Development of the ReaxFF Reactive Force Field for Cu/Si Systems with Application to Copper Cluster Formation during Cu Diffusion Inside Silicon

Abstract

Transition-metal impurities such as nickel, copper, and iron in solid-state materials like silicon have a significant impact on the electrical performance of integrated circuits and solar cells. To study the impact of copper impurities inside bulk silicon on the electrical properties of the material, one needs to understand the configurational space of copper atoms incorporated inside the silicon lattice. In this work, we developed a ReaxFF reactive force field and used it to perform molecular dynamics simulations on models with up to 762 atoms to study the various configurations of individual and crystalline clusters of copper atoms inside bulk silicon by examining copper's diffusional behavior in silicon. The ReaxFF Cu/Si parameter set was developed by training against density functional theory (DFT) data, including the energy barrier for an individual Cu atom traveling inside a silicon lattice. We found that the diffusion of copper atoms is dependent on temperature. Moreover, we show that individual copper atoms start to form clusters inside bulk silicon at temperatures above 500 K. Our simulation results provide a comprehensive understanding of the effects of temperature and copper concentration on the formation of copper clusters inside a silicon lattice. Finally, the stress–strain relationship of Cu/Si compounds under uniaxial tensile loading has been obtained. Our results indicate a decrease in the elastic modulus with increasing Cu-impurity concentration. We observe spontaneous microcracking of the Si during the stress–strain tests as a consequence of the formation of a small Cu cluster adjacent to the Si surface.

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