Method for determining and regulating a diameter of a single crystal during pulling of the single crystal

1. A method for determining a diameter (dK) of a single crystal during the pulling of a cylindrical section of the single crystal and of an end cone of the single crystal from a melt in a crucible of a device for pulling the single crystal, comprising

determining the diameter (dK) of the single crystal at an interface with the melt, from

a first lowering rate (v S ) of a surface of the melt relative to the crucible,

a first lifting rate (vK), with which the single crystal is raised relative to the crucible, and

a conservation of mass,

additionally determining a d K ′ diameter of the single crystal during the pulling of the cylindrical section of the single crystal by means of observing a bright ring on the surface of the melt,

employing the additionally determined dK diameter of the single crystal as a correction, a plausibility check, or a comparison of the determined diameter (d K ) of the single crystal, and wherein

either a variation of a height and/or of a shape of a boundary region between the melt and the solid single crystal is taken into account during the determination of the diameter (dK) of the single crystal by means of a correction factor in a transition region between a cylindrical section of the single crystal and the end cone,

or the determination of the diameter of the single crystal is interrupted in a transition region between a cylindrical section of the single crystal and the end cone, when a predetermined variation of a height and/or of a shape of a boundary region between the melt and the solid single crystal occurs.

2. The method of claim 1 , further comprising determining a second lowering rate (v*S) of the surface of the melt relative to the device, and a rate (v*T) with which the position of the crucible relative to the device is varied, in order to take into account the first lowering rate (v S ) of the surface of the melt relative to the crucible.

3. The method of claim 1 , wherein a rotation of the crucible and a variation of the rotation are taken into account during the determination of the second lowering rate (v*S).

4. The method of claim 1 , wherein a second lifting rate (v*K), with which the single crystal is raised relative to the device, and a rate (v*T) with which the position of the crucible relative to the device is varied, are determined in order to take into account the first lifting rate (vK) with which the single crystal is raised relative to the crucible.

5. The method of claim 1 , wherein a density difference between the density of the liquid material of the melt and the density of the single crystal is taken into account during the determination of the diameter (dK) of the single crystal.

6. The method of claim 1 , wherein the diameter of the crucible at the position of the surface of the melt is taken into account during the determination of the diameter (dK) of the single crystal.

7. The method of claim 1 , wherein a diameter (dT) of the crucible is taken into account during the determination of the diameter (d K ) of the single crystal during the pulling of the end cone of the single crystal ( 200 ), and the accuracy of the determination of the diameter (dK) of the single crystal is increased by correcting the diameter (dT) of the crucible by a constant offset.

8. The method of claim 1 , wherein noise suppression by means of a filter, an observer and/or an adaptive filter, is carried out during determination of the diameter (dK) of the single crystal.

9. The method of claim 1 , wherein the diameter (dK) of the single crystal which is determined is used as a variable to be regulated during the pulling of the constant diameter portion of single crystal.

10. The method of claim 1 , wherein the diameter (dK) of the single crystal which is determined is used as a variable to be regulated during the pulling of the end cone of single crystal.

11. The method of claim 9 , wherein the first lifting rate (vK) and/or the second lifting rate (v*K) of the single crystal, a rate (vT) with which the position of the crucible is varied, the power of one or more heaters for heating the melt and/or temperatures of the device, and/or a rotation rate of the single crystal and/or of the crucible are used as manipulated variables during the pulling of the single crystal.

12. The method of claim 10 , wherein the first lifting rate (vK) and/or the second lifting rate (v*K) of the single crystal, a rate (vT) with which the position of the crucible is varied, the power of one or more heaters for heating the melt and/or temperatures of the device, and/or a rotation rate of the single crystal and/or of the crucible are used as manipulated variables during the pulling of the single crystal.