The continuous scaling-down size of interconnects should be accompanied with ultrathin diffusion barrier layers, which is used to suppress Cu diffusion into the dielectrics. Unfortunately, conventional barrier layers with thicknesses less than 4 nm fail to perform well. With the advent of 2D layered materials, graphene and hexagonal boron nitride have been proposed as alternative Cu diffusion barriers with thicknesses of ≈ 1 nm. However, defects such as vacancies may evolve into a Cu diffusion path, which is a challenging problem in design of diffusion barrier layers. The energy barrier of Cu atom diffused through a di-vacancy defect in graphene and hexagonal boron nitride is calculated by density functional theory. It is found that graphene offers higher energy barrier to Cu than hexagonal boron nitride. The higher energy barrier is attributed to the stronger interaction between Cu and C atoms in graphene as shown by charge density difference and Bader's charge. Furthermore, we use the energy barriers of different vacancy structures and generate a dataset that will be used for machine learning. Our trained convolutional neural network is used to predict the energy barrier of Cu migration through randomly configured defected graphene and hexagonal boron nitride with R 2 of > 99% for 4 × 4 supercell. These results provide guides on choosing between 2D materials as barrier layers, and applying deep learning to predict the 2D barrier performance. INDEX TERMS machine learning, 2D materials, Cu interconnects.

This paper investigates the diffusion barrier performance of 2D layered materials with pre-existing vacancy defects using first-principles density functional theory. Vacancy defects in 2D materials may give rise to a large amount of Cu accumulation, and consequently, the defect becomes a diffusion path for Cu. Five 2D layered structures are investigated as diffusion barriers for Cu, i.e., graphene with C vacancy, hBN with B/N vacancy, and MoS2 with Mo/2S vacancy. The calculated energy barriers using climbing image - nudged elastic band show that MoS2-V2S has the highest diffusion energy barrier among other 2D layers, followed by hBN-VN and graphene. The obtained energy barrier of Cu on defected layer is found to be proportional to the length of the diffusion path. Moreover, the diffusion of Cu through vacancy defects is found to modulate the electronic structures and magnetic properties of the 2D layer. The charge density difference shows that there exists a considerable charge transfer between Cu and barrier layer as quantified by Bader charge. Given the current need for an ultra-thin diffusion barrier layer, the obtained results contribute to the field of application of 2D materials as Cu diffusion barrier in the presence of mono-vacancy defects.

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