Using modified conventional formulas to fit the measured characteristic curves of transistors appears feasible. Even if no equivalent circuits are considered, the fitting works and some important parameters (kN, Vth, λ) are successfully determined. Somehow, the fitting IDS versus VDS do not perfectly match the measured data as shown. The differences between both are squared and summed over and can be used to tell how match the fitting is. The bigger discrepancy is recognized at around VDS= (VGS-Vth) and named ``kink'' where the saturation is approached from triode region. Also the measured current data is always lower than the fitting data at the kinks. Eliminating the kinks is interesting and possible from the engineering point of view.
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Yang et al. (2024) studied this question.
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