A molecular dynamics exploration of the properties of bulk and nanosized single-crystal copper

peer-reviewedCopper has a history of use that is at least 10,000 years old and it is still one of the most useful metals in today’s world. Nanocrystals of copper are of great scientific interest as they are effectively a bridge between bulk materials and atomic structures. Nanocrystalline copper is used in medical, electronic and coating applications. As Integrated Circuit devices approach nanoscale dimensions copper is the metal of choice for interconnect design. While bulk copper will have constant physical properties regardless of its size, at the nanoscale size-dependent properties are often observed. One purpose of this study was to investigate the properties of reduced-dimension copper crystals and to compare the properties of these small crystals with those of bulk single crystal copper. Metal crystals contain inclusions such as vacancies and voids. These inclusions can change the properties of the crystal. Clusters of vacancies are also thought to result in void formation under certain conditions of stress. Another aim of this work was to investigate and characterize the stresses and energies introduced by single vacancies in copper single crystals. Voids can drastically alter the resistance of a current carrying copper film and can lead to line breaks and device failure through electromigration. As void formation and collapse is an integral component of the electromigration process, the final aim of this work was to determine the pressures required to expand/collapse various sized spherical voids under compressive and tensional strains. Since the study of vacancies and small voids in copper crystals requires techniques beyond the scope of modern technology, Molecular Dynamics simulation was the tool used to undertake this study. The potential energy function employed to model the dynamics of copper atoms was the Sutton Chen potential energy function. The original parameters of this potential energy function were modified to return the most up-to-date properties of copper. The melting process in spherical nanocrystals of copper was investigated and compared to those of bulk single crystal copper. An appropriate method for determining melting temperature in nanocrystals was obtained. It was found that the melting process proceeded from surface to interior with increasing temperature. Distance to interior rather than crystal size was found to be the determining factor in melting temperature. A study of the effect of surface on the elastic properties of copper was undertaken and a previous anomaly between theory and experimental results was explained. While a number of methods are in use to measure stress on an atomic level using a twobody potential, difficulties arise in implementing some of these methods with a many-body potential such as the Sutton Chen potential. A suitable method was identified and implemented. A single vacancy was introduced into both a bulk and a nanocrystal of copper and the stresses and strains in atoms surrounding the vacancy were studied and documented. The volume of a vacancy was found to be much larger than previous studies predicted. The energy introduced by the inclusion of a vacancy was found to reside mainly in those atoms closest to the vacancy. Atoms closest to a vacant atomic site were found to exist in a state of tension. Finally, single spherical voids of different radii were introduced in bulk single crystals and both compressive and tensional strains were applied. Under tension, voids expanded elastically until a critical radius was reached after which the void expanded freely. A clear relationship emerged between void radius at this point and system pressure. Under compression, contrary to previous studies, a barrier to void collapse was found to exist. This barrier is a function of void surface structure rather than void radius or applied pressure. Previous studies on copper tend to emphasise the effect of high current density on thin copper films. The rationale for the studies is to reduce line failure. The results often focus on theory developed on mesoscopic scales and without the addition of temperature effects. At the nanoscale these theories sometimes fail. This work forms a basis for understanding copper crystals on an atomic level