A generally applicable model is presented to describe the potential barrier shape in ultrasmall Schottky diodes. It is shown that for diodes smaller than a characteristic length lc (associated with the semiconductor doping level) the conventional description no longer holds. For such small diodes the Schottky barrier thickness decreases with decreasing diode size. As a consequence, the resistance of the diode is strongly reduced, due to enhanced tunneling. Without the necessity of assuming a reduced (non-bulk) Schottky barrier height, this effect provides an explanation for several experimental observations of enhanced conduction in small Schottky diodes.