On the elastic tensors of ultra-thin films: A study of ruthenium

Critical Dimensions (CD) of electronic device patterns have been reduced to the order of a few nanometers due to the extreme miniaturization of devices, setting the thickness of some of its constituting materials at the (sub-)nanometer level. At these length scales, the mechanical integrity of the constituting films begin to deviate strongly from their bulk material values, introducing a set of undesired reliability side-effects such as mechanical failure, delamination, and strain enhanced diffusion. Understanding the fundamentals behind these aspects is critical to further sustain technology developments. We use Density Functional Theory (DFT) to quantify how the mechanical properties of sub-10 nm thick films depend on their thickness and surface roughness, specifically for Ru [001], which is currently being investigated for CMOS interconnects, an antiferromagnetic layer, and an etch stop layer in Magnetic Random Access Memories (MRAM). Our findings underline that overlooking the impact of film dimensions and surface roughness on the mechanical properties at these CDs, hampers the optimization of device performances and challenges the validity of many experimental and modeling techniques relying on the assumption that bulk mechanical properties are preserved.