A process for producing a semiconductor substrate comprising a carrier wafer and a layer of single-crystalline semiconductor material:a) producing a layer containing recesses at the surface of a donor wafer of single-crystalline semiconductor material,b) joining the surface of the donor wafer containing recesses to the carrier wafer,c) heat treating to close the recesses at the interface between the carrier wafer and the donor wafer to form a layer of cavities within the donor wafer, andd) splitting the donor wafer along the layer of cavities, resulting in a layer of semiconductor material on the carrier wafer. Semiconductor substrates prepared thusly may have a single-crystalline semiconductor layer having a thickness of 100 nm or less, a layer thickness uniformity of 5% or less, and an HF defect density of 0.02/cm2 or less.