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Extraction of carrier mobilities of silicon nanowire FETs (SNWFETs) with Schottky source and drain contacts is performed using a newly developed compact model, which is suitable for efficient circuit simulation. The SNWFET model is based on an equivalent circuit including a Schottky diode model for two metal-semiconductor contacts and a SPICE LEVEL 3 MOSFET model for an intrinsic NW. The Schottky diode model is based on our recently developed Schottky diode model that includes thermionic field emission for reverse bias and thermionic emission mechanism for forward bias. It also includes a new analytical Schottky barrier height model dependent on the gate voltages as well as the drain-source voltages. The results simulated from the SNWFET model reproduce various, previously reported experimental results within 10% errors. The mobilities extracted from our model are compared with the mobility calculated without considering the Schottky contacts.