The small feature sizes of modern semiconductor devices push the validity of macroscopic simulation models to their limits. In order to meet the upcoming simulation challenges, new simulation models have been developed. One of these developments is a six moments transport model. The use of higher order transport models provides more detailed information about the distribution function of the electrons at the expense of a slightly increased computational effort. The additional information invoked in higher order transport models such as the six moments transport model not only enables a better modeling of non local effects such as impact ionization but also extends the model's accuracy to smaller feature sizes when compared to either the drift diffusion or hydrodynamic models.
The most complete description of carriers is provided by their distribution function. The distribution function can be obtained as the solution of Boltzmann's transport equation. Monte Carlo simulations provide a tried and tested way of calculating these solutions at a considerable expense of computational effort. Alternatives of computing the solution of Boltzmann's transport equation, such as a spherical harmonics expansion of the distribution function that makes a deterministic solution of the Boltzmann equation viable, are being explored. Besides possibly being less intensive on computational resources, this method is also capable of providing solutions in cases that have proved difficult for Monte Carlo simulations. None of the approaches mentioned thus far have the capacity of considering any kind of quantum effect.
One way to accomplish this is to use Wigner's equation to describe the behavior of the carriers. This endeavor has proven to be very challenging numerically. Very good results have been obtained by applying the Monte Carlo method to the solution of the Wigner equation.