Application of the Boltzmann Transport Equation in the Thickness Determination of Thin Films

Abstract

The diffusion approximation of the Boltzmann transport equation for an electron beam incident on a sample, is used to derive an analytical expression for the depth distribution of X-ray production Φ(ρz). This solution is used as a starting point for a numerical evaluation of Φ(ρz) in the case of a multicomponent sample. Results are applied to the prediction of the signal ratio involved in coating thickness measurements. Good agreement is found with experimental results and an exponential decay law is established.