Size-dependent conductivity based on modified energy-momentum dependent relaxation time

As modern CMOS devices are downscaling, it is important to keep the interconnect resistivity low. Copper has been traditionally used as an interconnect material thanks to its high bulk conductivity. But its increasing rate of resistivity with size reduction becomes drastically high. It, thus, requires new interconnect materials that may replace copper.

It is known that certain layered materials have 2D-like Fermi surfaces exhibiting much higher in-plane conductivity than their out-of-plane counterpart. Hence, thin films of these materials could be regarded to have a lower resistivity than copper. On the other hand, to find new interconnect materials better than copper when their sizes become smaller, one should evaluate how their conductivity changes as such materials become thin films. There has been a couple of models that explain the size dependence of conductivity, but they were all based on phenomenological fitting on experimental data. Thus, these methods cannot be used to predict the size-dependent conductivity of new materials. Here we present a new method that can evaluate the modified relaxation time, which is still a function of energy and momentum due to size reduction. Our method allows us to predict realistic conductivity values of any new materials with any shape and even with anisotropic Fermi surfaces by solving the Boltzmann transport equation. Based on this method, we demonstrate a few materials that would be better than copper for interconnects in reduced geometric dimensions.