On the Self-Consistent Event Biasing Schemes for Monte Carlo Simulations of Nanoscale MOSFETs

TL;DR

This paper explores event biasing techniques in Monte Carlo simulations of nanoscale MOSFETs to improve statistical accuracy and convergence, especially for rare carrier transport events, by deriving a self-consistent approach.

Contribution

It introduces a self-consistent event biasing scheme for particle-based Monte Carlo simulations of nanoscale MOSFETs, including derivation and generalization for Hartree carriers.

Findings

Enhanced channel statistics in simulations.

Faster convergence of terminal current calculations.

Biasing weights persist through Poisson coupling steps.

Abstract

Different techniques of event biasing have been implemented in the particle-based Monte Carlo simulations of a 15nm n-channel MOSFET. The primary goal is to achieve enhancement in the channel statistics and faster convergence in the calculation of terminal current. Enhancement algorithms are especially useful when the device behavior is governed by rare events in the carrier transport process. After presenting a brief overview on the Monte Carlo technique for solving the Boltzmann transport equation, the basic steps of deriving the approach in presence of both the initial and the boundary conditions have been discussed. In the derivation, the linearity of the transport problem has been utilized first, where Coulomb forces between the carriers are initially neglected. The generalization of the approach for Hartree carriers has been established in the iterative procedure of coupling with the Poisson equation. It is shown that the weight of the particles, as obtained by biasing of the Boltzmann equation, survives between the successive steps of solving the Poisson equation.