Parametric models are based on explicit or implicit functions or functionals which are characterized by a usually limited set of named parameters. Virtually all analytical models - e.g., Ohm's law - fall into this category. Non-parametric models are based on functions or functionals which are characterized by a usually unlimited set of named parameters. All table-based models - e.g., a variable-order polynomial approximation of an IV curve - fall into this category. The advantage of a parametric model is that it enables a better physical understanding through the individual parameters (as long as they are few), whereas a non-parametric model is more flexible concerning the object of modeling and it can achieve more accurate results over a wider range of operating conditions (provided the data are sufficient).
The circumstance that non-parametric models do not allow the same kind of physical insight has lead to the misconception of them being ``unphysical'' as against parametric models, which are then sloppily called ``physical'' or ``physically based'' models. The fact is that for both categories, the choice of the functions and parameters or data sets used can be motivated by physical derivations or by heuristic considerations. In particular, interpolation or approximation functions of all good table-based models are motivated by physical considerations. In contrast, the number of parameters of some parametric models - most notably the BSIM2 and BSIM3 models in SPICE [43,15] - has increased beyond what can be reasonably understood. For example, in BSIM3v3 the number of parameters is well over 100 and the number of DC parameters alone (without temperature and W/L dependence) is 41, most of them essentially fit parameters to achieve high accuracy [15].