An SOI wafer, includes a substrate made from silicon, an electrically insulating layer with a thermal conductivity of at least 1.6 W/(Km) and a single-crystal silicon layer with a thickness of from 10 nm to 10 .mu.m, a standard deviation of at most 5% from the mean layer thickness and a density of at most 0.5 HF defects/cm.sup.2.A process is for producing an SOI wafer of this type, in which a substrate wafer made from silicon is joined to a donor wafer via a layer of the electrically insulating material which has previously been applied. The donor wafer bears a donor layer of single-crystal silicon, with a concentration of vacancies of at most 10.sup.12/cm.sup.3 and of vacancy agglomerates of at most 10.sup.5/cm.sup.3. After the wafers have been joined, the thickness of the donor wafer is reduced in such a manner that the single-crystal silicon layer having these properties is formed from the donor layer, this single-crystal silicon layer being joined to the substrate wafer via the layer of electrically insulating material.