Machine Learning for Semiconductor Process Simulation Described by Coupled Partial Differential Equations

Technology computer-aided design (TCAD) simulation is an important tool for the development of semiconductor devices. Based on coupled partial differential equations (PDEs) for behaviors, TCAD can calculate objects such as impurities, point defects, and electronic carriers in semiconductors. However, over recent years semiconductor devices have become increasingly miniaturized and complicated, resulting in much longer calculation times for TCAD. Machine learning is one technology that may be used to overcome this simulation cost problem. In this study, a neural network architecture is proposed that considers the structure of the coupled PDEs. Features representing each concentration distribution of the calculation objects are extracted by convolution operations and their reaction is modeled by channel attention. The performance of the proposed architecture and of conventional neural network models is evaluated using a simulation dataset generated by 1D coupled PDEs that models the diffusion and reaction of vacancies and interstitial atoms. In addition, the advantage of the method is discussed through the analyses of error correlations of the two predictions and attention coefficients. The machine learning method developed in this study will be applicable to other physics described by coupled PDEs and is expected to speed up the computation of simulations in various fields.