A method for fabricating contact holes in a semiconductor body proceeds from a structure in which: a plurality of trenches isolated from one another by mesa regions are provided in the semiconductor body, and electrodes are provided in the trenches, which electrodes are electrically insulated from the semiconductor body by a first insulation layer, and the upper ends of which electrodes are situated at a deeper level than the upper ends of the trenches. The method comprises the steps of: producing a second insulation layer by subjecting parts of the surface of the structure to a thermal oxidation process, and carrying out a planarization process in such a way that the semiconductor body is uncovered in the region of the mesa regions, and forming the contact holes in the mesa regions using the residues of the second insulation layer remaining after the planarization process as a contact hole mask.