Using a first-principle pseudopotential approach, we have investigated the Schottky barrier heights of abrupt Al/Ge, Al/GaAs, Al/AlAs, and Al/ZnSe (100) junctions, and their dependence on the semiconductor chemical composition and surface termination. A model based on linear-response theory is developed, which provides a simple, yet accurate description of the barrier-height variations with the chemical composition of the semiconductor. The larger barrier values found for the anion-terminated surface than for the cation-terminated surface are explained in terms of the screened charge of the polar semiconductor surface and its image charge at the metal surface. Atomic-scale computations show how the classical image charge concept, valid for charges placed at large distances from the metal, extends to distances shorter than the decay length of the metal-induced-gap states.