Estimation of residual stresses in single crystal sapphire wafers through eigenmode analysis

Methods for growing high-quality single-crystalline sapphire boules are energy-intensive due to the material's high melting point. Residual stresses and stress gradients due to temperature gradients and/or growth direction may develop during manufacturing process. An approach is developed based on acoustic measurements to resolve residual stresses in sapphire wafers. Experimental analyses reveal distinct resonance frequencies depending on the processing conditions and wafer's original position within the boule. Natural frequencies are calculated for different modes using a finite element model on samples with and without residual stresses. Shifts in resonance frequency between wafers can be explained by the presence of residual stresses of few MPa, which may not be resolved with conventional residual stress measurement methods. The proposed acoustic method demonstrates precision and repeatability in discerning subtle differences even between wafers from a single boule in a non-destructive manner, offering potential for optimization of single-crystalline sapphire wafer production processes.