A Monte Carlo investigation of transport through Schottky barriers is presented. A WKB based injection-absorption model has been developed, thus allowing correctly reproducing the experimental J-V curves. The reverse-bias regime is analyzed in depth, and the main features of charge transport (including the evidence of quasiballistic phenomena) are discussed by considering internal quantities such as average energy, velocity and concentration of carriers, electric field and potential profiles, together with velocity distribution functions. Tunneling processes show to have a great importance for low and moderately high reverse applied voltages.