Current Transport in Graphene/Copper Hybrid Nano Ribbon Interconnect: A First Principle Study
Authors: Mohsin K M , Srivastava Ashok , Sharma Ashwani K , Mayberry Clay , Fahad Md S 
Published: February 2020

In search of emerging materials replacement of copper interconnect in nanometer CMOS technology nodes, graphene (G) and carbon nanotubes (CNT) have been studied intensively. There is also ongoing research to find hybrid materials, which can have better thermal and electrical conductivity [1]. Recently, reduction in temperature has been observed in graphene encapsulated copper wires [2]. It was argued that this excellent thermal property is inherent to copper not because of graphene. During graphene deposition process, Cu becomes annealed with larger grains. In addition, graphene works as a barrier layer for copper ion to diffuse into dielectric. Motivated by recent experiments we have studied theoretically G/Cu structure in bulk and in one-dimension (1D) as next generation wires for nano-electronic applications. Our purpose is to understand this structure and to study why it outperforms graphene only or Cu only interconnect. In this paper, we report density of states (DOS), current-voltage relation (I-V), and resistance (R) of G/Cu nano ribbon interconnect.
We used density functional theory (DFT) with pseudo- potential technique to study electronic band structure within Quantum-Espresso (QE) code. For ballistic transport study, we used Landauer-Buttiker (LB) formalism within Wannier90 Module [3]. We have considered a one-dimensional slice of G/Cu interconnect of width 0.6nm, height 0.8nm and length 10nm. Single layer of graphene is deposited on top of three atomic layers of Cu {111}. Cu {111} is chosen because this plane is closest to graphene lattice within 2% lattice mismatch. Among these three atomic layers, bottom two layers were fixed to their bulk lattice position to represent bulk atoms. Top Cu layer and graphene layer were relaxed to find minimum force position. After obtaining atomic positions from relaxation calculations in QE, we performed self-consistent field calculation and band structure calculation. Bloch states obtained from QE were used as an input for transport calculation in Wannier90 Code. Due to high computational cost, we have limited our study to a 10nm long wire which represent a short local interconnect and a good candidate to study ballistic transport. We believe this geometry will at least serve present purpose to compare performances with graphene only interconnect.
I-V characteristics of graphene interconnect and graphene on copper interconnect have been compared. Being one-dimensional wire, we have observed several stairs like and piece wise linear relationships. At zero bias, resistance is found to be the same as quantum resistance for single electronic channel, which is ~h/2e2. Since wire length 10nm is smaller than Cu mean free path (40nm), one should not compare resistivity of G/Cu with Cu only interconnect based on Fuchs-Sondheimer (FS) and Mavadas-Shatzkes (MS) models. For this G/Cu we found resistivity 1.25x10-6 Ω-m, which is one tenth of Cu-bulk resistivity. It is expected by FS & MS theory that Cu resistivity increases with decrease of width. However, in ballistic transport regime FS & MS theories were not applicable. Hence, we have used LB formalism. For comparison, we have studied same geometry for graphene only interconnect using same methodology. From DOS, it is apparent that there is no energy states available near Fermi energy for graphene only interconnect. This is why in I-V characteristics no current is observed near 0V. On other hand, hybrid structure shows better conductivity at low bias than graphene only interconnect. Graphene only nanoribbon might better perform as device not as interconnect. This calculation is useful to understand electrical performances of various nanostructures and to find true contender of next generation interconnect.

Acknowledgement: Part of the work is supported by the United States Air Force Research Laboratory under agreement number FA9453-10-1-0002. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation thereon.
References
[1] P. Goli et. al., Nano Letters, vol. 14, no. 3, p. 1497, April 12, 2014.
[2] R. Mehta et. al., Nano Letters, vol. 15, no. 3, p. 2024, March 11, 2015.
[3] A. A. Mostofi et. al., Computer Physics Communications, vol. 178, no. 9, p. 685, May 1, 2008.