A comprehensive physics-based compact model for three-terminal undoped Schottky-barrier (SB) gate-all-around silicon-nanowire MOSFETs is formulated based on a quasi-2-D surface-potential solution and the Miller-Good tunneling model. The energy-band model has accounted for the screening of the gate field by the electrons or holes, which has been largely missed in the literature. Although SB-MOSFETs are essentially ambipolar devices, we show that the separate modeling of electron and hole currents is simple yet accurately predicts the final ambipolar current. Thinner oxide thickness is confirmed to be beneficial to SB-MOSFETs for both ON - and OFF-state currents. However, smaller nanowire radius (or thinner body thickness) is found to be only beneficial to SB-MOSFETs with high SB heights (SBHs) despite the OFF-state current being reduced significantly. For SB-MOSFETs with low SBHs, the tunneling-current-density enhancement due to a smaller radius is not able to compensate the reduction in the contact size, which leads to a degradation of the ldquoONrdquo current. The drift current in the channel is shown to be negligible in SB-MOSFETs, and the tunneling/thermionic current through the SB represents the main current-limiting mechanism.