Quantitative basis for the rocking-curve measurement of preferred orientation in polycrystalline thin films

Abstract

A quantitative basis for the rocking-curve measurement of the preferred orientation in polycrystalline thin films is presented. Gaussian functions are used for modeling the density distribution of the normals to the crystal plane around the normal to the specimen surface. An intensity formula for the rocking curve is derived from the kinematical theory applied to the case of asymmetric Bragg reflection. The density distribution is determined by the least-squares fit of a theoretical rocking curve to the observed curve, and a volume fraction of crystallites, whose normals to the crystal plane are present within a defined angular range, can be obtained from it. AlN and Au polycrystalline thin films were used for testing the present procedure. Parameter values of the model function, refined using both synchrotron radiation and laboratory X-rays, agree well with each other within the experimental errors although these intensity data sets were collected under different experimental conditions in instrumentation and wavelength. A distribution of depth-dependent preferred orientation in the AlN thin film was revealed by using double-layer and multiple-layer models. A very small degree of preferred orientation in Au thin films could also be measured. Parallel-beam optics and integrated intensities instead of peak height intensities are important for reliable rocking curve measurement.