With the continuing reduction of the minimum feature size of semiconductor devices, the models used for simulations of these devices need to be updated and implemented. These updates include quantum corrections as well as models considering moments of higher order. Quantum corrections become increasingly important as the dimensions of the device approach the mean free path length of the electrons within the semiconductor, leading to quantization of the electrons' states. This has a profound influence on the density of states and on thereby the distribution of charge within the device. This is especially true for the lateral direction in the channel region but will also become important in the transversal direction as gate lengths are further reduced. Boltzmann's transport equation, the starting point for the derivation of the drift diffusion transport model, is no longer capable of giving satisfactory results under these conditions. Wigner's equation represents an attempt to cope with the effects encountered in these scaled devices. This method proposes to yield relatively simple macroscopic models capable of describing the electron transport within nanometer scale devices.

Beginning at about three hundred nanometers drift diffusion models predict less current than is actually encountered in devices. Energy transport and hydro-dynamic models continue to provide useful results down to a size of about one hundred nanometers, but then the calculated current starts to deviate from measured data. A model using six moments promises to remain accurate down to at least thirty nanometers.