Estimating the thermal expansion coefficient of graphene: the role of graphene–substrate interactions

Abstract

The temperature-dependent thermal expansion coefficient of graphene is estimated for as-grown chemical vapor deposited graphene using temperature-dependent Raman spectroscopy. For as-grown graphene on copper, the extent of thermal expansion mismatch between substrate and the graphene layer is significant across the entire measured temperature interval, T = 90-300 K. This mismatch induces lattice strain in graphene. However, graphene grown on copper substrates has a unique morphology in the form of quasi-periodic nanoripples. This crucially influences the profile of the strain in the graphene membrane, which is uniaxial. An estimate of the thermal expansion coefficient of grapheme α(T) is obtained after consideration of this strain profile and after incorporating temperature-dependent Grüneisen parameter corrections. The value of α(T), is found to be negative (average value, -3.75 × 10(-6) K(-1)) for the entire temperature range and it approaches close to zero for T < 150 K. For graphene wet-transferred to three kinds of substrates: copper, poly-dimethylsiloxane, and SiO2/Si, the Raman shifts can largely be modeled with lattice expansion and anharmonic contributions, and the data suggests limited interfacial interaction with the substrate.

Raman analysis of strained graphene grown on dewetted cobalt

“…Moreover, at the intercept, the energy is higher than the unstrained case, indicating the presence of isotropic compressive strain of graphene on Co. This agrees well with the belief that wrinkles are formed during cooling down due to the large difference of thermal expansion coefficient, reported to be negative in graphene . In the real case, such background compressive strain composes with an uniaxial tensile component that originates likely from the retraction of Co crystallized during dewetting and becomes dominant in some regions, displayed in Figure b, giving rise to the red shift of ξ .…”

“…This agrees well with the belief that wrinkles are formed during cooling down due to the large difference of thermal expansion coefficient, reported to be negative in graphene. [5,33,34] In the real case, such background compressive strain composes with an uniaxial tensile component that originates likely from the retraction of Co crystallized during dewetting and becomes dominant in some regions, displayed in Figure 6b, giving rise to the red shift of ξ. This scenario results in a distribution of the data gathering around a straight line shown in Figure 6a.…”

Tailoring stress in pyrolytic carbon for fabrication of nanomechanical string resonators

“…Apparently, the CTE of the more graphitic carbon is smaller than the one of Si resulting in compressive stress. Indeed, graphite is reported to have low or even negative CTE values [22,23]. The thermal stress due to the CTE mismatch is higher for processing at higher temperature.…”

The wrinkle formation in graphene on transition metal substrate: a molecular dynamics study

“…Currently, chemical vapor deposition (CVD) is the widely employed method to produce graphene in large areas and high quality at a reasonable lower price [9][10][11][12]. As we cool down the system from the temperature of graphene CVD growth (~ 1000°C) to room temperature, wrinkles are formed due to the compressive strain in graphene induced by the larger thermal expansion of the substrate than that of graphene [13][14][15][16][17]. Graphene wrinkles may greatly degrade the carrier mobility [18], mechanical strength [19], thermal conductivity [20], and strain sensitivity of the CVD graphene in applications [21].…”