We have determined the electrostatic potential at the junction between a metal and heavily doped n-type GaAs from the Poisson equation by including the majority carriers. At sufficiently high doping (donor concentration larger than 5x10 19 atoms/cm3), the electrostatic potential can be approximated by an exponential barrier shape. Consequently, the V-I characteristic and contact resistance are calculated by using the field emission and parabolic energy-momentum relationship. At low biases, we have also used the nonparabolic energy momentum relationship calculated from the density of states. Finally, we can show that, the transmission probabilities of localized electrons is negligible compared to that of delocalized electrons.