Simulation of a double-gate MOSFET by a non-parabolic energy-transport subband model for semiconductors based on the maximum entropy principle

Exploitation of the Maximum Entropy Principle in Mathematical Modeling of Charge Transport in Semiconductors

“…In this section, we consider the case of an ensemble of electrons (the treatment of holes would be analogous) confined along one dimension, called quasi 2Delectron gas (2DEG) [16,[18][19][20]44]. This situation arises when the length scale in one (the confined) space direction of the semiconductor device under study is of the order of de Broglie wavelength of electrons, while the nonconfined directions have a much bigger length scale.…”

“…Regarding the collision operator, in the non-degenerate approximation, each contribution has the general form [18][19][20] …”

“…In Si, the relevant 2D scattering mechanisms are the acoustic phonon scattering, and the non-polar optical phonon scattering. Their expressions are the 2D version of those shown in Section 2 and can be found in [18][19][20]47]. Attempts to directly solve the Schrödinger-Poisson-Boltzmann system can be found, for example, in [16,17,48] where numerical schemes based on finite differences have been employed.…”

“…This has again prompted the development of simpler macroscopic models for CAD purposes. These models can be obtained as moment equations of the Boltzmann transport equations under suitable closure relations [18][19][20].…”

“…However, the numerical integration of the transport part, which has been performed by employing Monte Carlo or deterministic methods [16,17], is also in this case very expensive, from a computational point of view, for CAD purposes. Consequently, it can be convenient to substitute the Boltzmann equations with macroscopic models again obtained by using the moment method and closing the moment equations with MEP [18][19][20].…”