Suppression and Prediction of Crack Tip Stress Concentration in Thermoelectric Elastic Materials

Abstract

In 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 investigates the fracture behavior of an n-type Bi2Te3 thermoelectric material containing a symmetric lip-type crack under combined mechanical and electrothermal loading. Through theoretical modeling, the stress intensity factors (SIFs), full-field stress distributions, and fracture angles are evaluated across varying loading angles and crack shape factors. The results reveal that applying vertical compressive or horizontal tensile preloads can significantly suppress crack-tip stress concentrations caused by thermoelectric effects. When suppression is not sufficient, the fracture angle, rather than the entire trajectory, can be predicted using the strain energy density criterion (S-criterion), enabling targeted reinforcement to delay or prevent crack propagation. These findings provide strategies to prevent crack propagation during thermal cycling for guiding more robust thermoelectric modules and semiconductor structures under multiphysics interactions.

Keywords: Thermoelectric materials, Electrothermal coupling, Electronic packaging reliability, Stress intensity factor, Fracture angle