Anisotropy Of Copper Research Articles

Modeling the copper microstructure and elastic anisotropy and studying its impact on reliability in nanoscale interconnects

BackgroundCopper is the primary metal used in integrated circuit manufacturing of today. Even though copper is face centered cubic it has significant mechanical anisotropy depending on the crystallographic orientations. Copper metal lines in integrated circuits are polycrystalline and typically have lognormal grain size distribution. The polycrystalline microstructure is known to impact the reliability and must be considered in modeling for better understanding of the failure mechanisms.MethodsIn this work, we used Voronoi tessellation to model the polycrystalline microstructure with lognormal grainsize distribution for the copper metal lines in test structures. Each of the grains is then assigned an orientation with distinct probabilistic texture and corresponding anisotropic elastic constants based on the assigned orientation. The test structure is then subjected to a thermal stress.ResultsA significant variation in hydrostatic stresses at the grain boundaries is observed by subjecting the test structure to thermal stress due to the elastic anisotropy of copper. This introduces new weak points within the metal interconnects leading to failure.ConclusionsInclusion of microstructures and corresponding anisotropic properties for copper grains is crucial to conduct a realistic study of stress voiding, hillock formation, delamination, and electromigration phenomena, especially at smaller nodes where the anisotropic effects are significant.

Effect of Microstructure and Anisotropy of Copper on Reliability in Nanoscale Interconnects

The mechanical behavior of copper is highly anisotropic. Although it is a face centered cubic crystal, the elastic constants vary considerably for different crystallographic orientations. Typically, the copper metal conductor lines in integrated circuits are polycrystalline in nature. In this paper, we utilize Voronoi tessellation to model the polycrystalline microstructure for the copper metal lines in test structures and then assign textured orientation to each grain and assign corresponding anisotropic elastic constants based on the assigned orientation. By subjecting the test structure through a thermal stress, we observe over 10x variation in normal stresses along the grain boundaries depending on the orientation, dimensions, surroundings, and location of the grains. This may introduce new weak points within the metal interconnects where normal stresses can be very high depending on the orientation of the grains leading to delamination and accumulation sites for vacancies. Hence, inclusion of microstructures and corresponding anisotropic properties for copper grains is critical to conduct a realistic study of both stress voiding and electromigration phenomena, especially at smaller nodes where the anisotropic effects are significant. Further, a comparison between stress levels in test structures with SiCOH and SiO2 as the inter level dielectric was conducted.

弾性相互作用エネルギーと界面エネルギーが析出物の形状と分布に及ぼす影響：異方性弾性論による 2 次元解析

Elastic interaction energy between two super-circular inclusions with purely dilatational misfit strains is evaluated. For the calculation, a two dimensional model is used together with linear elasticity for the cubic anisotropy of copper. When two inclusions lie parallel to <100> of the copper crystal, attractive interaction is observed between the inclusions. The maximum of the attractive interaction is realized when the two inclusions exist close to each other. As the inclusion shape becomes circular to square-like, the maximum interaction energy decreases and the distance between the two inclusions to give the maximum increases. Furthermore, the two inclusions are found to be most stable when they have the same size. In addition to the elastic interaction energy, interface energy of the matrix/inclusion interface is also considered. The results show that the two inclusions tend to become the same size even for a situation when the interface energy is much more dominant compared with the elastic interaction energy.

Crystallographic texture induced anisotropy in copper: An approach based on a tensorial Fourier expansion of the CODF

We consider a tensorial Fourier expansion of the crystallite orientation distribution function for aggregates of cubic crystals. The coefficient of rank four is determined explicitly. It is shown that this coefficient governs the anisotropic bounds of the linear elastic behavior of polycrystals. Recently, a phenomenological model has been proposed [4, 6], that describes the evolving elastic anisotropy in copper. The model also reproduces the cyclic Swift effect, which is due to a texture induced plastic anisotropy [7]. In the model the anisotropic part of the effective elastic stiffness tensor is used to define a texture dependent quadratic yield function. The present paper gives a new interpretation of the aforementioned model in terms of an approximation of the crystallographic texture by means of a 4th-order coefficient of the tensorial Fourier expansion of the crystallite orientation distribution function.

Experimental investigation of an anisotropy in copper subjected to predeformation due to constant and monotonic loadings

Experimental analysis of the plastic properties for both an aged pure copper and the same material subjected to various types of predeformation is presented. The analysis was made by studying; the position in stress space and by determination of dimensions of the yield surfaces. The initial yield surface has been determined using the probing technique of a single specimen and this surface was used as the starting point for comparative studies of yield surfaces of the prestrained material. The material predeformations of the same magnitude were induced either by a creep process at elevated temperature or by monotonic loading at ambient temperature. After required values of plastic prestrain were attained, yield surfaces were determined by the same method as for the non-prestrained material. The anisotropic yield condition was used to create a least squares fit of the experimental data.

Textural evolution in electrodeposits under the influence of adsorbed foreign species. Part II A simulation study on effects of potassium chloride on textural evolution in copper electrodeposits

The texture of copper deposits produced in the bath containing potassium chloride changes with the content of the potassium chloride. This change in texture was usually explained to be caused by chloride adsorption on the cathode. This paper reports simulation studies on textural evolution in copper electrodeposits under the influence of potassium chloride, using a Monte Carlo simulation approach. The study was conducted based on the assumption that the textural development results from the minimization of the system free energy in which the surface-energy anisotropy plays the most important role. The simulation demonstrates that adsorbed potassium ions may change the surface-energy anisotropy of copper, and therefore, they also affect texture variation in copper deposits in addition to the chloride effect. It was observed the potassium effect on textural variation in copper deposits is even stronger than that of the Cl- adsorption.

Anisotropy in the compton profile of copper

Directional Compton profiles of high statistical accuracy are measured by means of a 412 keV gamma-ray Compton spectrometer. The experimental anisotropies are in very satisfactory agreement with earlier measurements and there is good qualitative agreement between the experimental data and a recent band structure calculation. Quantitatively, however, the experimental anisotropy is significantly smaller than predicted by theory. A simple model calculation based on the Seitz approximation, in which higher order Fermi surface volumes all of spherical shape are taken into account in obtaining the momentum density, demonstrates that the major contribution to the Compton profile anisotropy in copper is due to the hybridization which has mixedd-electrons and nearly-free electrons in the top band. Any fine structure in the theoretical anisotropy due to the detailed shape of the Fermi surface cannot be resolved in the present experiment. The potential of analysing the electronic structure of transition metals in terms ofB(r), the Fourier transform of the momentum density, is discussed in detail. The major contribution to the anisotropy arises from localised peaks inB(r) centered on the sites of the translational lattice. Within the Seitz approximation it could be shown that these secondary maxima are caused by the presence of localisedd-electrons in the highest partly occupied band. In conclusion we anticipate that a proper treatment of electron correlation would produce a marked quantitative improvement in the agreement between the present experimental data and the Compton profiles obtained from current band structure calculations.

The observation of four types of hall constant anisotropy in copper and their role in the determination of the fermi surface

Abstract Four of five possible types of high field Hall constant anisotropy predicted for metals (Lifshitz and Peschanskii 1958) have been observed by us in copper and are reported in this letter. The fifth type is not expected for copper. The observed Hall constant behaviour is markedly different from the results reported for copper by earlier workers (Kittel 1956, Berlincourt 1958), primarily due to our use of samples that were both single crystals and highly pure (R 278°K/R 4·2°K as large as 8000). Generally when the magneto resistance saturates, the Hall constant can be directly related to the Fermi surface shape; the essential conditions are summarized and several Hall constant calculations, using the Pippard model, are compared with the corresponding experimental values. Finally, the utility of Hall voltage data for distinguishing between different possible Fermi surface topologies is illustrated for the first time.