Physics-Informed Learning for EPG-Based TDDB Assessment

Time-dependent dielectric breakdown (TDDB) is one of the important failure mechanisms for copper (Cu) interconnects. Many TDDB models have been proposed based on different physics kinetics in the past. Recently, a physics-based TDDB model, which is based on the breakdown concept of electric path generation (EPG), has been proposed and has shown advantage over widely accepted existing electrostatic field-based TDDB assessment. However, the determination of the time-to-failure from this EPG based TDDB model includes solving partial differential equation (PDE) with time-consuming finite-element method (FEM). In recent years, deep neural networks have been proposed to predict numerical solutions of PDEs. In this paper, we use physics-informed neural network to solve the diffusion equation of ions in an electric field extracted from EPG based TDDB model. The continuous definite condition and hard constrain optimization methods are used for improving the performance of PINN in terms of accuracy and speed. Compared with the FEM method, the proposed PINN method can lead to about 100 times speedup with less than 0.1% mean squared error.