Mechanics-Based Prediction of Total Thickness Variation in Silicon Carbide Substrates during Precision Grinding Based on an Equivalent Wheel-Deflection Model

Abstract

Ultra-precision grinding is a key technology for thinning ultra-hard semiconductor substrates. However, the surface accuracy often deteriorates due to Total Thickness Variation (TTV), which critically affects subsequent device fabrication and packaging. Existing research primarily focuses on correcting preset geometric alignment, such as the tilt between vacuum chucks and grinding wheels, while insufficiently considering the influence of force-induced structural deformation during grinding. In this paper, a mechanics-based model is developed to predict TTV in ultra-hard substrate grinding based on an equivalent wheel-deflection model. The model quantitatively incorporates grinding process parameters and the material and geometric properties of the grinding wheel and substrate. By equivalently representing the force-induced compliance of the grinding system as wheel deflection, the model captures the resulting change in effective inclination angle and its influence on non-uniform material removal. Experimental validation using 4H-SiC substrates shows that the model achieves high accuracy, with an average deviation of less than 4%. Although 4H-SiC is used as the validation material, the proposed framework is extendable to other ultra-hard substrates. This work provides a mechanics-based basis for surface-form prediction and parameter-sensitive TTV compensation in ultra-precision grinding.