identified as a plasmon energy loss. This intermediate bump has been seen also in preliminary work on Rb and Cs, and is found to become more pronounced and closer to the leading peak. The systematic trends therefore support the plasmon interpretation. The energy separation of the peaks is more consistent with a surface rather than a volume plasmon loss. The structure identified as plasmon energy loss is, however, superimposed on a large background, which is attributed to energy loss by pair creation. Rough estimates of the relative proportions indicate that pair creation dominates plasmon creation as the main scattering mechanism.