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This work presents a compact model, which includes scattering, for the silicon quantum well MOSFET. The model is based on the Landauer transmission theory and McKelvey's flux theory, and is continuous from below to above threshold and from linear to saturation regions. A good agreement with 2-D numerical simulations (nanoMOS) is obtained with the compact model. The effect of backscattering on both the channel conductance and the average velocity near the source end is studied in this work.