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

Abstract

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.

Impact ionization in high resistivity silicon induced by an intense terahertz field enhanced by an antenna array

“…In order to keep the simulation tractable we assume that the refractive index change is constant if the field strength is greater than the threshold value E th and negligible in the substrate regions with THz electric field smaller than the threshold. We use a Drude model to analyze the dielectric properties of the substrate near antenna tips with parameters adopted from Willis et al [37]. Even though it is difficult to determine the local refractive index change, we can still determine the average refractive index change of the substrate near the antenna tips.…”

Dielectric function and plasmons in graphene: A self-consistent-field calculation within a Markovian master equation formalism

“…However, Matthiessen's rule technically holds only when all mechanisms have the same relaxation time vs energy dependence 59 . Also, employing a single energyindependent relaxation time is generally not a good approximation for systems with pronounced non-Coulomb scattering mechanisms [60][61][62][63] , such as phonons in nonpolar materials; indeed, the use of a single relaxation time has been shown not to accurately capture the loss mechanisms in suspended and, to a lower degree, supported graphene 64 . What is needed is an accurate (and, ideally, computationally inexpensive) theoretical approach that can treat the interaction of light with charge carries in graphene (and in related nanomaterials) in the presence of both interband and intraband transitions due to multiple competing scattering mechanisms, where the transition rates can have pronounced and widely differing dependencies on both carrier energy and momentum.…”

Examination of silicon material properties using THz time-domain spectroscopy

“…THz TDS studies of silicon date back to early 1990-s and there have been a few follow-on studies [1][2][3][4][5][6][7][8][9]. Many other semiconductor materials were subject to TDS studies, which filled a gap between the electronic properties measured at DC to mm-wave frequencies, and optical characterization from far-IR to visible and beyond.…”

“…In cases where optical phonons contributed to THz response, such as ZnS, additional models had to be included [15]. More recently, detailed simulation and theoretical studies have been published which enable detailed and more firstprinciples-based comparison between theory and experiments [6] and modeling is moving beyond simple fitting of parameters to experimental data.…”

“…These two parameters are optimized to fit the measured results and can be used to calculate carrier concentration and mobility [9]. In certain situations ColeDavidson or Drude-Smith variants may provide a better fit [9], and a generalized form of conductivity was proposed in [6].…”