Simulation of statistical variability in nano-CMOS transistors using drift-diffusion, Monte Carlo and non-equilibrium Green’s function techniques

Abstract

In this paper, we present models and tools developed and used by the Device Modelling Group at the University of Glasgow to study statistical variability introduced by the discreteness of charge and matter in contemporary and future Nano-CMOS transistors. The models and tools, based on Drift-Diffusion (DD), Monte Carlo (MC) and NonEquilibrium Green's Function (NEGF) techniques, are encapsulated in the Glasgow 3D statistical 'atomistic' device simulator. The simulator can handle most of the known sources of statistical variability including Random Discrete Dopants (RDD), Line Edge Roughness (LER), Thickness Fluctuations in the Oxide (OTF) and Body (BTF), granularity of the Poly-Silicon (PSG), Metal Gate (MGG) and High-κ (HKG), and oxide trapped charges (OTC). The results of the statistical simulations are verified with respect to measurements carried out on fabricated devices. Predictions about the magnitude of the statistical variability in future generations of nano-CMOS devices are also presented.

3D multi-subband ensemble Monte Carlo simulator of FinFETs and nanowire transistors

“…Its results have been compared with those obtained from well-established tools using different approaches. In particular 3D NEGF and Drift Diffusion (DD) codes [10], [11], [12] have been used to benchmark ballistic and diffusive devices respectively. One of the effects that MSB-EMC codes cannot handle in a direct way is tunneling which may appear through source barrier as channel length is reduced.…”

Many-particle Monte Carlo Approach to Electron Transport

“…Such a problem can be avoided by properly identifying the spatial region where short-range Coulomb interactions have to be included. In particular, the Molecular dynamics routine uses a "corrected" short-range Coulomb interaction that excludes the long-range contribution from the Poisson equation (Gross et al, 1999;2000a;b). The problem comes then from the analytical nature of the short-range corrections, which can lead to unphysically large forces that cause artificial heating and cooling (for acceptors and donors respectively) of the carriers (Gross et al, 2000b;Ramey & Ferry, 2003).…”

Use of density gradient quantum corrections in the simulation of statistical variability in MOSFETs

“…As discussed elsewhere [33], updating the quantum correction during the course of the simulation is unnecessary, adding additional memory demands and increasing sensitivity to the noise inherent in MC simulations. The important elements to be captured are the V T shift and the quantum carrier distribution at the source end of the channel, which do not change significantly with the applied drain voltage.…”