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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

Unveiling the full potential of doped silicon for electronic, photonic, and plasmonic application at THz frequencies requires a thorough understanding of its high-frequency transport properties. In this letter, we present a comprehensive numerical characterization of the frequency-dependent (0–2.5 THz) complex conductivity of silicon at room temperature over a wide range of doping densities (1014−1018 cm−3). The conductivity was calculated using a multiphysics computational technique that self-consistently couples ensemble Monte Carlo (EMC) simulation of carrier transport, the finite-difference time-domain (FDTD) solution to Maxwell's equations, and molecular dynamics (MD) for the treatment of short-range Coulomb interactions. Our EMC/FDTD/MD numerical results complement the experimental data that only exist for a select few doping densities. Moreover, we show that the computed complex conductivity of Si at THz frequencies can be accurately described by a generalized Drude (GD) model with doping-dependent parameters that capture the cross-over from phonon-dominated to Coulomb-dominated electron transport as the doping density increases. The simplicity of the GD model enables one to readily compute the complex conductivity of silicon for any doping density within the range studied here.

The explanation of wave behavior upon total internal reflection from a gainy medium has defied consensus for 40 years. We examine this question using both the finite-difference time-domain (FDTD) method and theoretical analyses. FDTD simulations of a localized wave impinging on a gainy half space are based directly on Maxwell's equations and make no underlying assumptions. They reveal that amplification occurs upon total internal reflection from a gainy medium; conversely, amplification does not occur for incidence below the critical angle. Excellent agreement is obtained between the FDTD results and an analytical formulation that employs a new branch cut in the complex "propagation-constant" plane.

We calculate the room-temperature complex conductivity σ (ω) of suspended and supported graphene at terahertz frequencies (100 GHz-10 THz) by employing a self-consistent coupled simulation of carrier transport and electrodynamics. We consider a wide range of electron (n = 10 12 -10 13 cm −2 ) and impurity (N i = 8 × 10 10 -2 × 10 12 cm −2 ) densities. For graphene supported on SiO 2 , there is excellent agreement between the calculation with clustered impurities and the experimentally measured σ (ω). The choice of substrate (SiO 2 or h-BN) is important at frequencies below 4 THz. We show that carrier scattering with substrate phonons governs transport in supported graphene for N i /n < 0.1. Electron-impurity interactions dominate for N i /n > 0.1, and transport enters the electron-hole puddle regime for N i /n > 0.5. The simple Drude model, with an effective scattering rate and Drude weight D as parameters, fits the calculated σ (ω) for supported graphene very well, owing to electron-impurity scattering. decreases with increasing n faster than n −1/2 and is insensitive to electron-electron interaction. Both electron-electron and electron-impurity interactions reduce the Drude weight D, and its dependence on n is sublinear.