ReaxFF Reactive Force Field Development for Cu/Si Systems and application to Copper Cluster Formation During Cu Diffusion Inside Silicon

TL;DR

This study develops a ReaxFF force field for Cu/Si systems and uses it to investigate copper diffusion, clustering, and mechanical properties in silicon, revealing temperature-dependent behaviors and effects of copper impurities.

Contribution

The paper introduces a new ReaxFF parameter set for Cu/Si and applies it to simulate copper diffusion, clustering, and mechanical response in silicon, providing insights into impurity effects.

Findings

Copper diffusion increases with temperature.

Copper atoms tend to cluster at higher temperatures.

Impurities reduce silicon's elastic modulus and induce microcracking.

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 performed ReaxFF reactive force field based molecular dynamics simulations, studying different configurations of individual and crystalline copper atoms inside bulk silicon by looking at the diffusional behavior of copper in silicon. The ReaxFF Cu/Si parameter set was developed by training against DFT data, including the energy barrier for an individual Cu-atom inside a silicon lattice. We found that the diffusion of copper atoms has a direct relationship with the temperature. Moreover, it is also shown that individual copper atoms start to clusterize inside bulk silicon at elevated temperatures. Our simulation results provide a comprehensive picture of the effects of temperature and copper concentration on the crystallization of individual copper inside silicon lattice. Finally, the stress-strain relationship of Cu/Si compounds under uniaxial tensile loading have been obtained. Our results indicate a decrease in the elastic modulus with increasing level of 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 clusters adjacent to the Si surface.