We examine the subthreshold behavior of metal oxide semiconductor field effect transistors (MOSFETs) with Schottky barrier (SB) source/drain and large on/off ratios. Thermionic emission dominates the drain current versus gate voltage curves and the sharp turn on is attributed to a decrease in the effective hole barrier with gate bias. We present a simple 1D model and find excellent agreement between the experimentally determined effective barriers and the calculated results. Smaller devices exhibit significantly degraded characteristics, which are attributed to a sub-surface punch-through of the source and drain depletion widths at zero gate bias. Implications for SBMOSFETs are discussed.