Global modeling of carrier-field dynamics in semiconductors using EMC–FDTD

Abstract

The interactions between carriers and fields in semiconductors at low frequencies (<100 GHz) can be adequately described by numerical solution of the Boltzmann transport equation coupled with Poisson's equation. As the frequency approaches the THz regime, the quasi-static approximation fails and full-wave dynamics must be considered. Here, we review recent advances in global modeling techniques-numerical techniques that couple carrier dynamics with full wave dynamics. We focus on the coupling between the stochastic ensemble Monte Carlo (EMC) simulation of carrier transport and the finite-difference timedomain (FDTD) solution to Maxwell's curl equations. We discuss the stability and accuracy requirements for different types of high-frequency excitation (wave illumination vs. ac bias), and present simulation results for the THz-regime conductivity of doped bulk silicon, ultrafast carrier dynamics and radiation patterns in GaAs filaments, and the ac response of GaAs MESFETs.

Multiphysics simulation of high-frequency carrier dynamics in conductive materials

“…6 Even a technologically important material like silicon is not fully characterized in this range. 1,7 This gap in our understanding of THz-frequency materials properties can be filled in part by the development and employment of a comprehensive simulation tool for carrier dynamics under THz-frequency stimulation in conducting materials. The central challenge of this work is to develop such a simulation tool: an electromagnetic, particle-based solver that maintains high accuracy over a broad frequency spectrum and a broad range of carrier densities.…”

“…9 The vast majority of EMC implementations describe carrier dynamics under either dc or low-frequency stimulation, where xs ( 1. 7 In this case, the stimulation period is very long compared to the time scale of relevant scattering processes, and electric fields may be assumed to be constant over a simulation time step. Most state-of-the-art EMC implementations use grid-based quasielectrostatic solvers (essentially solving Poisson's equation) to incorporate electric field effects.…”

“…Both the charge and current densities influence the electromagnetic field calculation. 7,[13][14][15] The particle-in-cell (PIC) technique is a powerful method for describing mobile charge interactions with time-varying electromagnetic fields. Early development of the PIC technique was prompted by interest in plasma fusion devices.…”

“…21 FDTD is well suited for high-frequency analyses in which the quasielectrostatic assumption fails. 7,22,23 By combining EMC with FDTD, we may describe the carrier dynamics of a realistic ensemble under electromagnetic stimulation at THz frequencies. 7,15,22,23 However, grid-based field solvers, such as FDTD and the quasielectrostatic Poisson's equation solvers mentioned above, cannot describe the strong forces among charges separated by distances smaller than the simulation grid cell.…”

Frequency-domain multiscale quantum mechanics/electromagnetics simulation method

“…15 By Fourier transformation of the time-domain equations in the EM solver, the coupled frequency-dependent EM and drift-diffusion equations can be solved to model electronic devices, interconnects, substrates, and dielectrics. [16][17][18][19][20] Based on the finite volume method (FVM), 21 the potential formalism of Maxwell's equations and a mimetic discretization of differential operators are adopted to guarantee local charge conservation. Instead of the electric field E and the magnetic field H , the scalar potential V and vector potential A are chosen as basic variables which facilitate the interface with conventional engineering solvers and the QM method.…”