Controlled ripple texturing and Raman
spectroscopy in suspending graphene
林永昌
20, Aug. 2010
Wrinkling of skin
polyethylene
The wrinkles are orthogonal to the boundary
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)
Wenzhong Bao et al., Nature nanotech 4, 562 (2009).
Compression wrinkles
Wrinkling of graphene
Exfoliated graphene
(shear)
Trench
Depth=100~250nm
Width=2~4um
(1)
(2)
d
   trans
daxial
transverse strain (negative for axial tension
(stretching), positive for axial compression)
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).
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).
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
Fpin
Fstretch
Fb
Wenzhong Bao et al., Nature nanotech 4, 562 (2009).
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.
x
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.
Wenzhong Bao et al., Nature nanotech 4, 562 (2009).
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).
Strain-induced downshifts
of the G band
(first principals calculations)
G
 58cm1%

Uniaxial strain
G
 30cm1%


biaxial strain

G
 58cm1%

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).
Estimated compression from Raman G shift
Compress strain
Tensile strain
Chun-Chung Chen et al., Nanolett 9, 4172 (2009).
Raman G peak and linewidth shifts
Chun-Chung Chen et al., Nanolett 9, 4172 (2009).
Electric transport properties
higher mobility
Containing ripple on suspended graphene
Smaller density of charged impurities
Wenzhong Bao et al., Nature nanotech 4, 562 (2009).
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%.
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).