Using magnetron sputtering with low energy electron beam irradiation, epitaxial growth of CeO₂ layers on Si(100) substrates has been studied for the application to microelectronics. We have found that orientation selective epitaxial (OSE) growth of　 CeO₂(100) and (110) layers on Si(100) is capable by controlling surface potential distribution. With the aim of application to hybrid orientation technology for higher speed CMOS devices, we are studying the hybrid orientation structure of the CeO₂(100) and (110) regions on Si(100) substrates using electron beam-induced OSE growth by reactive magnetron sputtering. Two separate areas of growth are seen, with CeO₂(100) layers found to grow in areas irradiated by electrons during the growth process, and the CeO₂(110) layers growing in the areas without irradiation. The lateral orientation mapping by X-ray diffraction measurements reveal the existence of transition regions between these two orientation areas. The width of the transition region is found to　be considerably large and  decrease proportionally as the logarithm of the underlying Si substrate resistivity. To make a breakthrough in the limitation in reduction of the transition region width, we propose a new method of OSE growth on silicon on insulator (SOI) substrates with lithographically formed trenches. The trenches prevent spread of the potential distribution to the neighboring Si islands. We report the experimental results showing perfect isolation between OSE grown regions having different crystallographic orientations, optimizing the Si layer thickness of SOI and the cross-sectional geometry of the trenches.