Method for producing solid-state layers, in particular for use as wafers, having the following steps: providing at least one workpiece for detaching the solid-state layers, wherein the workpiece has at least one exposed surface, generating and/or providing a carrier unit for receiving at least one solid-state layer, wherein the carrier unit has at least one receiving layer for holding the solid-state layer, a detachment layer being superimposed at least in certain portions on said receiving layer, connecting the receiving layer at least in certain portions to the exposed surface of the workpiece, to form a composite structure, wherein the detachment layer surrounds the workpiece at least in certain portions in a peripheral direction and wherein the receiving layer and the detachment layer are in contact with one another, subjecting the composite structure to an internal and/or external stress field in such a way that the solid-state layer is detached from the workpiece along a plane extending within the workpiece, by crack propagation, wherein the crack initially propagates in the region of the detachment layer and is introduced into the workpiece by means of the detachment layer, characterized in that, when the composite structure is subjected to the stress field, the crack for detachment of the solid-state layer initially propagates within the detachment layer in such a way that a part of the detachment layer is separated off, wherein, in the peripheral direction of the workpiece, the detachment layer is configured in such a way, in particular at a distance of less than 10 mm, preferably of less than 5 mm, and particularly preferably of less than 2 mm, from the workpiece, that the crack profile in the detachment layer and in the workpiece lies in the same plane. providing at least one workpiece for detaching the solid-state layers, wherein the workpiece has at least one exposed surface, generating and/or providing a carrier unit for receiving at least one solid-state layer, wherein the carrier unit has at least one receiving layer for holding the solid-state layer, a detachment layer being superimposed at least in certain portions on said receiving layer, connecting the receiving layer at least in certain portions to the exposed surface of the workpiece, to form a composite structure, wherein the detachment layer surrounds the workpiece at least in certain portions in a peripheral direction and wherein the receiving layer and the detachment layer are in contact with one another, subjecting the composite structure to an internal and/or external stress field in such a way that the solid-state layer is detached from the workpiece along a plane extending within the workpiece, by crack propagation, wherein the crack initially propagates in the region of the detachment layer and is introduced into the workpiece by means of the detachment layer, characterized in that, when the composite structure is subjected to the stress field, the crack for detachment of the solid-state layer initially propagates within the detachment layer in such a way that a part of the detachment layer is separated off, wherein, in the peripheral direction of the workpiece, the detachment layer is configured in such a way, in particular at a distance of less than 10 mm, preferably of less than 5 mm, and particularly preferably of less than 2 mm, from the workpiece, that the crack profile in the detachment layer and in the workpiece lies in the same plane.