Fully resolved kinematics of grazing-incidence (e,2e) experiments

The capability of grazing-incidence (e,2e) spetroscopy to map the spectral momentum density ρ(ε, q) of the valence electronic states in surfaces was demonstrated by a pioneering experiment in which both the band structure (binding energy, ε, versus momentum, q) and the momentum density, ρ, were obtained [S. Rioual et al., Phys. Rev. B 57 (1998) 2545]. (e,2e) experiments reveal, in coincidence, after energy and angle selection, the two final electrons generated by the impact of a primary electron on the surface. The momentum resolution achieved by the first experiment was limited because of the integration over the wide solid angle accepted by the ejected-electrons analyzer. This limitation has been overcome in the present work by upgrading the ejected-electrons analyzer with a position-sensitive detector (PSD). The PSD allows us to measure the azimuth angle of the ejected electrons, and hence to collect in a parallel mode (e,2e) spectra that are fully differential in momentum. Preliminary data relative to the ionization of the π-band of highly oriented pyrolitic graphite (HOPG) show that a momentum resolution better than 0.2 Å−1 has been achieved without degrading the overall spectrometer luminosity.