ABSTRACT
The distribution function is a derivate of the equilibrium distribution farther and largely varies with space and time. In some cases, it is recognized that the concepts of the Boltzmann equation and the distribution function are still effective, whose three main assumptions, that is, effective mass, energy band model, and electron collisions at space and time are instantaneous, are all tenable. But the Boltzmann equation cannot be solved by the ordinary perturbation method, while it can be by other methods, for example, the Monte Carlo method. Silicon metal-oxide semiconductor field-effect transistors have been investigated using a large variety of physical models, from full-band Monte Carlo simulations to parabolic-band approximations coupled to Monte Carlo or simplified solutions to the transport equation. Modulation of the momentum equations can be made by assuming a drift Fermi-Dirac distribution function, which results in a degeneracy correction factor to the effective electron temperature.
