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 afterdepositing thin films are first measured using a high-resolution x-ray rocking curvetechnique with high-quality monochromatic and high-intensity synchrotron radiation. Theresidual stresses in the films are then calculated from the change in substrate curvaturebased on the well-known modified Stoney’s equation. The formulae for calculation ofS1 and (1/2)S2 are deduced based on measured residual stress and the lattice spacingdψ versus sin2ψ curves before and after a mechanical loading, while the magnitudeof the external loading does not need to be known. Values of(1/2)S2 of films can even be obtained without loading.Pb(Zr0.52Ti0.48) and LaNiO3 films grown on a single-crystal silicon substrate using pulsed laser deposition are employedto demonstrate the measurement method.