Strain relaxation in single crystal SrTiO$_{3}$ grown on Si (001)

A layer of SrTiO$_{3}$ grown directly on Si may be used as a pseudo-substrate in perovskite deposition. As grown, SrTiO$_{3}$ is compressively strained, however, by subsequent annealing in oxygen at elevated temperature, a strain relieving SiO$_{x}$ buffer layer can be grown between the substrate and the perovskite layer. We perform a systematic study of strain relaxation in SrTiO$_{3}$ films grown on Si by molecular beam epitaxy as a function of the process conditions (annealing time, temperature, and oxygen partial pressure). Using a combination of X-ray diffraction, reflection high energy electron diffraction, and transmission electron microscopy we explore the oxidation and strain relaxation of SrTiO$_{3}$. We compare the kinetics of the buried oxide growth to that predicted by the conventional Deal-Grove model. An understanding of strain relaxation of SrTiO$_{3}$ on silicon can potentially be used to control the SrTiO$_{3}$ lattice constant for lattice matching with functional oxide overlayers.