Numerical investigation of the influence of cooling flux on the generation of dislocations in cylindrical mono-like silicon growth

• Reduce dislocations during seeded growth of mono-like Si by controlling cooling flux.
• Relationship between dislocations and cooling flux has been numerically studied.
• Dislocations are determined by cooling flux difference, not by cooling flux.
• Cooling flux difference in r and z direction is linearly related to square root of maximum dislocations.
• Good control of input and output cooling fluxes during crystal growth is essential.

To effectively reduce dislocations during seeded growth of cylindrical monocrystalline-like silicon by controlling the cooling flux, the relationship between the generation of dislocations and cooling flux has been numerically studied. The results show that the generation of dislocations is determined by the cooling flux difference, not by the cooling flux inside the crystal. Good control of the input and output cooling fluxes during practical crystal growth is essential to reduce the generation of dislocations. Further analysis shows that the cooling flux difference in the radial or axial direction is linearly related to the square root of the maximum dislocation density. In other words, a linear decrease of the cooling flux difference in the radial or axial direction results in a quadratic decrease of the maximum dislocation density. Therefore, the most effective method to reduce dislocations during the cooling process is to decrease the cooling flux difference between the input and output fluxes, i.e., to decrease the energy accumulation or dissipation rate inside the whole crystal.