Seeking Shapes of Interconnects for Higher Flexibility

Abstract

Thermal loads during the production and service process of power semiconductor devices can induce significant stress on interconnects, potentially leading to the fracture and even the ultimate failure of the devices. Increasing the flexibility of interconnects can mitigate this issue. Herein, we seek optimized shapes of interconnects that offer higher flexibility. An initial attempt using the Euler–Lagrange equation fails due to the involved nonlinearity. Another attempt using the Ritz method is performed successfully, but its satisfactory convergence depends on the ingenious selection of the function system. Therefore, we propose a self-adaptive method to eliminate such dependence, which can automatically generate the optimal solution with good computational efficiency. Detailed parameter analyses of the length, asymmetry, limitation on the radius of curvature, and thickness are subsequently provided based on our self-adaptive method. Although these geometric parameters play a role, our results show that the normalized profiles of various optimal solutions consistently approximate a parabolic curve. This concise shape is convenient for engineering design. Finally, we highlight the potential for extending our self-adaptive method to other isoperimetric problems.