A Hybrid EM/QM Framework Based on the ADHIE-FDTD Method for the Modeling of Nanowires

Abstract

A new modeling formalism to compute the timedependent behavior of combined electromagnetic (EM) and quantum mechanical (QM) systems is proposed. The method is geared towards highly multiscale geometries, which is vital for the future design of nanoelectronic devices. The advocated multiphysics modeling formalism leverages the alternating-direction hybrid implicit-explicit (ADHIE) finite-difference time-domain (FDTD) method for the EM fields and is combined with a novel ADHIE method for the EM potentials. Additionally, we tackle the QM problem using a new split real and imaginary part formulation that includes higher-order spatial differences and arbitrary timedependent EM potentials. The validity of the proposed formalism is theoretically discussed by deriving its stability condition and calculating the numerical dispersion relation. Furthermore, the applicability of our modeling approach is proven through several numerical experiments, including a single-particle Maxwell-Schrödinger (MS) system as well as a many-particle Maxwell-Kohn-Sham (MKS) system within the time-dependent density-functional theory (TDDFT) framework. These experiments confirm that the novel ADHIE method drastically decreases the computation time while retaining the accuracy, leading to efficient and accurate simulations of light-matter interactions in multiscale nanoelectronic devices.

An ADHIE-TDDFT Method for the EM/QM Co-simulation of Coupled 1-D Nanowires

“…In this section, we study the EM near-field coupling (or crosstalk) between two GaAs nanowires located in each other's vicinity (see Figure 1 implementation of those PMLs is outlined in [11]. Along the x− and y-directions, the grid is uniformly subdivided in cells with dimensions ∆x = ∆y = 6.55 nm.…”

“…To eliminate the stability constraint of the small time step here as well, a dedicated ADHIE-FDTD method has been put forward in [11]. This scheme consists of an explicit update for the vector potential:…”

“…In this paper, we provide an extension to the ADHIE-method that allows to determine the EM potentials described in the Lorenz gauge [11]. These enter the Hamiltonians of the QM systems and are thus important to examine the influence of EM fields [12].…”