Quantum Treatment of Inelastic Interactions for the Modeling of Nanowire Field-Effect Transistors

Abstract

During the last decades, the Nonequilibrium Green's function (NEGF) formalism has been proposed to develop nano-scaled device-simulation tools since it is especially convenient to deal with open device systems on a quantum-mechanical base and allows the treatment of inelastic scattering. In particular, it is able to account for inelastic effects on the electronic and thermal current, originating from the interactions of electron-phonon and phonon-phonon, respectively. However, the treatment of inelastic mechanisms within the NEGF framework usually relies on a numerically expensive scheme, implementing the self-consistent Born approximation (SCBA). In this article, we review an alternative approach, the so-called Lowest Order Approximation (LOA), which is realized by a rescaling technique and coupled with Padé approximants, to efficiently model inelastic scattering in nanostructures. Its main advantage is to provide a numerically efficient and physically meaningful quantum treatment of scattering processes. This approach is successfully applied to the three-dimensional (3D) atomistic quantum transport OMEN code to study the impact of electron-phonon and anharmonic phonon-phonon scattering in nanowire field-effect transistors. A reduction of the computational time by about ×6 for the electronic current and ×2 for the thermal current calculation is obtained. We also review the possibility to apply the first-order Richardson extrapolation to the Padé N/N − 1 sequence in order to accelerate the convergence of divergent LOA series. More in general, the reviewed approach shows the potentiality to significantly and systematically lighten the computational burden associated to the atomistic quantum simulations of dissipative transport in realistic 3D systems.

Atomistic Simulation of Nanoscale Devices

“…All these effects can be cast into dedicated scattering self-energies (SSE) that depend on the Green's functions (GF), which in turn hinge on the SSE. Hence, the GF and SSE equations must be solved self-consistently within the so called self-consistent Born approximation (SCBA) or deterministically by a diagrammatic perturbative approach [25]. When the GF and SSE do not vary by more than a pre-defined criterion between two consecutive iterations, the SCBA is assumed to have converged.…”

Special Issue: Nanowire Field-Effect Transistor (FET)

“…Finally, Lee et al [7], in their article, reviewed the theory regarding the lowest order approximation combined with Padé approaches for the quantum-mechanical treatment of electron-phonon and phonon-phonon inelastic scattering developed within the non-equilibrium Green's function (NEGF) formalism. The method was applied to the Si Gate-All-Around NW FET with a gate length of 13 nm.…”