Cohesive Zone Model for the Interface of Multiwalled Carbon Nanotubes and Copper: Molecular Dynamics Simulation

Abstract

Due to their superior mechanical and electrical properties, multiwalled carbon nanotubes (MWCNTs) have the potential to be used in many nano-/micro-electronic applications, e.g., through silicon vias (TSVs), interconnects, transistors, etc. In particular, use of MWCNT bundles inside annular cylinders of copper (Cu) as TSV is proposed in this study. However, the significant difference in scale makes it difficult to evaluate the interfacial mechanical integrity. Cohesive zone models (CZM) are typically used at large scale to determine the mechanical adherence at the interface. However, at molecular level, no routine technique is available. Molecular dynamic (MD) simulations is used to determine the stresses that are required to separate MWCNTs from a copper slab and generate normal stress–displacement curves for CZM. Only van der Waals (vdW) interaction is considered for MWCNT/Cu interface. A displacement controlled loading was applied in a direction perpendicular to MWCNT's axis in different cases with different number of walls and at different temperatures and CZM is obtained for each case. Furthermore, their effect on the CZM key parameters (normal cohesive strength (σmax) and the corresponding displacement (δn) has been studied. By increasing the number of the walls of the MWCNT, σmax was found to nonlinearly decrease. Displacement at maximum stress, δn, showed a nonlinear decrease as well with increasing the number of walls. Temperature effect on the stress–displacement curves was studied. When temperature was increased beyond 1 K, no relationship was found between the maximum normal stress and temperature. Likewise, the displacement at maximum load did not show any dependency to temperature.

Vertically aligned CNT-Cu nano-composite material for stacked through-silicon-via interconnects

“…A number of published studies have reported that a CNT-Cu composite material could have several advantages over any of the individual materials. Results from molecular dynamics simulations predict that the addition of CNTs can dramatically decrease the skin effect of copper and show strong van der Waal (vdW) interfacial bonds to copper [28,29]. Subramanian et al [30] synthesized a novel CNT-Cu composite film using electroplating, and showed a hundredfold increase in ampacity when compared with Cu.…”

A multiscale modeling framework for predicting strain‐dependent electrical conductivity of carbon nanotube‐incorporated nanocomposites considering the electron tunneling effect

“…The molecular interactions at the interfaces between CNTs and the PDMS matrix in ReaxFF can affect changes in distance between CNTs when uniaxial tension is applied to a molecular structure. 44 The MD simulations are conducted at different energy tolerances of 1.00E-3, 1.00E-4, and 1.00E-5 43 with varying the values of the strain increments of 0.01, 0.006, and 0.004 to consider the effect of the molecular interactions and appplied loading rate on changes in distance. 43 The average distance was obtained by averaging the three distances between CNTs in the MD simulations.…”

“…Figure 3 provides the average distance between CNTs against the strain in CNT/PDMS nanocomposites under uniaxial tension along the x ‐direction. The molecular interactions at the interfaces between CNTs and the PDMS matrix in ReaxFF can affect changes in distance between CNTs when uniaxial tension is applied to a molecular structure 44 . The MD simulations are conducted at different energy tolerances of 1.00E‐3, 1.00E‐4, and 1.00E‐5 43 with varying the values of the strain increments of 0.01, 0.006, and 0.004 to consider the effect of the molecular interactions and appplied loading rate on changes in distance 43 .…”

Mechanical integrity of a carbon nanotube/copper-based through-silicon via for 3D integrated circuits: a multi-scale modeling approach

“…However, there has been debate over how far virial stress expresses mechanical stress [38][39][40][41][42][43][44]. As concluded from a previous study [45], since stresses were time-averaged for all times and nearest image convention boundary conditions are activated in the stress calculation direction (y-direction), mechanical stress could be represented by virial stress when the kinetic part is ignored. This is given in the following:…”