Moments of the Inverse Scattering Operator of the Boltzmann Equation: Theory and Applications

Abstract

In this paper useful physical objects called moments of the inverse scattering operator (MISO) of the Boltzmann equation (BE) are studied. The existence and uniqueness of the MISO is proven and a simple, generally valid, iterative scheme to actually compute those objects is given. The applications of the MISO extend from the computation of the solution for the space-homogeneous BE for small electric and magnetic fields to the exact computation of any transport parameter. This can be done for all moments of the space-inhomogeneous BE and for arbitrary electric and magnetic field intensities. The concept of MISO offers an elegant way to avoid the relaxation time approximation (RTA) every time it comes into play, not only theoretically but also in practical computations.

Comparison of Monte Carlo Transport Models for Nanometer-Size MOSFETs

“…Most of these transport models [3,5,6,7] (hereafter referenced as A, C, D and E, respectively) adopt a full-band description of the energy-wavevector dispersion relationship with usual 0 th order phonon description and parameter values suggested in [1], with the exception of acoustic phonons in model A. Model B [4] assumes a non-parabolic ellipsoidal analytical model of silicon bands; 0 th order phonon model is assumed for f 2 , f 3 , g 3 ∆ − ∆ intervalley transitions, while a 1 st order model is assumed for the f 1 , g 1 , g 2 phonons.…”

“…Surface roughness (SR) is treated by the reflective-diffusive model in [4,5,6,7], while [3] adopts an effective-field dependent scattering rate. In all cases, SR parameters are tuned in order to fit the universal mobility curve for n-MOSFETs.…”

“…This activity proved very valuable as it led to building up a general consensus on the selection of key ingredients such as band structure and scattering models. This paper aims at a substantial step forward with respect to [2] by comparing simulations of advanced nanoMOSFET obtained with five well assessed MC simulators [3,4,5,6,7]. Our results put in evidence a non-satisfactory status of the modeling of IIS at large doping concentrations and for far-from-equilibrium conditions.…”

Exact method to solve the Boltzmann equation to any order in the driving forces: Application to transport parameters

“…2 Theory In Ref. [7] the existence and uniqueness of an inverse of the scattering operator (ISO) of the BTE was proven and the concept of moments of the ISO (MISO) was introduced. Using the idea of MISO, the degenerate spacehomogeneous BTE can be solved iteratively in all orders in the electric and magnetic field [5].…”

“…3 Transport parameters The theory exposed in the previous section can now be used to compute TPs as function of the DFs. In [7] the diffusivity tensor D and the mobility tensor µ are defined as:…”