Multiphysics simulation of high-frequency carrier dynamics in conductive materials

Abstract

We present a multiphysics numerical technique for the characterization of high-frequency carrier dynamics in high-conductivity materials. The technique combines the ensemble Monte Carlo (EMC) simulation of carrier transport with the finite-difference time-domain (FDTD) solver of Maxwell's curl equations and the molecular dynamics (MD) technique for short-range Coulomb interactions (electron-electron and electron-ion) as well as the exchange interaction among indistinguishable electrons. We describe the combined solver and highlight three key issues for a successful integration of the constituent techniques: (1) satisfying Gauss's law in FDTD through proper field initialization and enforcement of the continuity equation, (2) avoiding double-counting of Coulomb fields in FDTD and MD, and (3) attributing finite radii to electrons and ions in MD for accurate calculation of the short-range Coulomb forces. We demonstrate the strength of the EMC=FDTD=MD technique by comparing the calculated terahertz conductivity of doped silicon with available experimental data for two doping densities and showing their excellent agreement. V

EMC/FDTD/MD simulation of carrier transport and electrodynamics in two-dimensional electron systems

“…Carrier transport is simulated by including both electrons and holes in the graphene layer, while the positively charged ions near the interface and within the SiO2 substrate remain stationary. the usual Drude model fails, with good agreement to experimental data [14,25].…”

“…Molecular dynamics simulates short-range interactions in classical many-particle systems [34]. For a collection of electrons, holes, and charged ions, the particle-particle short-range interactions we include are the direct and exchange Coulomb forces among carriers (electrons and holes), and the direct Coulomb forces between carriers and ions [14]. We only calculate the pairwise interactions among the particles present within a 3 × 3 × 3-cell volume of one another, in order to minimize the computational burden in MD, which scales as N 2 , N being the number of interacting particles [35].…”

Clustered impurities and carrier transport in supported graphene

“…In a nutshell, EMC solves the Boltzmann transport equation, FDTD solves Maxwell's curl equations, while MD accounts for the interaction of charges when very close to one another. The coupled EMC/FDTD/MD technique was successfully used to calculate the high-frequency conductivity of bulk silicon, with very good agreement to experimental data [38,40]. Below, we briefly describe the key elements of the constituent techniques and refer the interested reader to references [38] and [39] for extensive computational detail.…”

A fast time‐domain EM–TCAD coupled simulation framework via matrix exponential with stiffness reduction

“…So far, only a few frameworks have been developed to allow such coupling, for example, [1][2][3], based on different selections of EM and TCAD solvers for combination. One experimentally verified co-simulation framework was firstly proposed in [4,5] in the frequency domain.…”

“…Electromagnetic-technology computer-aided design co-simulation refers to a concurrent solution of the Maxwell's equations that describe the EM dynamics and transport models that describe the charge carrier dynamics in semiconductor devices. So far, only a few frameworks have been developed to allow such coupling, for example, [1][2][3], based on different selections of EM and TCAD solvers for combination. One experimentally verified co-simulation framework was firstly proposed in [4,5] in the frequency domain.…”