For the purpose of producing a method for detaching a segment—disposed on a carrier—from a material layer extending in a layer plane and having a specific layer thickness, by means of a laser pulse passing through the carrier in such a way as to detach segments from a material layer with as little thermal stress and as few thermal secondary effects as possible, it is proposed that the laser pulse within a segment layer-component volume butting against the carrier, the said layer-component volume lying in the plane of the layer within an extent of the beam cross-section of the laser pulse and extending transversely to the layer plane via a part of the layer thickness, produces superheated matter of a density similar to the solid state in a state of thermodynamic non-equilibrium and in particular at a temperature above the critical temperature, and that a cohesive, solid partial layer remains in the segment on the side of the layer-component volume opposite to the carrier, the said partial layer being urged away from the carrier by the superheated matter.