Controlled ripple texturing and Raman spectroscopy in suspending graphene

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

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

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

4. Thin-film elasticity theory (The applied stress is dominated by in-plane shear) Thicker film: ~0.016-0.3% Thinner film: up to 1.5% (1), (2) 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: • Fpin: the substrate-pinning force that prevents the graphene membrane from sliding. • Fb: the bending/buckling critical compression force, which is generally much less than Fpin. • Fstretch: the elastic restoring force under tension. Fstretch Fstretch Fpin Fb Wenzhong Bao et al., Nature nanotech 4, 562 (2009).

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

7. Thermal expansion coefficient (α) of suspended graphene 700K -> 450K -> 300K A sagging graphene Graphene ‘s TEC α(T) is calculated from slope of the curve Graphene α ≈ -7x10-6 K-1 at 300K. αSi≈3x10-6 K-1 αSiO2≈5x10-6 K-1 αNi≈13x10-6 K-1 αCu≈17x10-6 K-1 Wenzhong Bao et al., Nature nanotech 4, 562 (2009).

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

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

10. Estimated compression from Raman G shift Compress strain Tensile 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 higher mobility Containing ripple on suspended graphene Smaller density of charged impurities Wenzhong Bao et al., Nature nanotech 4, 562 (2009).

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).