Terahertz characterization of graphene conductivity via time-domain reflection spectroscopy on metal-backed dielectric substrates

Abstract

A theoretical and experimental framework for the characterization of the terahertz (THz) conductivity of graphene on metal-backed substrates is presented. Analytical equations are derived for the general problem of oblique incidence of the THz beam in a time-domain spectroscopic (TDS) setup working in reflection. The recorded time-domain signals are post-processed in order to retrieve the substrate thickness, its dielectric dispersion, and the complex graphene conductivity, which is described by a generalized Drude-Smith model. The method is tested on two samples of chemical vapor deposited graphene, transferred on polyethylene terephthalate and cyclo-olefin polymeric substrates of sub-millimetric thickness, and characterized by Raman spectroscopy. By working only with the amplitude spectra, the proposed method circumvents issues stemming from phase uncertainties that typically affect TDS measurements in reflection mode. More important, it allows for a rapid, nondestructive characterization of graphene sheets that can be directly integrated in the production flow of graphene-based passive or active components employing metal-backed resonant cavities, such as THz absorbers, metasurface lenses, or leaky-wave antennas.

Dielectric Terahertz Characterization of Microwave Substrates and Dry Resist

“…The aim of this work is to provide a first-time THz characterization in terms of both dielectric permittivity and the loss tangent of the following dielectric materials: Rogers RO3006, Rogers CLTE-MW, Rogers Ultralam 3850HT, Rogers Duroid 6035HTC, and Ordyl FP 415. The measurements have been performed in reflection mode and the frequency dispersion of the complex permittivity has been described by the Havriliak-Negami variation of the Debye model [15]. This model replicates with remarkable accuracy the experimentally measured reflectance spectra through a fitting optimization procedure based on an analytical transmission-line model.…”

“…In this work, the substrates were investigated in reflection mode using the THz timedomain spectrometer TeraFlash Pro [20]. The measurement procedure has been fully described in [15] and is summarized next for the readers' convenience Figure 2. shows the diagram of the reflection-mode configuration of the THz-TDS setup.…”

“…The reflection spectra in the frequency domain were obtained in the range 0.2-2 THz, which ensures almost 80 dB of dynamic range compared to the noise floor. The THz-TDS measurements were post-processed taking into account the losses and their frequency dispersion, as discussed in [15,21]. To this aim, the samples were modeled by means of an equivalent circuit (Figure 3), and the correspondent theoretical amplitude reflection coefficient R th was derived at the air-substrate interface, viz., z = 0.…”

“…Even if most THz-TDS measurements are performed in transmission mode [11], the reflection mode represents an effective technique for retrieving the complex-valued frequency dispersion of the dielectric properties of moderately reflective and lossy materials [12][13][14][15]. It also represents a powerful tool for the THz characterization of back-metallized substrates employed in THz planar antennas [16] and in the synthesis of metasurfaces for THz-wave manipulation, e.g., absorption [17] or beam steering [18].…”

Graphene Saturable Absorber Mirrors for Silicon Photonic Platforms

“…Generally, σ is a strong function of the chemical potential µ c , since for µ c > ℏω/2 interband electronic transitions are prohibited and graphene becomes transparent. In the THz region, intraband transitions usually dominate [38] while in the optical regime interband transitions are more important. Formulas for the calculation of the graphene conductivity can be found in [39].…”