1. Controlled ripple texturing and Raman spectroscopy in suspending graphene 林永昌 20, Aug. 2010

2. Wrinkling of skin E. Cerda and L. Mahadevan, PRL 90, 074302(2003) polyethylene L=25cm, W=10cm, t=0.01cm Uniaxial tensile strain ϒ =0.1. A drying apple The wrinkles are orthogonal to the boundary Compression wrinkles Human skin Out-of-plane displacement of the ripples Wenzhong Bao et al., Nature nanotech 4, 562 (2009).

3. Wrinkling of graphene Wenzhong Bao et al., Nature nanotech 4, 562 (2009). ϒ : longitudinal tensile strain ν: the Poisson ratio transverse strain (negative for axial tension (stretching), positive for axial compression) Single-layer graphene ν ≈ 0.1-0.3 (graphite = 0.165) axial strain (positive for axial tension, negative for axial compression) A: amplitude, λ: wavelength (1) (2) Trench Depth=100~250nm Width=2~4um Exfoliated graphene (shear)

4. Thin-film elasticity theory (The applied stress is dominated by in-plane shear) (1), (2) Thicker film: ~0.016-0.3% Thinner film: up to 1.5% Wenzhong Bao et al., Nature nanotech 4, 562 (2009).

5. Controllably produce ripples by thermal manipulation Process: – Heating the sample up to 700K then cool down slowly. – Ripples appear during the cooling down to 300K. During thermal cycling, the graphene membranes experience a competition between three forces: – F pin : the substrate-pinning force that prevents the graphene membrane from sliding. – F b : the bending/buckling critical compression force, which is generally much less than F pin. – F stretch : the elastic restoring force under tension. Wenzhong Bao et al., Nature nanotech 4, 562 (2009). F pin FbFb F stretch

6. Biaxial compression When T increase, Substrate and trench width expand biaxially while graphene contracts. F stretch > F pin : The taut membrane slides over the substrate into the trench, hence erasing any pre-existing ripples. Cooling process applies compressive stress, F b << F pin : The ends of the graphene remain pinned to the banks of the trench, resulting in transverse (y) ripples and longitudinal (x) buckling. Wenzhong Bao et al., Nature nanotech 4, 562 (2009). y x

7. Thermal expansion coefficient (α) of suspended graphene Graphene ‘s TEC α(T) is calculated from slope of the curve 700K -> 450K -> 300K A sagging graphene Graphene α ≈ -7x10 -6 K -1 at 300K. Wenzhong Bao et al., Nature nanotech 4, 562 (2009). α Si ≈3x10 -6 K -1 α SiO2 ≈5x10 -6 K -1 α Ni ≈13x10 -6 K -1 α Cu ≈17x10 -6 K -1

8. Uniaxial strain biaxial strain Strain-induced downshifts of the G band (first principals calculations)

9. Biaxial compression induced Raman G shift Upshift 25cm -1 Effective contraction of graphene ≈0.40% Average amplitude A=5.2nm Wavelength λ=0.26μm Chun-Chung Chen et al., Nanolett 9, 4172 (2009). (Taylor expansion)

10. Estimated compression from Raman G shift Tensile strain Compress strain Chun-Chung Chen et al., Nanolett 9, 4172 (2009).

11. Raman G peak and linewidth shifts Chun-Chung Chen et al., Nanolett 9, 4172 (2009).

12. Electric transport properties Wenzhong Bao et al., Nature nanotech 4, 562 (2009). higher mobility Smaller density of charged impuritiesContaining ripple on suspended graphene

13. Summary Control and manipulate the ripples in graphene sheets represents the first step towards strain-based graphene engineering. Large and negative thermal expansion coefficient of graphene ≈ -7x10 -6 K -1 at 300K Significant upshift of Raman G peak (25cm -1 ) corresponds to compressions in the substrate region up to 0.4%.

14. reference Wenzhong Bao et al., Nature nanotech 4, 562 (2009). Chun-Chung Chen et al., Nanolett 9, 4172 (2009). E. Cerda and L. Mahadevan, PRL 90, 074302(2003).