Czochralski Growth System Research Articles

Flow transitions in Czochralski oxide melts

The interface inversion observed in Gd3Ga5O12 and other oxide systems with the resulting wave formation in the molten oxide has been found to represent a form of baroclinic instability. With suitable modifications, the correlations developed for baroclinic instabilities in simulated meteorological systems can be applied to the Czochralski geometry. Furthermore, it has been found that the radial liquid temperature gradient in a RF Czochralski growth system is most strongly influeced by the crucible radius with the furnace insulation playing a secondary role.

The effect of mechanical instability on crystallization rate in czochralski growth system

AbstractThe effect of mutual displacement of crucible and crystal or melt level change on crystallization rate is described in one‐dimensional heat‐transfer approximation. It is found that Czochralski growth system is very sensitive to mechanical instability and crystallization rate follows the jitter pattern. As an example crystallization rate behaviour is examined for fluorite and silicon crystal growth.

Crystallization Rate Behaviour under Change of Czochralski Growth System Parameters

AbstractA comparative analysis of growth system parameters' (pulling rate, melt temperature and crucible position or melt level) change influence on crystallization rate in Czochralski growth system is represented.

The melt temperature change influence on the crystallization rate in czochralski growth system

AbstractThis paper opens a series of publications about growth system parameters change influence on the crystallization rate. The influence of crucible melt temperature fluctuations and mechanical instability will be investigated. In approximation of one‐dimensional heat transfer the behaviour of crystallization rate in case of crucible melt temperature small change is investigated in this paper. As an example characteristic time values and system sensitivity are given for fluorite and silicon crystals.

The effect upon Czochralski growth of periodic modulation of the growth rate

In this paper we describe the results of a mathematical treatment of the Czochralski growth system when the growth rate is periodically modulated. Such a modulation simulates the effect of fluctuations in temperature which occur in the melt from which the crystal is grown. In this treatment we consider the system in the limits Sc → ∞, R → ∞, σ → 0, Δ → 0, where Sc is the Schmidt number, R is the Reynolds number of the liquid phase, σ the Prandtl number, and Δ the ratio of the solution diffusivities in the liquid and solid phases. Here we describe the effect of the modulation upon the solute, temperature and velocity fields. The velocity filed is perturbed by an amount O(Sc -1/2) from the steady-state flow induced by the rotation of the crystal, while the temperature field in the liquid exhibits a three-region structure. (Here the symbol O( x) means of order x. We use it here in its mathematical sense. That is if y = O( x), then there exists a constant k independent of y and x such that - kx < y < kx for all x.) A solute boundary layer of thickness O(Sc -1/2) forms adjacent to the crystal interface in the liquid. When the crystal does not melt back the effect of solute diffusion in the solid is confined to a perturbation O(Δ). However if the crystal melts back the effect of solute diffusion in the crystal becomes important, producing a time dependent solute boundary layer in the crystal.