Plasmon Scattering Intensity in Small Aluminum Spheres

Abstract

It has generally been assumed that a relative thickness determination in thin samples can be made by observing the variation of the bulk plasmon scattering intensity. This method, of course, relies on the assumption that the plasmon scattering varies with the thickness,1 Here Ip is the plasmon intensity, I0 is the incident beam intensity, λ is the total scattering mean free path, t is the sample thickness, and ɛ is the bulk dielectric constant for the material being probed. It can be shown1 that the unscattered beam intensity is just , and therefore a simple ratio of the plasmon intensity to the unscattered beam intensity would seem to give t, provided ʵ is known. It has been shown by Ritchie2, however, that for thin films two more terms occur in addition to that shown in (1). He found for the scattered intensity, where f and g arc some functions periodic in the thickness t. The third term here is the normal surface plasmon scattering. The second is a surface interference term at the bulk plasmon energy and is a manifestation of a spatial quantization of the bulk plasmon in the direction perpendicular to the film surfaces. (2) can be evaluated at the plasmon frequency ωp,