Modeling of copper–carbon solid solutions

doi:10.1016/S1369-8001(00)00019-6

Materials Science in Semiconductor Processing

Volume 3, Issues 1–2, 1 March 2000, Pages 123-127

https://doi.org/10.1016/S1369-8001(00)00019-6 Get rights and content

Abstract

The atomistic simulations in the framework of the Generalized Simulated Annealing approach (GSA) and classical force fields lead to very reasonable relaxed geometries around the carbon interstitial in O-, T-, and TS-sites. We have thus shown that a highly efficient energy-sampling and relaxation scheme, implemented with tight constraints on a limited volume, provides a powerful steering mechanism for selection of geometries suitable for detailed investigation by first-principles methods. The results, based upon harmonic interactions between Cu atoms and a van der Waals interaction between Cu and C, predict the relaxed O-site to be more stable than the T-site by ∼1.2 eV, in accordance with general expectations. The TS barrier to OO diffusion is found to be ∼0.8 eV, at a temperature of 0 K; the TS exhibits a strong local axial distortion of the pseudo-octahedral environment. The Density Functional results indicate a charge transfer of ∼1 e to carbon, mostly from the first neighbor shell, in all relaxed environments studied. Bond-order data show the Cu–C interaction to be bonding in nature, despite the net ‘repulsive interaction’ leading to a surface state of lower net energy.

Introduction

For high temperature applications, matrix-embedded carbon fibers have also been considered to provide stiffness and prevent ductile failure, and may be useful to reduce sliding friction [1]. Wetting of the fiber by Cu is poor, however, due to the extremely low solubility of C, not exceeding 0.02 at % even at elevated temperature. It is therefore generally necessary to force impregnation to form a composite, with not entirely satisfactory results. An understanding of C behavior at the Cu/C interface is fundamental to developing successful strategies for improving fiber-matrix composite performance. In microelectronics carbon is considered an important material to form a Si(C) alloy with a band gap smaller than that of silicon [2]. On the other hand Cu is one of the promising contact materials. For this reason an understanding of Cu–C interaction in highly diluted solid solutions and C diffusion in Cu is essential for improvement of performance of some electronic devices. In this paper we report combined theoretical and experimental analyses of the Cu–C interaction, using atomistic simulations, density functional methodology, and high-resolution scanning electron microscopy (HRSEM).

Section snippets

Experimental study of Cu–C interface

Sample for investigation comprised of a compact cylindrical carbon disc with polished bases embedded into a copper powder matrix. Copper powder was of 99.5% purity, typically 10 microns average size or less, produced by CERAC Ltd. The purity indicated is based on 100% minus spectrographic analysis of trace metallic contents. Spectrographically pure carbon rods of 6.1 mm diameter and 300 mm long, produced by AGAR Ltd. were used. The total content of impurities was less than 20 ppm. The rod was

Atomistic simulations

Here we briefly describe the Molecular Dynamics (MD) and Monte Carlo (MC) methodology used in the present atomistic simulations. The MC method is used in the Generalized Simulated Annealing approach (GSA) [3], [10], [4]. GSA is based on the correlation between the minimization of a cost function (conformational energy) and the geometry randomly obtained through a slow cooling. In this technique, an artificial temperature is introduced and the system is gradually cooled in complete analogy with

Atomistic simulation results

A simple MD model consisting of van der Waals interactions between C and Cu, and harmonic forces among the Cu atoms was used to simulate the lattice relaxation and migration of carbon. Tests on a pure copper ‘sample’ of 48 atoms confined to a box of experimentally correct dimension showed that the parameterization reproduced the bulk structure adequately. As a first approximation, a repulsive Cu–C interaction was adopted, consistent with the reported pseudopotential studies, see Table 1.

During

Conclusions

The atomistic simulations reported here, in the framework of the GSA approach and classical force fields, lead to very reasonable relaxed geometries around the carbon interstitial in O-, T-, and TS-sites, which are qualitatively consistent with the continuum results just quoted, but smaller in magnitude. NN relaxation is found to be −0.12 Å (6%) and NNN expansion is +0.01 Å (0.5%). The predicted rapid decay with distance is almost certainly due to the chosen parameterization of the Cu–C

Acknowledgements

This research was supported by Grant No. 94-00044 from the United States — Israel Binational Science Foundation (BSF), Jerusalem, Israel and by the special program of the Israel Ministry of Absorption.

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¹: On sabbatical leave from Ben-Gurion University of the Negev, Beer-Sheva, Israel

View full text

Modeling of copper–carbon solid solutions

Abstract

Introduction

Section snippets

Experimental study of Cu–C interface

Atomistic simulations

Atomistic simulation results

Conclusions

Acknowledgements

Composites

Composite Interfaces

J. Appl. Phys.

Int. J. Quant. Chem.

J. Phys. Chem.

Phys. Rev. B