A one-dimensional solution of the Boltzmann transport equation including electron–electron interactions

Abstract

In this article a technique is described for solving the one-dimensional spatially dependent Boltzmann transport equation with electron–electron interactions included in the scattering model. The analysis is illustrated by solving the Boltzmann transport equation over a potential profile typical of that found in the channel of a metal–oxide–semiconductor field-effect transistor. A comparison is made between the distribution functions obtained when electron–electron interactions are included and excluded from the scattering model. It is found that electron–electron interactions significantly increase the electron population at energies greater than are available from the electric field.

The Energy-Driven Hot Carrier Degradation Modes

“…In a similar approach, it is possible to describe interface traps generation rate function S it [2] considering that the dominant energy in linear regime is V eff (LEM picture) (S it =1/(τ.I d )) and in quadratic regime is n.V eff (n=1.6 in our case)(S it =1/(τ.I d 2 )) since EES induces a second knee in EEDF at just less than 2.V eff [7][8](cf. Fig.…”

Dominant mechanisms of hot-carrier degradation in short- and long-channel transistors

“…This process was shown to populate the carrier ensemble fraction which is characterized by energies higher than that obtained by the electric field [16,17]. As a result, EES substantially enforces hot-carrier degradation in the devices fabricated according to the 180 nm process node and in shorter counterparts [14,15].…”

The energy-driven paradigm of NMOSFET hot-carrier effects

“…Also, e-e scattering induces a second weaker knee at just less than 2 V EFF [6], [7], [11]- [13] (and an even weaker knee at somewhat below 3 V EFF , etc., which will be neglected here). Adding e-e-scattering effects to the EEDF and a (as yet) hypothetical ISG cross section, S IT will result in something like that shown in Fig.…”

“…(b) Experimental data for the quadratic regime compared to (10c) using the proposed S IT function(11).…”