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,