Distributed NEGF Algorithms for the Simulation of Nanoelectronic Devices with Scattering

TL;DR

This paper develops parallel algorithms for NEGF-based nanoelectronic device simulation, enabling efficient handling of large matrices with scattering effects, thus making realistic device modeling computationally feasible.

Contribution

It introduces parallel methods for representing and computing Green's functions in NEGF simulations, significantly reducing memory and computation requirements for large devices.

Findings

Efficient distributed representation of Green's functions.

Scalable computation of electron density and current.

Successful simulation of nanowires up to 4.5nm cross-section.

Abstract

Through the Non-Equilibrium Green's Function (NEGF) formalism, quantum-scale device simulation can be performed with the inclusion of electron-phonon scattering. However, the simulation of realistically sized devices under the NEGF formalism typically requires prohibitive amounts of memory and computation time. Two of the most demanding computational problems for NEGF simulation involve mathematical operations with structured matrices called semiseparable matrices. In this work, we present parallel approaches for these computational problems which allow for efficient distribution of both memory and computation based upon the underlying device structure. This is critical when simulating realistically sized devices due to the aforementioned computational burdens. First, we consider determining a distributed compact representation for the retarded Green's function matrix $G^{R}$. This compact representation is exact and allows for any entry in the matrix to be generated through the inherent semiseparable structure. The second parallel operation allows for the computation of electron density and current characteristics for the device. Specifically, matrix products between the distributed representation for the semiseparable matrix $G^{R}$ and the self-energy scattering terms in $\Sigma^{<}$ produce the less-than Green's function $G^{<}$. As an illustration of the computational efficiency of our approach, we stably generate the mobility for nanowires with cross-sectional sizes of up to 4.5nm, assuming an atomistic model with scattering.