Accurate determination of surface orientation of single-crystal wafers using high-resolution X-ray rocking curve measurements

Theoretical models of the variations of the peak positions of X-ray rocking curves as a function of the azimuthal angle of a single-crystal wafer have been proposed. These models completely describe the variations of the peak positions both when the surface normal of a wafer is parallel and when it is not parallel to the rotation axis of the goniometer used. Based on the models, an accurate measurement method for the surface orientation of a single-crystal wafer with a small surface miscut of <∼3° has been proposed through rocking curve measurements using a high-resolution X-ray diffractometer. The method measures the misalignment of the sample surface normal with respect to the rotation axis of the goniometer as well as the surface orientation of the wafer. The surface orientation has been measured for a 6 inch (152.4 mm) single-crystal sapphire wafer, and the misalignment of the surface normal from the rotation axis was determined. The results were compared with those from a different method. In addition, a simple and accurate method to obtain the surface orientation of a wafer is proposed by measuring only four rocking curves, two each at two sample azimuths 180° apart.