Mathematically, a device model is an approximation of the device behavior which can be measured or obtained from device simulations. At a first glance, model accuracy is determined by the deviation of the approximation from the measured data, e.g., current-voltage (IV) data. However, this is not sufficient, because it does not guarantee the accuracy of the derivative which is at least as important as pointed out before. The approximation or interpolation of given data with a small error of the derivatives turns out to be a challenging task, especially, when the functional relation involves changes between exponential, polynomial, and linear behavior, which is the case for MOSFETs. The essential problem is the tradeoff between the error of the nth-order and the n-1st-order derivative. In practice, when the error of the derivatives are under control the error of the value itself is not a problem anymore.
Most conventional models approximate currents and conductances (and capacitances) separately, which form a small-signal model for AC analysis. However, this approach suffers from the inconsistency of the DC and AC models. This can also lead to large errors as the AC results depend on the operating point which may be affected by a poor DC model accuracy. Furthermore, distortion and intermodulation analyses, which are important in communications applications, cannot be performed using this small-signal model.