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Superlattices and Microstructures

Volume 34, Issues 3–6, September–December 2003, Pages 361-366
Superlattices and Microstructures

Quantum fluctuations in atomistic semiconductor devices

https://doi.org/10.1016/j.spmi.2004.03.028Get rights and content

Abstract

Atomistic Green function simulations of model 25 nm×25 nm Si MOSFETs predict strong fluctuation effects derived from mode fluctuations in the quantum transport through the inhomogeneous 2DEG channel caused by the spatial distribution of non-self-averaged discrete dopants.

Introduction

The self-averaging of impurity scattering in ultra-small semiconductor devices fails when less than 1000 impurities are present [1] and the standard treatment of impurity scattering (classical or quantum mechanical) is inadequate [2]. This atomistic regime is important for limiting scale MOSFET devices from 50 nm scales down to the currently perceived limits near 4 nm. Semi-classical device modelling shows that the different spatial micro-configurations of individual impurities at the same nominal doping densities lead to severe fluctuations in device parameters such as threshold voltage [3]. Unfortunately, there are no reported atomistic device simulations based on a full quantum mechanical analysis. The true scale and importance of atomistic fluctuations therefore remains unknown. Here we report the first non-perturbative calculations for quantum transport in a simplified model 2D Si FET device containing finite numbers of discrete Coulomb scattering centres (attractive and repulsive). The aim is to expose the physics of atomicity at this stage rather than precision device modelling. The formalism is based on non-equilibrium Green function (NEGF) methodology adapted to describe impurity scattering and interface roughness non-perturbatively with no self-averaging assumptions. NEGF methods have been deployed elsewhere (e.g. [4]), but not for atomistic scattering.

Section snippets

The model

The basic model MOSFET device and simulation domain is outlined in Fig. 1.The computationally challenging 3D self-consistent problem is reduced hierarchically as follows. (i) A model calculation is made for the self-consistent electrostatic profiles ψ(x,y) along the two-dimensional continuously doped channel, assuming the y–z plane is occupied by the ground state of the 2DEG formed by quantisation of the quasi-triangular well formed by band-bending at the Si oxide interface. This phase uses

Transmission function

Fig. 2shows calculations for the strong fluctuations in channel transmission as a function of energy for five different micro-configurations of three ionised impurities distributed in the channel at very low electric field Ey, corresponding, for example, to sub-threshold transport. The fluctuations derive from the excitation of different transverse modes in the channel. For the model device, assuming an isotropic effective mass ratio m∗=0.3283, the transverse mode ground state energy is

Densities and flows

Fig. 4shows the corresponding carrier charge density and current density as functions of position in a model 25×25 nm2 silicon device at an energy close to kBT for a distribution of three ionised donors under zero bias. Fig. 4(a) is for strongly screened interactions (short range), Fig. 4(b) is for long range Coulomb scattering; Fig. 4(c) shows the effect of adding in atomistic interface roughness non-perturbatively (Δ=0.15 nm,λ=3 nm). In each case the flow comprises open meandering orbits

Current–voltage characteristics

The Ids–Vg characteristics at Vds=1.0 V for the 25×25 nm2 n-channel device are shown in Fig. 5(computed points at 0.05 V intervals). The upper curve corresponds to no atomistic scattering but does include elastic acoustic phonon scattering contributions to the self-energy. Despite the crude model the results are similar to a recent NEGF non-atomistic self-consistent simulation of the “ballistic” 25 nm MIT well-tempered device that uses a 2D simulation domain in the traditional vertical plane

Discussion and conclusions

As predicted by our recent analytical study [1] of atomistic multiple scattering on hard spheres, the numerical simulations show: strong interference between the waves scattered from individual impurities; interference with the incoming flows; and interactions with the boundary scattering. The current flow comprises open meandering orbits and by trapped vortex flows that block the channel [7]. It is found that the most severe fluctuations occur for short range Coulomb scattering at weak applied

Acknowledgements

This work was partly supported by grants from the Engineering and Physical Sciences Research Council (UK).

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