Determination of the x-ray elastic constants of solid thin films

Abstract

A new experimental method for determining the x-ray elastic constants (S1 and (1/2)S2) of thin films is proposed. The curvatures of the single-crystal substrates before and after depositing thin films are first measured using a high-resolution x-ray rocking curve technique with high-quality monochromatic and high-intensity synchrotron radiation. The residual stresses in the films are then calculated from the change in substrate curvature based on the well-known modified Stoney's equation. The formulae for calculation of S1 and (1/2)S2 are deduced based on measured residual stress and the lattice spacing dψ versus sin2ψ curves before and after a mechanical loading, while the magnitude of the external loading does not need to be known. Values of (1/2)S2 of films can even be obtained without loading. Pb(Zr 0.52Ti0.48) and LaNiO3 films grown on a single-crystal silicon substrate using pulsed laser deposition are employed to demonstrate the measurement method. © IOP Publishing Ltd.