K. J. Willis

Terahertz conductivity of doped silicon calculated using the ensemble Monte Carlo/finite-difference time-domain simulation technique

We present terahertz-frequency characterization of doped silicon via a multiphysics numerical technique that couples ensemble Monte Carlo (EMC) simulation of carrier transport and a finite-difference time-domain (FDTD) solver of Maxwell’s curl equations. We elucidate the importance of rigorous enforcement of Gauss’s law, in order to avoid unphysical charge buildup and enhance solver accuracy. The calculated complex conductivity of doped bulk silicon shows excellent agreement with available experimental data. This comprehensive microscopic simulator is a valuable predictive tool in the terahertz frequency range, where experimental data are scarce and the Drude model inadequate.

A High-Q Terahertz Resonator for the Measurement of Electronic Properties of Conductors and Low-Loss Dielectrics

The successful engineering of sources and components in the terahertz (THz) regime benefits from good characterization of materials properties. Previous research reports have shown that calculations of material parameters that are valid at radio frequencies are no longer accurate at THz frequencies. A high-quality-factor quasi-optical hemispherical resonator operating between 300 GHz-1 THz has been designed and implemented for the measurement of electronic properties of conductors as well as low-loss dielectrics. This apparatus is the first quasi-optical resonator to achieve Q≈ 4×105 at frequencies greater than 400 GHz in the THz regime. It is also the first open resonator designed to measure effective conductivity at these frequencies. This paper discusses the techniques that enabled high-Q operation in the THz regime. It also includes measurements of silicon with different doping densities and conductors of various surface roughness values with comparison to theoretical predictions.

Multiphysics simulation of high-frequency carrier dynamics in conductive materials

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 conductivit...

A generalized Drude model for doped silicon at terahertz frequencies derived from microscopic transport simulation

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 Maxwells 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...

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

We present the implementation and application of a multiphysics simulation technique to carrier dynamics under electromagnetic excitation in supported two-dimensional electronic systems. The technique combines ensemble Monte Carlo (EMC) for carrier transport with finite-difference time-domain (FDTD) for electrodynamics and molecular dynamics (MD) for short-range Coulomb interactions among particles. We demonstrate the use of this EMC/FDTD/MD technique by calculating the room-temperature dc and ac conductivity of graphene supported on SiO2.

A Global EMC-FDTD Simulation Tool for High-Frequency Carrier Transport in Semiconductors

We present a computational tool for the characterization of conductive media at THz frequencies. By coupling the Ensemble Monte Carlo (EMC) simulator of carrier dynamics and the finite-difference time-domain (FDTD) solver of Maxwells equations, we develop and characterize a robust and versatile global simulator that interactively tracks field-particle dynamics. In this report the EMC-FDTD simulator is used to model the interaction of bulk doped silicon with THz frequency electromagnetic plane waves. The performance of the simulation tool is investigated in terms of several simulation parameters, including grid cell size and carrier ensemble size. The complex conductivity of doped silicon at THz frequencies obtained from the combined EMC-FDTD solver is in good agreement with available experimental results.

Simulation of carrier dynamics in graphene on a substrate at terahertz and mid-infrared frequencies

We calculate the complex conductivity of graphene in the terahertz (THz) to mid-infrared (mid-IR) frequency range using a numerical simulation that couples the two-dimensional (2D) ensemble Monte Carlo technique (EMC) for carrier transport, the three-dimensional (3D) finite-difference time-domain (FDTD) technique for electrodynamics, and molecular dynamics (MD) for short range Coulomb interactions. We demonstrate the effect of the typically used silicon-dioxide substrate on the high-frequency carrier dynamics in graphene and show good agreement between recent experimental results and our numerical simulations.

Coupled simulation of carrier transport and electrodynamics: the EMC/FDTD/MD technique

In order to understand the response of conductive materials to high-frequency electrical or optical excitations, the interplay between carrier transport and electrodynamics must be captured. We present our recent work on developing EMC/FDTD/MD, a self-consistent coupled simulation of semiclassical carrier transport, described by ensemble Monte Carlo (EMC), with full-wave electrodynamics, described by the finite-difference time-domain (FDTD) technique and molecular dynamics (MD) for sub-grid-cell interactions. Examples of room-temperature terahertz-frequency transport simulation of doped silicon and back-gated graphene are shown.

Multiphysics simulations of carrier transport and electrodynamics in two-dimensional electron systems

We present a multiphysics numerical technique and use it for simulating carrier dynamics under electromagnetic excitation in supported two-dimensional electronic systems. The technique combines ensemble Monte Carlo (EMC) for carrier transport with finite-difference time-domain (FDTD) for electrodynamics and molecular dynamics (MD) for short-range Coulomb interactions among particles. We explain the important criteria required for coupling the constituent methods and demonstrate the use of this coupled EMC/FDTD/MD technique by calculating the room-temperature dc and ac conductivity of graphene supported on SiO2.

A Time-Domain Analysis of Enhanced Total Internal Reflection Using the FDTD Method

There is a long-standing debate surrounding whether or not enhanced total internal reflection (ETIR) is possible. ETIR implies that the magnitude of the reflection coefficient is greater than unity and is conjectured to be possible when a field is incident from a lossless material to a gainy material beyond the critical angle. In this letter, we examine this problem through finite-difference time-domain (FDTD) modeling. The two-dimensional simulations employ a Gaussian incident beam and make no a priori assumptions about the reflection coefficient. We consider illumination of gainy, lossless, and lossy materials. The Poynting vector is used to examine the flow of energy. For a gainy material, the magnitude of the reflection coefficient is found to be greater than unity, but there is a delay between when energy enters the gainy material and when the “excess” energy is reflected from the interface. Thus, given the Goos-Hänchen shift associated with total internal reflection, where the reflected beam is shifted relative to the incident beam (so that fields must travel in the gainy material before being reflected), the existence of ETIR appears not only to be plausible, but to be inevitable.