Self-Focusing Control for Depth-Precise Wafer Slicing of 4H-SiC in Femtosecond Laser Processing
4H-SiC has emerged as a third-generation chip material because its superior thermal conductivity and high breakdown field enable the material to achieve high power density and higher switching frequencies in power-electronics applications. As chip architectures evolve toward 3D and heterogeneous integration, the mechanical and thermal design space tightens while yield risks grow. In particular, advanced packages require mid-process wafer thinning to < 100 $\mu$m to shorten interconnects and control thermo-mechanical stress. Femtosecond laser slicing for 4H-SiC wafers offers a non-contact processing approach to produce thin layers with low defects, while strong optical nonlinearities obscure the relationship between the laser parameters and the resulting slicing quality. Here, we systematically investigate Kerr-induced self-focusing using a femtosecond laser in 4H-SiC slicing by combining experiments, a semi-empirical analytical model, and numerical ray optics simulations. We demonstrate that the interplay between pulse energy and processing depth governs the self-focusing behavior, which directly correlates with post-separation surface texture parameters and separation stress, thereby linking nonlinear beam propagation to slicing quality. Based on this relationship, we define a processability map in the pulse energy with self-focusing depth space over a normalized irradiance background. Analytically, the model extends the Marburger formula to focused beams by replacing the power ratio with a normalized irradiance. Ray optics simulations capture the geometric features at the self-focusing point and are validated against experimental observations. Within physically defined thresholds, the processability map directly connects laser parameters to separation stress and surface texture metrics, providing practical guidance for depth control beyond trial-and-error.