There is a significant precaution when performing random dopant fluctuation by using the drift-diffusion model that is the basis of the conventional device simulation. Because the continuation by a long wavelength approximation was done to derive said drift-diffusion model. That is how to recover the location dependence of discrete impurity ions in the long wavelength approximation. For example, in the case that there is an impurity ion near to the interface to an insulating film, the charge density of an impurity ion, which was made continuous in the conventional method, is unable to catch the charge density change due to polarization at the interface. Because this polarization is dependent of the location of a discrete impurity ion near to the interface.
A method for simply implementing the effect of polarization to the device simulation is provided by appending an image charge inside the insulating film to linearize the charge of discrete impurity ion which locates near to the interface to satisfy the consistency to the drift-diffusion model while keeping the location dependency of the discrete ion.