The intrinsic lower limit of contact resistivity (rho(LL)(c)) for InAs, In0.53Ga0.47As, GaSb, and Si is calculated using a full band ballistic quantum transport approach. Surprisingly, our results show that rho(LL)(c) is almost independent of the semiconductor. An analytical model, derived for 1D, 2D, and 3D, correctly reproduces the numerical results and explains why rho(LL)(c) is very similar in all cases. Our analysis sets a minimal carrier density required to meet the International Technology Roadmap for Semiconductors call for rho(c) x 10(-9) Omega-cm(2) by 2023. Comparison with experiments shows there is room for improvement, which will come from optimizing interfacial properties. (C) 2013 American Institute of Physics. [http://dx.doi.org/10.1063/1.4798238]