Short-range and long-range Coulomb interactions for 3D Monte Carlo device simulation with discrete impurity distribution

Many-particle Monte Carlo Approach to Electron Transport

“…In the last decade, several works have remarked the necessity of paying maximum attention not only to electron-electron (e-e) but also to electron-impurity (e-i) Coulomb interactions when developing new approaches to electron transport (Barraud et al, 2002;Gross et al, 1999;2000b;Wordelman & Ravaioli, 2000). In the MC solution of the BTE, historically the e-i (and also a part of the e-e) interactions have been introduced perturbatively as "instantaneous" and "local" transitions of electrons between different regions of the k-space.…”

“…On the other hand, far enough from them (∼ tens of nanometers), the shape of the scalar potential depends on the particular spatial charge distribution. In this regard, a common strategy consists on introducing a long-range part of the Coulomb interaction numerically through the solution of the mesh-dependent mean-field Poisson equation, and a short-range part analytically (the so-called Monte Carlo/Molecular dynamics approach, MCMD, (Gross et al, 1999;Wordelman & Ravaioli, 2000)), or perturbativelly (Barraud et al, 2002). The MCMD approach, however, shows some inconvenients.…”

3D Monte Carlo analysis of discrete dopant effects on electron noise in Si devices

“…The necessary correction usually consists in defining around each impurity a short-range zone (SRZ) in which the longrange Coulomb interaction is removed and replaced by a short-range mechanism. In our self-consistent MC model the short-range interaction is described by an instantaneous scattering mechanism characterized by a scattering rate [10] as for all other types of scattering experienced by carriers. This approach is valid if we take care to consider three questions simultaneously: the choice of the mesh size, the choice of the SRZ size and the model of scattering rate.…”

“…A mesh size of one tenth of the average distance between impurities, i.e. X = N −1/3 /10, is proved to be a good compromise between accuracy and computational resources [10].…”

“…In the case of attractive impurities, the SRZ must be large enough to avoid inconsistencies between a classical description of particles and a thin impurity potential that looks like a quantum dot [10]. But to simplify the calculation of electron-ion scattering rate, the SRZ should be as small as possible.…”