First-Principles Calculating the Stress Response of $\mathrm{E}_{2}(\text{TO})$ Raman Phonon Deformation Potential in 4H-SiC under Mechanical Loadings

H-SiC is widely employed in power electronic devices operating under high frequencies, voltages, and temperatures due to its exceptional physical properties. However, its inherent high hardness and elastic modulus induce inevitable residual stress during device fabrication. Raman spectroscopy, which leverages lattice dynamics, offers an effective, non-destructive, rapid, and contactless method for measuring these stresses. Nevertheless, its accuracy critically depends on precisely determining the Raman phonon deformation potential constant. This work investigates mechanically induced Raman shifts in 4 H -SiC via firstprinciples calculations and in-situ Raman spectroscopy under hydrostatic and non-hydrostatic stress conditions. The <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbf{E}_{2}$</tex> (TO) and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$A_{1}(L O)$</tex> phonon modes exhibit sensitivity to hydrostatic stress, whereas <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$A_{1}(L O)$</tex> remains largely unaffected under shear, reflecting directional vibrational differences. Theoretical predictions and experimental measurements agree well within 16 % error, highlighting the effectiveness of Raman-based stress detection for 4 H -SiC. This integrated theoretical-experimental approach provides a robust framework for stress and strain analysis, facilitating the design and fabrication of nextgeneration 4H-SiC electronic devices.