Study of Thermal Expansion Coefficient of Graphene via Raman Micro‐Spectroscopy: Revisited

Abstract

2D materials have generated enormous interest because of its unique physical properties and promising applications. 2D materials such as graphene, h-BN, silicene, h-MoS 2 , and black phosphorus are expected to play a central role in nextgeneration electronic and optoelectronic devices. [1-3] The The thermal expansion coefficient (TEC) of a 2D material is a fundamental parameter for both material property and applications. A joint study is hereby reported, using Raman microspectroscopy and molecular dynamics (MD) simulations, of the substrate effects on thermal properties of graphene. It is found that besides the lateral strain induced by the substrate, out-of-plane coupling strongly affects the temperature-dependent vibrational modes and TEC of graphene. MD simulation shows significant reduction of the density of states for longer wavelength out-of-plane vibrations when the graphene is supported on an alkane substrate. The negative TEC of freestanding graphene becomes smaller when out-of-plane rippling is suppressed. In order to measure TEC of 2D materials with the out-of-plane coupling being taken into consideration, a Raman microspectroscopic scheme to separate the contributions of lateral strain and out-of-plane coupling to TEC is developed. The TEC of graphene on octadecyltrichlorosilane substrate is found to be (−0.6 ± 0.5) × 10 −6 K −1 at room temperature, which is fundamentally smaller than that of freestanding graphene. These results shed light on the fundamental understanding of the interaction between 2D material and substrate, and offer a general recipe for studying separately in-plane and out-of-plane couplings on supported materials.

Contactless Scanning Near‐Field Optical Dilatometry Imaging at the Nanoscale

“…[56] Furthermore, the linear TEC above 175 layers undergo a plateau at (33.75 ± 3.24)×10 −6 K −1 which is consistent with the out-of-plane thermal expansion of graphite along the crystallographic c-axis, [55][56][57][58] which corroborates the validity of SNOD as an accurate and quantitative method for thermal expansivity measurements. Conversely, a value of (−5.77 ± 3.79)×10 −6 K −1 is observed via SNOD for the thinnest ML-G platelets, below ≈ 90 layers, which can be assigned to the in-plane bending modes of graphene, [55,56] and is consistent with previous macroscopic measurements, [56][57][58][59][60][61][62][63][64][65][66][67][68][69] as shown in Table 2. A significant advantage of SNOD over all of such techniques rests in that it provides site-specific thermal expansion information, while other probing methods only yield an ensemble aver-age of the thermally induced expansion and offer minimal information on the distribution of the thermal expansion throughout the whole sample.…”

“…Our apparatus, a scanning near-field dilatometer, is all-optical in nature and, therefore, does not require any external heater or electrical contact to vary the sample's temperature, nor it requires any physical thermometer or nano-thermocouple to probe it. Our method is a 𝜔-2𝜔 pump-probe method, where the probe is an aperture-type reflection-mode SNOM, which makes it uniquely suited for probing optically absorbing and thermally conducting See References Graphite 0-40 [57][58][59] Nano EELS Graphene/ Cu Mesh Mono−2.14 ± 0.79 Bilayer−1.09 ± 0.25 Trilayer−0.87 ± 0.17 Bulk−0.07 ± 0.01 [60] Low Temperature Resonance Au/Graphene/SiO 2 /Si −7.4 [61] Raman Spectroscopy Graphene/LiNbO 3 −10 to -5 [62] Au/Graphene/ SiO 2 /Si Mono−3.2 ± 0.2 [63] Bilayer−3.6 ± 0.4…”

Optical and thermal responses of silicene in Xene heterostructures

“…In fact, due to the relatively small thicknesses involved in the case of 2D materials, even a low absorbed laser power can result in local heating and subsequent temperature rise in the surroundings of the illuminated area. This increase in temperature in turn produces appreciable changes in the Raman spectrum that can be related to several physical properties at the very 2D level, which include anharmonic effects in the phonon-phonon interactions, 11 thermal properties, [12][13][14][15] and thermal-mechanical responses of the 2D layer 16,17 to the optically absorbed power, all of them being completely unexplored in silicene. The increase in the local temperature as a function of the incident power is related to the thermal properties of the sample.…”

Perturbative renormalization and thermodynamics of quantum crystalline membranes

“…[26] for an analysis on the role of tension and Refs. [47,61] for discussions on the effects of a supporting substrate).…”