Semiconductor device structures with reduced junction capacitance and drain induced barrier lowering, methods for fabricating such device structures, and methods for forming a semiconductor-on-insulator substrate. The semiconductor structure comprises a semiconductor layer and a dielectric layer disposed between the semiconductor layer and the substrate. The dielectric layer includes a first dielectric region with a first dielectric constant and a second dielectric region with a second dielectric constant that is greater than the first dielectric constant. In one embodiment, the dielectric constant of the first dielectric region may be less than about 3.9 and the dielectric constant of the second dielectric region may be greater than about ten (10). The semiconductor-on-insulator substrate comprises a semiconductor layer separated from a bulk layer by an insulator layer of a high-dielectric constant material. The fabrication methods comprise modifying a region of the dielectric layer to have a lower dielectric constant.