Influence of electron diffraction on measured energy-resolved momentum densities in single-crystalline silicon

Abstract

Electron momentum spectroscopy is used to determine the spectral function of silicon single crystals. In these experiments 50 keV electrons impinge on a self-supporting thin silicon film and scattered and ejected electrons emerging from this sample with energies near 25 keV are detected in coincidence. Diffraction effects are present that give rise to additional structures in the measured spectral momentum densities. Spectra for a specific momentum value can be obtained at different orientations of the crystal relative to the analysers. By comparing these spectra for which the measured momentum density is the same, but the diffraction conditions of the incoming and outgoing electron trajectories differ, one can distinguish between features due to diffraction of the incoming and/or outgoing electrons, and those due to the electronic structure of the target itself. q

EMS Measurement of the Valence Spectral Function of Silicon – A Test of Many‐body Theory

“…In a crystal coherent elastic scattering by the nuclear sites (dynamic diffraction) of the incident and/or the emitted electrons can shift the observed momentum distribution by a reciprocal lattice vector G [41,42,43]. In the present experiment the electron momenta are all very large (k 0 = 62.1 a.u., k 1,2 = 43.4 a.u.…”

“…In this way contributions due to diffraction can be removed on the assumption that there is no interference between the direct and diffracted electron waves. The study of any possible interference effects could lead to additional information on the structure of silicon [41].…”

“…Thus this diffracted beam causes a weak replication of the main spectrum shifted by 2.44 a.u. For the outgoing electrons the diffraction depends on which crystal direction is aligned with the y−axis of the spectrometer [41].…”

“…In the case where the surface normal (the 100 direction) is aligned with k 0 the smallest G 0 contributing to diffraction are of type ±2 ±2 0 (see ref. [41] for a detailed discussion). The smallest vector q that can be accessed is 1.22 a.u.…”

“…shifting density from Γ (1,1,1) to Γ (1,0,0) . Rotation by 10 • around the spectrometer y−axis removes this peak at low binding energies [41]. In this way, by examining the diffracted contributions in regions where the spectral density should be zero, it is possible to remove the diffracted components from the measured spectral momentum density.…”