Crystal Growth and Design of Sapphire: Experimental and Calculation Studies of Anisotropic Crystal Growth upon Pulling Directions

The anisotropic growth of large-size sapphire single crystals along different pulling directions was studied on the basis of the chemical bonding theory of single crystal growth and practical Czochralski growth. The projection of thermodynamic morphology of sapphire single crystal respectively along [210], [110], [001], and [001] rotated 57.62° directions can be used to confirm the growth directions of surfaces that are preferred to be exposed thermodynamically in Czochralski growth. Starting from these thermodynamically preferred directions, the possible radial directions that are normal to the four typical pulling directions by kinetic controls have been identified by anisotropic chemical bonding distributions of sapphire single crystal. Chemical bonding calculations demonstrate that the lower pulling rate should be designed when <i>R</i>_axial/<i>R</i>_radial > 1, whereas the higher pulling rate should be designed when <i>R</i>_axial/<i>R</i>_radial < 1. The anisotropic chemical bonding conditions demonstrate the lowest chemical bonding density along the radial directions of sapphire single crystal when it grows along the [001] pulling direction. Taking [001] as the pulling direction in practical growth, a ϕ 2″ sapphire single crystal was grown via the Czochralski method with a growth rate of 2–3 mm/h. Our present work shows the effect of anisotropy on the Czochralski growth of large-size single crystals, which can provide a theoretical guide in practical growth from both thermodynamic and kinetic viewpoints