General methods for the determination of the stiffness tensor and mass density of thin films using Brillouin light scattering: Study of tungsten carbide films

摘要

Methods of film preparation and data evaluation are presented to determine the stiffness tensor and mass density of thin films using Brillouin light scattering from surface phonons. The combined use of stepped films of progressively increasing thickness d, and an optimized variation of the magnitude of the surface wave vector q_‖ provides a particularly wide range of uniformly distributed values of the product q_‖d in the study of the velocity dispersion of the observed surface acoustic waves. Furthermore by the independent variation of q_‖ and d, the microstructure can be assessed as a function of film thickness. In the present case of tungsten carbide (WC) films on a silicon substrate, being a slow-on-fast system, the Rayleigh mode and several Sezawa modes are observed. Using the extensive velocity dispersion data, five independent material parameters of the WC films, i.e., four elastic constants and the mass density, are determined by two independent approaches. One employs a least-squares fit to the experimental velocity dispersion curves to determine these material parameters, whereas the other investigates the structure of the parameter space in the vicinity of the solution being sought by a Monte Carlo technique. Both approaches yield identical and self-consistent results. In a Green's-function formulation that uses the vertical displacement component of the acoustic excitations at the free surface, the experimental Brillouin spectra are simulated in the discrete as well as in the continuous part of the mode spectrum.