Elastic anisotropy of Cu and its impact on stress management for 3D IC: Nanoindentation and TCAD simulation study

Abstract

This article presents a study on elastic anisotropy of Cu by indentations at different penetration depth ranges (sub-10 nm, several-10 nm, and several-100 nm), and the impact of elastic anisotropy on the stress in 3D stacked integrated circuits (3D ICs). The reduced modulus, E-R, values determined at sub-10 nm indentations on Cu single crystals are very close to the unidirectional values. Similarly, cross-sectional sub-10 nm indentation tests on the Cu grains in a through-silicon via (TSV) show unidirectional E-R values. In contrast, the Hill's average values are observed at several-100 nm indentations. We propose that before lattice rotation happens within a volume beneath the indentation, elastic anisotropy can be strongly reflected in the E-R value. When the experimentally measured Cu elastic anisotropy is used in a technology computer-aided design simulation of a Cu-filled TSV, significant impacts are observed on the stress field and the carrier mobility variation in an active Si region

Nanometer deformation of elastically anisotropic materials studied by nanoindentation

“…Si(100), result in a S-shape pattern in the plot of E R vs. h. As shown in Figure 4, after adding a systematic offset of þ10 GPa to the theoretical unidirectional values (blue dashed-lines) and the theoretical weighted average values (red dashed-lines), it is clear that the experimentally determined E R values evolve from unidirectional values to weighted average values from Vlassak and Nix analysis [10]. This E R evolution was observed in our recent indentation study on Cu single crystals as well [26]. In the case of Si, the systematic offset (þ10 GPa) from the weighted average values was previously observed [27], and it is due to changes in elastic constants by different dopant contents [15,28].…”

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

“…Experimental data have shown reliability lifetimes of copper interconnects to be dependent on microstructure, texture distribution, and grain size distribution (KIM 2006;Ryu et al 1999;Choi et al 2007;Choi et al 2008). Further, Copper has a very anisotropic mechanical behavior (Kocks et al 2000;Yeap et al 2011) and is known to impact stress voiding and electromigration lifetime (Nucci et al 1997;Ryu et al 1997). Hence, it is critical to consider the microstructure and corresponding anisotropy in copper grains while studying reliability of copper interconnects.…”

Thickness and microstructure influence on the nanocrystalline Cu thin films’ mechanical properties

“…On the other hand, X-ray data showed that as the film thickness increases it becomes more textured in the (111) direction. Nevertheless, the decrease of the films E and H values by increasing the thickness is not related to this effect since the (111) surface is actually harder than the (100) one [30,31]. It is important to notice that the influence of the substrate can be seen for low indentation depths, even lower than 10% of the film thickness ( t ).…”