H. S. Skulason

110 GHz measurement of large-area graphene integrated in low-loss microwave structures

We report high-frequency scattering parameter measurement of large-area monolayer graphene integrated on low-loss quartz substrates. High-quality graphene was grown by chemical vapour deposition on copper, chemically hole doped, and transferred to quartz. Microwave measurements were performed from 0.01 to 110 GHz. Simple microwave models were used to extract graphene impedance parameters. We find that contact resistance is effectively shunted above 3 GHz. Atomically thin large area graphene behaves as a wideband resistor with negligible kinetic inductance and negligible skin effect.

Counting graphene layers on glass via optical reflection microscopy

We show that optical reflection microscopy is a reliable method to simultaneously locate and count graphene layers deposited on bulk, transparent substrates such as soda-lime glass. The visible contrast in optical reflection versus graphene layer number is resolvable on bulk substrates. A simple Fresnel theory based on the universal optical conductance of graphene layers accurately models optical reflection images taken at a wavelength of 550±5 nm. We directly count one to nine layers of graphene using reflection microscopy.

Faraday rotation in magnetically biased graphene at microwave frequencies

Faraday rotation is experimentally observed at microwave frequencies in a large-area graphene sheet biased with a static magnetic field, and interrogated by polarized fields in a hollow circular waveguide. A Faraday rotation of up to 1.5° and an isolation of more than 30 dB is observed, suggesting possible applications to graphene based isolators, circulators, and other non-reciprocal devices. An analytic model is developed for the scattering parameters of the measured structure. The model shows excellent agreement with the measurements and is used to extract the graphene conductivity, carrier density, and mobility.

Optical reflection and transmission properties of exfoliated graphite from a graphene monolayer to several hundred graphene layers.

The optical reflection contrast and optical transmission contrast of graphitic films on glass ranging in thickness from a monolayer to the limit of bulk graphite have been experimentally measured. For samples with more than 10 graphene layers where optical contrast quantization becomes difficult to observe, atomic force microscopy was used to measure the sample thickness. The visible optical reflection and transmission of thin graphitic films is found to depend strongly on the real component of the optical conductance per graphene layer, and comparatively weakly on the imaginary component of optical conductance. This observation in part explains the significant variation in the refractive index of graphene and graphite reported in the literature to date. Spectroscopic measurements reveal a strong dispersion in the optical conductance of even a 10 layer film, consistent with an imaginary conductance arising from virtual transitions at the band edges of the pi and sigma bands at the M and Gamma points, respectively.

High spatial resolution ellipsometer for characterization of epitaxial graphene

An ellipsometer with 3μm×5μm spot size constructed with a single focusing and imaging element is used to measure the layer number of exfoliated graphene on glass and expitaxial graphene on SiC. Ellipsometric sensitivity to graphene layer number increases with decreasing layer number and decreasing substrate refractive index. Single-atomic-layer sensitivity has been achieved. High spatial resolution imaging and ellipsometry is useful for rapid characterization of epitaxially grown graphene films.

Field effect tuning of microwave Faraday rotation and isolation with large-area graphene

We have demonstrated field effect tuning of microwave frequency Faraday rotation in magnetically biased large-area graphene in a hollow circular waveguide isolator geometry. Oxidized intrinsic silicon was used as a microwave transparent back-gate for large-area graphene devices. A 26 dB modulation of isolation in the K-band was achieved with a gate voltage modulation of 10 V corresponding to a carrier density modulation of 7×1011/cm2. We have developed a simple analytical model for transmission and isolation of the structure. Field effect modulation of Faraday rotation can be extended to other two dimensional electronic systems and is anticipated to be useful for gate voltage controlled isolators, circulators, and other non-reciprocal devices.

Contactless impedance measurement of large-area high-quality graphene

We present experimental work on the contactless measurement of graphene sheet impedance at frequencies up to 110 GHz in different waveguide geometries. Low-loss coplanar waveguides in series and shunt configuration have been demonstrated. A new coaxial waveguide coupled Corbino disk geometry with facile fabrication is introduced. Critical to the success of these measurements is a low contact impedance at high-frequencies, wherein the dc contact resistance is shunted by a contact capacitance that ultimately enables contactless measurement. The quasi-optic nature of waveguide measurements minimizes the effect of inevitable cracks in the graphene sheet, in contrast with typical transport measurements. We have applied our technique to the characterization of the sheet impedance and contact impedance of large-area, high-quality graphene grown by chemical vapour deposition.

Optical reflectometry and ellipsometry measurements of graphene and thin graphitic films on bulk low-index substrates

Optical reflectometry and ellipsometry measurements are taken on graphene layers on a variety of bulk substrates using visible light sources. Using a universal optical conductance model allows accurate determination of layer number. Extension of reflectometry to ellipsometry has the potential to probe anisotropy in optical conductance, and is expected to be useful for graphene sample and device characterization for transparent graphene electrode technology.

Large area graphene electromagnetic devices

Large area graphene growth provides a facile route to the development of microwave devices based on the interaction of electromagnetic waves with the two dimensional gas of electrons in a graphene sheet. The strength of microwave scattering with graphene is determined by an impedance mismatch Zσ whose natural scale is itself determined by the fine structure constant α = e2/(4πε0hc). Scattering measurements of graphene monolayer loaded waveguides from 17 Hz to 110 GHz reveal a constant sheet conductance with negligible skin effect owing to monolayer atomic thickness. A Drude conductivity tensor can be used to describe the microwave scattering of a graphene sheet under a static magnetic field bias. Measurement of longitudinal conductivity in a Corbino disk geometry can be used to estimate mobility. Transverse conductivity leads to Faraday rotation, which can be used in hollow waveguide structures to implement a gate voltage tunable isolator. As graphene mobility improves, there is potential to exploit both classical and quantum effects in non-reciprocal devices.

Optical Reflection and Transmission Properties from a Graphene Monolayer to Graphite

Optical reflection, transmission and AFM measurements of exfoliated graphitic films on glass from graphene monolayers to 700 layers are reported. A simple model based on pi-pi* and sigma-sigma* transitions account for the observed behavior.