Abstract: In this contribution, we report a fundamental study of the factors that set the contact resistivity between metals and highly doped n-type 2D and 3D semiconductors. We investigate the case of n-type doped Si contacted with amorphous TiSi combining first principles calculations with Non-Equilibrium Green functions transport simulations. The evolution of the intrinsic contact resistivity with the doping concentration is found to saturate at similar to 2 x 10(-10) Omega.cm(2) for the case of TiSi and imposes an intrinsic limit to the ultimate contact resistance achievable for n-doped Silamorphous-TiSi (aTiSi). The limit arises from the intrinsic properties of the semiconductors and of the metals such as their electron effective masses and Fermi energies. We illustrate that, in this regime, contacting heavy electron effective mass metals with semiconductor helps reducing the interface intrinsic contact resistivity. This observation seems to hold true regardless of the 3D character of the semiconductor, as illustrated for the case of three 2D semiconducting materials, namely MoS2, ZrS2 and HfS2. (C) The Author(s) 2018. Published by ECS.