Optimization of ReaxFF Reactive Force Field Parameters for Cu/Si/O Systems via Neural Network Inversion with Application to Copper Oxide Interaction with Silicon

The presence of transition metal oxide impurities introduced during crystal formation or during the fabrication process may lead to a significant yield loss in microelectronics and device manufacturing. To enable a large-scale molecular dynamics study of the effects of copper oxide impurities inside silicon on the structural evolution and mechanical properties of Cu/Si/O systems, one needs to understand the diffusional characteristics of copper and oxygen compounds next to the silicon lattice. In this work, we introduce an accelerated deep learning-based reactive force field parametrization platform. In this platform, we train a deep neural network to learn the production of ReaxFF outputs, given a set of force field parameters. Subsequently, the trained neural network is used, as an alternative to ReaxFF, by means of the neural network inversion algorithm to seek the inputs to the neural network (force field parameters) that produce the experimental and quantum mechanics reference property values of the system. We compared the performance of the neural network inversion optimization algorithm with that of the previously used brute force search method by looking at the total optimization time and the total reduction of the discrepancies between the results of molecular dynamic simulation and the reference property values within the force field training set. The neural network inversion algorithm significantly reduces the average optimization time, which directly translates into less computational resources required for the optimization process. Moreover, we compared the quality of the force fields optimized by both algorithms in describing the chemical properties of the Cu/O systems, including the heat of formation and the relative phase stability. We demonstrated that the results of the force field, optimized using the proposed neural network inversion algorithm, align more closely with the reference chemical properties of Cu/O systems within the force field training set than those optimized by the brute force algorithm. We used this platform to develop a Cu/Si/O ReaxFF reactive force field by training on density functional theory (DFT) data, including heat of formation values for various Cu/Si/O materials. The developed force field was further used to perform molecular dynamics simulations on models with up to 3542 atoms to study atomistic interactions between copper oxide compounds and silicon by looking at the diffusional behavior of copper and oxygen atoms adjacent to the Si substrate. We found that the temperature substantially impacts the Cu oxide diffusion coefficient. Our simulation results enable us to comprehensively understand the effects of oxygen atoms on the diffusion of copper impurities into the silicon lattice. We showed that a Cu oxide cluster shows diffusion faster than that of a pure Cu cluster adjacent to a Si supercell. By studying the interaction between Cu oxide and Si nanolayers at different temperatures, we observed that at higher temperatures, oxygen atoms migrate from the initial CuOx material to diffuse into the Si phase. In addition, we showed that the absolute decay rate of the average Cu–Cu bond length is directly dependent on the simulation temperature.