Abstract: In this contribution, we report a fundamental study of the factors that set the contact resistivity between metals and highly doped 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 intrinsic contact resistivity is found to saturate at similar to 2x10(-10) Omega.cm(2) with the doping concentration and sets an intrinsic limit to the ultimate contact resistance achievable for n-doped Si vertical bar amorphous-TiSi. This limit arises from the intrinsic properties of the semiconductor and of the metal such as their electron effective masses and Fermi energies. We illustrate that, in this regime, contacting metals with a heavy electron effective mass helps reducing the interface intrinsic contact resistivity.