The effect of the scattering-direction of hot electrons in the drain of ballistic n + -i-n + diodes is studied by a semi-classical Monte Carlo method. At low doping concentrations, the ionized impurity scattering has a weak influence on hot electron transport, although it is an elastic scattering. At sufficiently high doping concentrations on the other hand, the ionized impurity scattering enhances the backward flow of hot electrons, and severely degrades the peak of mean carrier-velocity in the channel and also the steady-state current. We argue that the scattering direction of hot electrons is the main reason behind these results.