Electron energy loss studies in solids; The transition metal dichalcogenides

Abstract

The theory of characteristic electron energy losses is discussed in terms of the electronic band structure of a solid. The relationship between the observed plasmon energies, the average interband energy gap and the background dielectric constant of the solid is developed. The transmission energy loss spectra of a number of the layer-type transition metal dichalcogenides, MX₂, where M=Zr, Hf, Nb, Ta, Mo and W and X=S and Se, have been measured in the range of 0–50 eV. In the experiments, a beam of 50 keV electrons is incident along the c-axis of the crystals and electrons inelastically scattered through an angle of 1 m radian are selected for energy analysis. This ensures that the momentum transfer and hence the electric vector for the excitations lies in the basal plane of the crystal (E⊥c). Kramers-Kronig analysis has been applied to the energy loss data to deduce the complex dielectric function of each material. From this function, all other ‘optical’ constants, such as the reflectivity, and the oscillator integral function and joint density of states function have been calculated. The results give substantial support to the existing band model for the family of materials and, in addition, provide the basis for a quantitative understanding of the band structure of individual compounds.