Liao, Yi-LunYi-LunLiaoISHIHARA, MasayukiMasayukiISHIHARAChao, Ching-KongChing-KongChaoYU-HSI HUANG2025-09-172025-09-172025-10-15https://scholars.lib.ntu.edu.tw/handle/123456789/732138In semiconductor packaging, thermal and electrical loading during bonding, curing, or burn-in testing generates thermomechanical stresses that often result in cracks and reduced device reliability. This study advances the theoretical understanding of fracture behavior in n-type Bi₂Te₃ thermoelectric materials containing symmetric lip-type cracks by developing a novel analytical framework that accounts for combined mechanical and electrothermal loading at arbitrary angles. Through this model, stress intensity factors (SIFs), full-field stress distributions, and fracture angles are evaluated across varying loading orientations and crack geometries. A key innovation lies in demonstrating that tailored vertical compressive or horizontal tensile preloads can effectively suppress crack-tip stress concentrations induced by thermoelectric effects, with critical thresholds identified for practical application. When suppression is insufficient, the failure initiation and fracture direction can be accurately predicted using the strain energy density criterion (S-criterion), enabling targeted reinforcement to delay or prevent crack propagation. These findings offer novel and actionable strategies to mitigate crack growth during thermal cycling, thereby informing the design of more robust thermoelectric modules and semiconductor devices that operate under complex multiphysics interactions.Electrothermal couplingFracture angleFracture mechanicsStress intensity factorStress suppressionThermoelectric materialsjournal article10.1016/j.ijmecsci.2025.110736