Observation of Vacuum Ultraviolet Optical Critical Points and Excitons in Graphene and Monolayer MoS2

Graphene and MoS₂ are considered to be among the most promising candidates for next generation of electronic and photonic devices. Accurate optical properties provide fundamental information necessary for the rational design of electronic and photonic devices and intended applications. In this abstract, we report the findings from broad band optical measurements of the dielectric function by spectroscopic ellipsometry (SE) on graphene and MoS₂ grown by chemical vapor deposition (CVD). The extended spectral range (1-9 eV) afforded by our measurement instrumentation permits us to observe  previously unreported new optical critical point transitions and excitons . 

                Monolayer graphene grown on a copper foil was transferred onto a fused silica substrate by using a copper etch, cleaning, and float  method previously reported on by our group [1-3]; two and three graphene layers were formed by the sequential transfer of each monolayer. The use of thick fused silica as the substrate is to optimize the measurement sensitivity to a monolayer film thickness. The thickness of 3.35, 6.7 and 10.05  were used for the SE data fitting of monolayer, two-layer and three-layer graphene films, respectively. An exciton transition at 4.8 eV and two additional higher energy absorption peaks at 6.3 eV and 8.5 eV were observed from the absorption spectra of graphene. The peak positions correspond to the resonant excitons that arise from dipole transitions of the single-particle continuum [4]. In the IR region, both refractive index (n) and k increase with wavelength, which is consistent with the previous reported results [5]. It is notable that n increases whereas k decreases as the number of graphene layers increased. This is attributed to the relatively weak van de Waals interaction between transferred graphene monolayers. Such weak interaction is consistent with the relatively small red shift of the 4.8 eV exciton peak we observe in two-layer (0.04 eV shift) and three-layers (0.07 eV shift) graphene relative to that of monolayer graphene. The theory predicts that the transmittance of monolayer graphene depends solely on the universal fine structure constant a = e²/ħc, which is related to the graphene’s opacity.  We find the opacity linearly increased for each of added layer. Specifically, at 550 nm wavelength the transmittance of one, two, and three layers of graphene decreases from 96.9%, 93.6%, to 90.3%, respectively. Independent UV-Visible transmittance measurements performed are found to be consistent with the calculated transmittance as obtained from the complex refractive index measured by SE.

                Monolayer MoS₂ grown on SiO₂/Si substrate was transferred onto a backside roughed fused silica substrate [6]. Raman spectroscopy was performed on the transferred sample to characterize the monolayer characteristics, and the uniformity and general quality of the film. Optical absorption shows a band gap of 1.81 eV.  Photoluminescence (PL) and optical absorption measurements reveal two distinct excitonic  transitions at 1.88 eV and 2.02 eV due to direct d-d transitions separated by spin-orbit splitting. The transitions display a blue shift compared with bulk MoS₂ as a result of the decreased screening. A series of exciton and optical transition peaks in UV energy range are detected at 3.0, 4.2, 4.9, 5.8, 6.8, and 8.4 eV, of which the 3.0 eV peak has the strongest absorption.

                In conclusion, the optical functions of CVD-grown graphene and monolayer MoS₂ are measured by spectrally extended spectroscopic ellipsometry. The UV energy exciton peaks and a set of optical critical points are observed and related to theoretical predictions. The optical functions and the observed absorption peaks we report here provide a better understanding of graphene and monlayer MoS₂ optical properties for the design of optoelectronic devices. 

References

[1] X. Liang, et al., ACS nano 5, 9144 (2011).

[2] W. Li, et al., Appl. Phys. Lett. 102, 183110 (2013).

[3] W. Li, et al., arXiv:1303.1353

[4] K. F. Mak, et al., Phys. Rev. Lett. 101, 196405 (2008).

[5] F. J. Nelson, et al., Appl. Phys. Lett. 97, 253110 (2010)

[6] Y. H. Lee, et al., Adv Mater 24, 2320 (2012). 1706 (2005).