Electron energy band shapes from angular dependent electron energy loss spectroscopy

Abstract

Because the electron energy loss technique can be used to excite interband transitions with a finite momentum transfer, the possibility exists of using this experiment to determine the shapes as well as separations of energy bands. Angular dependent electron energy loss measurements allow the frequency- and wavevector-dependent dielectric function epsilon (q, omega ) to be determined and the relationship of this function to the joint density of valence and conduction states J(q, omega ) is discussed. To examine the feasibility of determining energy band shapes, J(q, omega ) is calculated for typical energy bands in one, two and three dimensions. Rules relating the q dependence of J(q, omega ) to the band shapes are obtained and the sensitivity of the dependence is found to decrease markedly on going from two to three dimensions.