To obtain information about the distribution function additional to the average energy several authors
proposed usage of higher order moment equations, see for example  .
These equations were based on a distribution function expanded around a Maxwellian distribution.
SONODA  added two equations for the fourth and fifths moment of BOLTZMANN's transport equation
to a standard energy transport model, taken from . A more consistent approach has been
presented in Chapter 2 where a transport model using six moments of
BOLTZMANN's transport equation has been derived, with the kurtosis as an additional state variable
Although this approach appears promising from a physical point of view, it has not been used
to tackle the SOI problem as the additional balance equation significantly increases
numerical complexity and computation times. Convergence behavior also worsens considerably.
Instead, the framework of energy transport equations was adopted and corrections accounting for distribution function
effects were introduced.
M. Gritsch: Numerical Modeling of Silicon-on-Insulator MOSFETs PDF