Strain and adhesion of graphene sheets in shallow trenches.

Detailed high resolution micro Raman mapping of graphene exfoliated over shallow trenches demonstrates that single layer graphene adheres to the bottom of shallow trenches instead of remaining freely suspended. The analysis shows that the strain is surprisingly uniform. The high resolution Raman mapping of G and 2D Raman shift are consistent with uniaxial strain measurements, and the strain map concurs with our theoretical calculations that predict that a graphene sheet reaches minimal free energy sticking to the trench bottom even if that leads to moderate strain of about 0.6{\%} in the sheet.