Method for pulling a single crystal composed of semiconductor material from a melt contained in a crucible
Single crystal semiconductor ingots are pulled from a melt contained in a crucible by a method of controlling the pulling the single crystal in a phase in which an initial cone of the single crystal is grown until a phase in which the pulling of a cylindrical section of the single crystal is begun, by measuring the diameter Dcr of the initial cone of the single crystal and calculating the change in the diameter dDcr/dt; pulling the initial cone of the single crystal from the melt at a pulling rate vp(t) from a point in time t 1 until a point in time t 2 , starting from which the pulling of the cylindrical section of the single crystal in conjunction with a target diameter Dcrs is begun, wherein the profile of the pulling rate vp(t) from the point in time t 1 until the point in time t 2 during the pulling of the initial cone is predetermined by means of an iterative computation process.
1. A method for pulling a single crystal composed of semiconductor material having a constant diameter portion with a target diameter Dcrs from a melt contained in a crucible, comprising
pulling the single crystal in a phase in which an initial cone of the single crystal is grown until a phase in which the pulling of a cylindrical section of the single crystal is begun, by:
measuring a diameter Dcr of the initial cone of the single crystal and calculating a change in the diameter dDcr/dt;
pulling the initial cone of the single crystal from the melt at a pulling rate vp(t) from a point in time t 1 until a point in time t 2 , wherein following t 2 the pulling of the cylindrical section of the single crystal in conjunction with the target diameter Dcrs begins, wherein a profile of the pulling rate vp(t) from the point in time t 1 until the point in time t 2 is predetermined, and a difference Δt=t 2 −t 1 is changed during the pulling of the initial cone by iteratively evaluating equations
∂Men H/∂t=vp ( t )− vcr ( t )
∂ Dcr/∂t=vcr ( t )*2 tan β cr ( t )
until the point in time t 2 matches an attainment of the target diameter Dcrs, wherein MenH, vcr and βcr denote a meniscus height, a growth rate of the single crystal and a crystal angle, respectively.
2. The method of claim 1 , further comprising:
feeding heat to a phase boundary between an edge of the single crystal and the melt by open-loop control of a heating power LstR(t) of a ring-shaped heating device arranged above the melt, and
predetermining a profile of the heating power LstR(t) of the ring-shaped heating device from the point in time t 1 until the point in time t 2 by iteratively evaluating the equations such that the growth rate of the single crystal at the point in time t 2 has a target value vcrs.