Nonlocal dislocation-density-based crystal plasticity simulation of the dislocation evolution in single crystal sapphire

With the growing demand for single-crystal and semiconductor materials, the design and control of defect-free single crystals have become a central focus in both research and industrial development. In this context, an established nonlocal dislocation-density-based crystal plasticity (CP) framework is extended and parameterized to simulate the evolution of dislocations in single-crystal sapphire during crystal growth and cooling. The model incorporates both mobile and dipole dislocation densities and accounts for their spatial transport, enabling an accurate description of dislocation generation, motion, and redistribution under large thermal gradients. The CP model is implemented within a thermo-mechanically coupled finite-element framework and validated against experimental measurements obtained from etched sapphire wafers. The simulations reproduce the measured dislocation-density trends and predict the formation of the characteristic dislocation pattern associated with the anisotropy of slip systems in sapphire. Using the validated model, optimized process parameters and furnace configurations are derived. The results show that a properly designed heating configuration combined with the derived growth and cooling rates can produce sapphire crystals with significantly reduced dislocation densities, minimal wafer deflection, and no cracking. The resulting nonlocal CP model thus provides a physically consistent and computationally efficient design tool for optimizing manufacturing processes in sapphire and other single-crystal semiconductors.