Depth-resolved strain measurements in thin films by energy-variable X-ray diffraction

An energy-variable synchrotron diffraction technique is established as a novel method for the depth-resolved measurement of d-spacings and residual strains in polycrystalline films. Depth sensitivity is achieved by the controlled varying of the X-ray energy and, hence, X-ray penetration into the sample. In this paper, an analytical expression for the energy-dependent shape of the diffraction peak taken from a polycrystalline thin film is given. We show that the maximum diffraction intensity recorded in the detector originates at a certain depth, which is composed of the film thickness and the X-ray penetration length. This finding opens a way for strain measurements with high depth resolution by varying the X-ray energy and, as a result, the X-ray penetration, in small enough steps. The technique developed is applied to the characterization of thin-film Co/Cu multilayers produced by electro-deposition. Strain variations with spatial periodicity of the order of 100 nm are clearly seen. An ability to collect experimental data in steps of 10 nm when working not far away from absorption edges is demonstrated.