The use of two generalised carrier transport models to account for the N(D)-1 dependence of the specific contact resistance (rho(c)) of metal-semiconductor Ohmic contacts to n-type GaAs is proposed. Both models include the effects of thermionic emission and diffusion across the high-low barrier junction a priori. Calculations of rho(c), and comparison with experimental data, show conclusively that thermionic emission is the dominant transport mechanism across the barrier. It is stressed that these models do not rely on prior choices of either of the transport processes. These conclusions are arrived at a posteriori.