@User An Analytical model of a semiconductor device aims to describe the device operation by using the underlying physics, so its behavior is simulated by evaluating all the equations (Conduction, charge models, p-n junctions, carrier density) needed to describe it and evaluate its current/voltage characteristics. Empirical models just estimate the device behavior by measuring key parameters of these devices and fitting with interpolation / extrapolation. Analytical models are in general slower but way more precise and reliable. Empirical models are in general fast but should never be trusted outside the 'observation window'.