Thickness determination of thin films based onx-ray signal decay law

Abstract

A non-destructive method for evaluation of the thickness of films over bulk substrates is presented. This method is based on evaluation of the parameters of the decay part of the x-ray signal ratio. For a selected energy range of each film thickness it is demonstrated that the decay part follows an exponential law. The physical parameters involved in this law are the energy exponent and a constant that depends mainly upon the film thickness. The values found for the energy exponent are in the range 2.0–3.0. This is confirmed in a variety of cases (Al/Si, Ti/Si, Cu/Si, Pt/Si, Cu/Ni, Ti/Au and Pt/Au) for film thicknesses larger than a critical value. The experimental results are compared to those obtained by two theoretical methods and a Monte-Carlo approach. The first method is based on solution of the Boltzmann transport equation for the electron beam, an approach developed by one of the authors for e-beam lithography. The second is based on a previously developed semi-empirical formula for the x-ray depth distribution function. The energy dependence of the signal ratio is also discussed using this approach. © 1998 John Wiley & Sons, Ltd.