Surface-state resonances in low-energy electron diffraction

Abstract

Theory of scattering resonances at crystal surfaces is developed for low-energy electron diffraction. The resonance mechanism considered involves a quasistationary surface state of the “intrinsic” type. The description is based on equations describing the matching of crystal to vacuum wavefunctions across a selvedge (crystal surface region) containing a surface potential barrier. It is shown that the resonances may be correlated with conditions for emergence of diffracted beams parallel to the crystal surface (grazing emergence), and each resonance is located slightly to the low-energy side of the corresponding grazing-emergence condition. The maximum displacement of a resonance from the corresponding grazing-emergence condition is of the order of the height of the surface potential barrier (≲ 10 eV). The factors affected resonance widths are analyzed. Purely elastic scattering mechanisms confer a resonance width of the order of 0.1 eV. The contribution to the resonance width due to inelastic scattering is estimated to be of the order of 1 eV below the threshold of any dominant electronic excitation of the crystal substrate and ∼ 10 eV above threshold. In the simplest cases, most likely to be realized in the case of narrow resonances, the resonance profile is expected to have the form deriving from a Breit-Wigner amplitude term. A comparison with experiment and with previous theory is given. It is suggested that the study of surface-state resonances may be of value in the characterization of crystal surfaces, because the resonance location is highly sensitive to the scattering potential in the immediate vicinity of the surface.