Strain measurement in heteroepitaxial layers—Silicon on sapphire

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Abstract
An x-ray diffraction technique is presented for the determination of the strain tensor in an epitaxial layer grown on a crystallographically distinct substrate. The technique utilizes different diffracting planes in the layer and in a reference crystal fixed to the layer, and is illustrated by application to an ∼4000 Å (001) silicon layer grown on a (01$\overline 1$2 sapphire wafer. The principal strains were measured, and the measured strain normal to the layer was found to agree with the normal strain calculated from the measured in-plane strains within the experimental uncertainty of strain measurement. The principal stresses in the plane of the silicon film, calculated from the measured strains were −0.92 ± 0.16 GPa in the [100] direction and −0.98 ± 0.17 GPa in the [010] direction.