A single crystal of semiconductor material is produced by a method of melting semiconductor material granules by means of a first induction heating coil on a dish with a run-off tube consisting of the semiconductor material, forming a melt of molten granules which extends from the run-off tube in the form of a melt neck and a melt waist to a phase boundary, delivering heat to the melt by means of a second induction heating coil which has an opening through which the melt neck passes, crystallizing the melt at the phase boundary, and delivering a cooling gas to the run-off tube and to the melt neck in order to control the axial position of an interface between the run-off tube and the melt neck.