THICKNESS DETERMINATION OF THIN-FILMS BASED ON X-RAY SIGNAL DECAY LAW

A non-destructive method for evaluation of the thickness of films over bulk substrates is presented, This method is based on evaluation of t he parameters of the decay part of the x-ray signal ratio. For a selec ted energy range of each film thickness it is demonstrated that the de cay 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 lar ger than a critical value. The experimental results are compared to th ose obtained by two theoretical methods and a Monte-Carlo approach. Th e first method is based on solution of the Boltzmann transport equatio n for the electron beam, an approach developed by one of the authors f or e-beam lithography. The second is based on a previously developed s emi-empirical formula for the x-ray depth distribution function. The e nergy dependence of the signal ratio is also discussed using this appr oach. (C) 1998 John Wiley & Sons, Ltd.