the crucible is fully filled with molten semiconductor material and has been raised to the maximum extent the cooling body 9b is made of a heat resistant solid material having high thermal conductivity such as metal like silver which forms the lower part of the cooling means which comes up close to the surface of the melt the cooling body 9b like the heat shield is constructed as a tube is arranged coaxially with respect to the single crystal and preferably has a diameter tapered toward the melt the duct system 9a and the cooling body 9b are in areal contact with one another and are linked by fastening means 12 such as a low melting solder joint the gap 20 between the bottom edge of the cooling body 9b and the surface of the melt 23 is preferably from 10 to 150 mm the gap 21 between a bottom edge 22 of the cooling body 9b and a crystallization front 24 of the growing single crystal 7 is preferably from 25 to 60 mm the cooling body 9b has an inside surface 26 which faces the single crystal 7 and which inside surface 26 is a heat radiation absorbing surface the cooling body 9b has an outside surface 28 situated opposite the inside surface 26 and the outside surface 28 is a heat radiation reflecting surface the advantages of the.