Numerical study of silicon crystal ridge growth

• A numerical 2-dimensional model was proposed for the calculation of the size of the crystal ridges.
• The size of the crystal ridges was calculated for the 〈100〉 silicon crystals grown by the Czochralski process.
• It was shown that the crystal ridge growth is sensitive to the physical conditions at the triple phase line.

The size of the ridge-like protrusions appearing on the external surface of dislocation-free 〈100〉〈100〉 silicon crystals grown from a melt was studied theoretically. According to existing models the growth of the ridges is caused by the presence of {111}{111} crystal planes at the crystal–melt interface. They affect the height of triple phase line, free surface orientation and the crystal growth angle. A numerical 2-dimensional model was proposed for the calculation of the size of the crystal ridges. The model included the effect of the undercooling of the crystal–melt interface on the crystal growth angle. The numerical model estimated the effect of the ridge size on the free surface at the triple phase line. The size of the crystal ridges was calculated for the 〈100〉〈100〉 silicon crystals grown by the Czochralski process. It was shown that the crystal ridge growth is sensitive to the physical conditions at the triple phase line.