Fourier-transform analysis of normal photoelectron diffraction data for surface-structure determination

Abstract

A direct method for surface-structure determination from normal emission photoelectron diffraction (NPD) data is presented. Fourier Following the prediction by Liebsch (1) that diffraction effects are present in photoemission from adsorbate-atom core levels, such effects have been observed in several experimental configurations (2-4). In each case comparison of experimental results with curves derived from microscopic theory based on certain surface structures (5) showed good agreement, thereby establishing photoelectron diffraction (PD) as a technique for structure determination. Unfortunately, PD data analysis appeared to require a scattering-theory computation ofcomplexity up to the low-energy electron diffraction (LEED) level for each trial structure. In this paper, however, we propose a direct method for analysis of normal photoelectron diffraction (NPD) data that is independent of model calculations. This method is based on Fourier transformation of NPD intensity curves to yield peaks in the transform at perpendicular distances d1 + nb, n = 0, 1, 2, ... Here d1 is the adsorbate-substrate spacing and b is the substrate interlayer spacing. Fourier-transform NPD (FTNPD) is thus comparable to extended x-ray absorption fine structure (EXAFS) in its simplicity ofanalysis. The validity of FTNPD is tested by extensive Fourier analysis of theoretical NPD curves. Arguments are presented to show that FTNPD is less dependent on phase shifts than is EXAFS, and the reasons that perpendicular distances dominate the transform are discussed.First we note some similarities between NPD and EXAFS, in which both differ from LEED. The intensity-versus-energy (I/E) curve in NPD is similar in appearance to either a LEED I/V curve or an EXAFS absorption curve. However, like the latter, NPD is atom specific. In fact, both the NPD and EXAFS I/E curves result from (photoelectric) excitation of an atomic core level. Most ofthe diffractive structure in an NPD (EXAFS) curve carries information about the distance from the source atom to other planes (atoms). For both NPD and EXAFS, the diffractive structure appears as sinusoidal modulation of the photoexcitation curve, and for both cases phase coherence between the scattered wave and the primary unscattered wave is provided by their common origin-the source atom. A different mechanism exists in LEED, which is not atom specific and for which coherence must be provided by long-range order over 102-103 A in the sample. Just as in EXAFS, in which multiple scattering effects are unimportant or average out and singlescattering theory prevails (6), the modulation pattern in NPD at higher kinetic energies depends largely on single backscattering. In fact, Li and Tong (7) have shown that only a single backscattering event need be considered to calculate NPD curves for kinetic energies in the 100-to 400-eV range. Finally, in NPD, as in EXAFS, the periodicity in k space of the sinusoidal modulation increases with decreasing d1 where the theoretical curves are calculated over a small rang...