Calculate the transconductance of an n-channel MOSFET with W = 10 m, n = 450 cm

Calculate the transconductance of an n-channel MOSFET with W = 10 µm, μ_n = 450 cm²/(V–s), and ℰ_c = 1·5 × 10⁶ V/m using channel lengths from 10 µm to 0.4 µm. Assume that t_ox = L / 50 and that the device operates in the active region with V_GS − V_t = 0.1 V. Compare the result to a calculation that ignores velocity saturation. For what range of channel lengths is the model without velocity saturation accurate within 10 percent?