Temperature-dependence of stress and elasticity in wet-transferred graphene membranes

We report measurements of the mechanical properties of two suspended graphene membranes in the temperature range of 80 K to 550 K. For this entire range, the resonant frequency and quality factor of each device were monitored continuously during cooling and heating. Below 300 K, we have additionally measured the resonant frequency's tunability via electrostatic force, and modeled this data to determine graphene's tension and elastic modulus; both of these parameters are found to be strongly temperature-dependent in this range. Above 300 K, we observe a resonant frequency (and therefore tension) minimum near room temperature. This suggests that the thermal expansion coefficient is positive for temperatures below roughly 315 K, and negative for higher temperatures. Lastly, we observe a large, reproducible hysteresis in the resonant frequency as our graphene devices are cycled between 300 K and 550 K. After returning to 300 K, the measured frequency evolves exponentially in time with a time constant of ∼24 h. Our results clash with expectations for pristine graphene membranes, but are consistent with expectations for composite membranes composed of graphene coated by a thin layer of polymer residue.