Calculation and Study of Graphene Conductivity Based on Terahertz Spectroscopy

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Calculation and Study of Graphene Conductivity Based on Terahertz Spectroscopy J Infrared Milli Terahz Waves DOI 10.1007/s10762-017-0362-5 Calculation and Study of Graphene Conductivity Based on Terahertz Spectroscopy Xiaodong Feng1 & Min Hu 1 & Jun Zhou 1 & Shenggang Liu 1 Received: 4 December 2016 /Accepted: 22 January 2017 # Springer Science+Business Media New York 2017 Abstract Based on terahertz time-domain spectroscopy system and two-dimensional scan- ning control system, terahertz transmission and reflection intensity mapping images on a graphene film are obtained, respectively. Then, graphene conductivity mapping images in the frequency range 0.5 to 2.5 THz are acquired according to the calculation formula. The conductivity of graphene at some typical regions is fitted by Drude-Smith formula to quanti- tatively compare the transmission and reflection measurements. The results show that terahertz reflection spectroscopy has a higher signal-to-noise ratio with less interference of impurities on the back of substrates. The effect of a red laser excitation on the graphene conductivity by terahertz time-domain transmission spectroscopy is also studied. The results show that the graphene conductivity in the excitation region is enhanced while that in the adjacent area is weakened which indicates carriers transport in graphene under laser excitation. This paper can make great contribution to the study on graphene electrical and optical properties in the terahertz regime and help design graphene terahertz devices. Keywords Graphene conductivity. Terahertz spectroscopy. Drude-Smith formula . Laser excitation 1 Introduction Terahertz (THz) radiation with frequencies typically from 0.1 to 30 THz, which occupies a middle ground between microwaves and infrared waves, is becoming a hot topic in the world [1–5]. Graphene with the structure of a two-dimensional, single-atomic-scale, honeycomb lattice, has been receiving more and more attention in the terahertz science field such as * Min Hu [email protected] 1 University of Electronic Science and Technology of China, Terahertz Science and Technology Research Center, Chengdu, China J Infrared Milli Terahz Waves terahertz sources [6, 7], terahertz modulators [8–10], terahertz detectors [11–13], and terahertz absorbers [14–16] since it was isolated and characterized by A. K. Geim et al. [17–19]. As graphene chemical potential, carrier density, carrier mobility, and relaxation time can be achieved from graphene conductivity [20, 21], researches related to graphene conductivity make full sense. Most works like Ref. [21, 22] have been carried out for graphene conductivity calculation using terahertz transmission spectroscopy [23–27] but few based on terahertz reflection spectroscopy. However, not all substrates allow THz waves to transmit with high transmittance. Ref. [28] also images of a single-layer graphene film based on terahertz transmission spectroscopy without graphene conductivity fitting by Drude or Drude-Smith model. Ref. [29] studies gate-induced change of graphene conductivity without mapping. Ref. [30] measures of the optical absorption spectra of epitaxial graphene from terahertz to visible without mapping, too. Ref. [31] presents an identification method of the dynamic range of the detectable absorption coefficient in the analysis of transmission and reflection THz time- domain spectroscopy data, which does not cover any experimental measurement of graphene conductivity. In this paper, graphene conductivity mapping images on a damaged monolayer graphene/ quartz sample based on THz transmission and reflection spectroscopy are obtained and Drude- Smith formula is adopted to fit the calculated conductivity in the 0.5–2.5-THz frequency range. The results by transmission and reflection measurements are compared. In addition, the effect of a red laser excitation on the graphene conductivity is studied. The red laser is a cylindrical, low-power, red (632.8 nm) Helium-Neon laser with output power range from 2 to 5mW. The paper is organized as follows: Section 2 introduces the graphene conductivity algo- rithm in detail by transmission and reflection measurements respectively; Section 3 presents experimental measurement, transmission and reflection mapping images of graphene/quartz sample, and discontinuity analysis; Section 4 gives graphene conductivity images, Drude- Smith fitting, and comparison between the transmission and reflection data as well as the graphene conductivity change mapping images with laser excitation; Section 5 concludes the paper. 2 Graphene Conductivity Calculation Algorithm When a THz pulse passes through the graphene/substrate sample, a portion of the pulse transmits while some is reflected at the interfaces as shown in Fig. 1. Graphene is treated as an infinitely thin conducting film and the THz pulse is treated as vertically incident in both transmission and reflection measurements as incident angles are both very small. The first- order transmission coefficient through the air-graphene interface is given by Ref. [22] tG ¼ 2=ðÞnS þ 1 þ Z0σ ð1Þ where nS is the refractive index of substrates, σ is the graphene conductivity, and Z0 =377Ω is the vacuum wave impedance. From Fresnel formula, we can get the first-order transmission coefficient at the air/substrate interface given by t0 ¼ 2=ðÞ1 þ nS ð2Þ J Infrared Milli Terahz Waves Fig. 1 THz pulses pass through THz pulse THz pulse the graphene/substrate sample 1st-order 1st-order 2nd-order 2nd-order Graphene Substrate 2nd-order 2nd-order 1st-order 1st-order Combined with Eqs. (1) and (1), we get the calculation formula of graphene conductivity given by σ ¼ ðÞt0=tG−1 ðÞ1 þ nS =Z0 ð3Þ where t0/tG is the relative transmittance of the first-order transmitted pulses for areas without and with graphene coverage. From the relationship between the transmission and reflection coefficients, we get first- order reflection coefficient at the air-graphene interface is given by rG ¼ tG−1 ¼ ðÞ1−nS−Z0σ =ðÞ1 þ nS þ Z0σ ð4Þ and the first-order reflection coefficient at the air/substrate interface is given by r0 ¼ ðÞ1−nS =ðÞ1 þ nS ð5Þ Combined with Eqs. (3)and(4), we get the graphene conductivity expression given by ðÞ1−n ðÞ1 þ n ðÞ1−r =r σ ¼ S S G 0 ð6Þ ðÞðÞ1−nS rG=r0 þ ðÞ1 þ nS Z0 where rG/r0 is the relative reflectance of the 1-th transmitted pulses for areas with and without graphene coverage. Using Eqs. (2) and (5) and the relative transmittance/reflectance in frequency domain, we can obtain the graphene conductivity via the transmission as well as reflection measurement. 3 Experimental Measurement of Transmission and Reflection Images For comparison between transmission and reflection measurement, a long time placed dam- aged commercial monolayer graphene film and another less damaged commercial monolayer are prepared with dimensions of about 1 × 1 cm while the quartz substrate is about 3 mm in thickness and 1 in. in diameter. The refractive index of quartz is 1.96 in the terahertz frequency range 0.5 to 2.5 THz measured by terahertz spectroscopy. J Infrared Milli Terahz Waves Terahertz transmission and reflection time domain signals (TDS) are obtained with a THz Spectroscope(TPS 3000 assembled by the British company TeraView Ltd) by means of a two- dimensional raster scanning on the graphene/quartz sample in 0.1 mm steps between the fiber coupled emitter and receiver through transmission and reflection configurations separately. The scanning step is 0.1 mm. By Fourier transform of TDS, their corresponding terahertz transmission and reflection frequency-domain signals (FDS) range from 0.5 to 2 THz with a frequency resolution of 0.05 THz are acquired. As time delay for second-order transmission and reflection signals are at least 2nd t ¼ ð7Þ c where n is the refractive index of the substrate, d is the thickness of the substrate and c is the speed of light in vacuum. For the graphene/quartz sample, the time delay for second-order signal is at least 39.2 ps. Since only short time signals of 10 ps are chosen, so the second-order signals or other high-order signals are ignored. The chosen measured transmission and reflection signals for example in time domain and corresponding frequency domain signals by Fourier transformation for graphene/quartz sample are shown in Fig. 2. (a) (b) 0.4 quartz 1.0 quartz graphene/quartz graphene/quartz 0.2 0.8 0.0 0.6 0.4 -0.2 Electric field/a.u. Transmittance/a.u. 0.2 -0.4 0.0 0 246810 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Time delay/ps Frequency/ (c) (d) quartz 1.0 0.20 quartz graphene/quartz graphene/quartz 0.15 0.8 0.10 0.6 0.05 0.00 0.4 Electric field/a.u. -0.05 Reflectance/a.u. 0.2 -0.10 -0.15 0.0 0246810 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Time delay/ps Frequency/THz Fig. 2 Transmission and reflection signals in time domain and frequency domain. a transmission signals in time domain. b Transmission signals in frequency domain. c Reflection signals in time domain. d Reflection signals in frequency domain J Infrared Milli Terahz Waves Fig. 3 (color online) THz transmission (up) and reflection (down) intensity mapping images of graphene/quartz sample at 1.0, 1.5, and 2.0 THz (from left to right, normalized). Scale bars are1mm.Theareaenclosedbythered rectangle is about where graphene locates and the area enclosed by the white ellipse is about where the crack locates As shown in Fig. 2, the transmittance is lower for quartz with graphene coverage while the reflectance is higher, which can be derived from Eqs. (1), (1), (3), and (4). Besides, since THz pulses transmit the sample which increases the time delay as the velocity of THz pulses is slower in the sample than that in the air, it can be seen that the transmission signals own a longer time delay resulting in a narrower bandwidth in frequency as shown in Fig.
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