Biaxial Compressive Strain Of Graphene On Substrate Of Hexagonal Boron Nitride

Graphene has attracted wide attention for both fundamental physics and potential application in electronics. Recently, hexagonal boron nitride (h-BN, abbreviated as BN in the following) has been proposed as an ideal substrate for graphene devices because it is atomically flat with little dangling bonds and charge traps. Graphene on BN (GBN) has shown much higher mobility, less intrinsic doping and reduced electron-puddles than on SiO2substrate. On the other hand, because of the reduced interaction with substrate, GBN is also an appealing system to study intrinsic mechanical properties of graphene as well as strain engineering. Different from suspended graphene clamped over a trench, which is essentially a1D system, GBN is a2D system where biaxial strain can be formed and engineered. It is suggested that exploiting the different TEC between graphene and the substrate could realize the desirable strain distribution for electronic device applications. In particular, strains with triangular symmetry have been proposed to create a pseudo-magnetic field and energy gap, which was observed in individual nanometer-sized graphene bubbles. However, so far only a few experiments have been attempted to measure the TEC of graphene up to-400K. Bao et al. measured the TEC of graphene based on1D ripple textures in suspended graphene, yet the experimental values did not quantitatively agree with theory. In another experiment, Yoon et al. used temperature-dependent Raman spectroscopy to measure the TEC of graphene on SiO2substrate, but the measurement was indirect as the Raman frequency shift had multiple contributions at different temperatures. Neither experiment was able to measure the TEC beyond～400K.In this work, we study the biaxial strain formation in GBN samples. After thermal cycling, we consistently observe triangular and polygonal bubbles formed in graphene as a result of buckling under biaxial compressive strain. The strain was caused by TEC mismatch between graphene and underlying BN. Finite element mechanical simulations of different graphene bubble shapes show good agreement with experiment, which confirms the origin of the bubbles. We use Raman spectroscopy to quantitatively probe the temperature-dependent compressive strain in GBN over a wide temperature range, from which the TEC of graphene is derived. The TEC stays negative up to～800C and agrees well with first-principle calculations.