Biaxial Strain Transfer in Supported Graphene

Understanding the mechanism and limits of strain transfer between supported 2D systems and their substrate is a most needed step toward the development of strain engineering at the nanoscale. This includes applications in straintronics, nanoelectromechanical devices, or new nanocomposites. Here, we have studied the limits of biaxial compressive strain transfer among SiO2, diamond, and sapphire substrates and graphene. Using high pressure-which allows maximizing the adhesion between graphene and the substrate on which it is deposited we show that the relevant parameter governing the graphene mechanical response is not the applied pressure but rather the strain that is transmitted from the substrate.. Under these experimental conditions, we also show the existence of a critical biaxial stress beyond which strain transfer become partial and introduce a parameter, a, to characterize strain transfer efficiency. The critical stress and a appear to be dependent on the nature of the substrate. Under ideal biaxial strain transfer conditions, the phonon Raman G-band dependence with strain appears to be linear with a slope of -60 +/- 3 cm(-1)/% down to biaxial strains of -0.9%. This evolution appears to be general for both biaxial compression and tension for different experimental setups, at least in the biaxial strain range -0.9% epsilon < 1.8%, thus providing a criterion to validate total biaxial strain transfer hypotheses. These results invite us to cast a new look at mechanical strain experiments,on deposited graphene as well as to other 2D layered materials.